A
THESIS
entitled
APPLICATION OF REGIONAL STREAM SEDIMENT GEOCHEMISTRY
IN FORECASTING BASE METAL PRODUCTION, NORTHERN ENGLAND
submitted for the
degree of
DOCTOR - OF PHILOSOPHY
in the
FACULTY OF SCIENCE OF THE
UNIVERSITY OF LONDON
by
ALFREDO CAMILO EMILIO CRUZAT
Royal School of Mines Imperial College of Science and Technology November, 1973. ABSTRACT
The results of a stream sediment regiOnal geochemical survey in Northern England are investigated in relation to their possible use in the forecast of the base metal potential of that area. More than 4000 samples were collected at an average density of one sample per square mile, and were analyzed by spectrographic, atomic absorption spectrophotometric, and color- imetric techniques for more than twenty elements, fourteen of which were selected as possible indicators of lead-zinc and copper mineralization.
Forecasting models for lead, zinc, and copper reserves were designed using stepwise multiple linear regression of geological, geochem- ical, and production parameters measured in 106.cells of one hundred square kilometres in area. The analysis of more than 1500 models brought the conclusion that the best method of forecasting was the prediction of the number of deposits present in each cell, and of the average value of the reserves contained in them independently, both estimates being combined afterwards in a final model that expresses the mineral:potential in terms of present expected value. Three types of model were designed for each metal: geochemical, geological and combined geochemical-geological, their interpretation being done in terms of geological criteria. '
The best models obtained were evaluated by statistical methods, as well as by comparison with predictions obtained by conventional means. It was concluded that, even though the performance of the different models varies for the three metals considered, the overall performance of the geochemical models is similar or slightly better than that of the geological models, the combination of both kinds of information rendering the best results. According to a suggested two-stage forecasting procedure, it is estimated that 93 lead deposits, 130 zinc deposits, and 149 copper deposits are still lying in the area, with reserves valued at £130m, £80m, and £45m respectively.
Finally, the results of preliminary geochemical investigations performed in three selected areas of Northern England are indicated. Several anomalies probably related to mineralization are discussed, and further investigation for the evaluation of those anomalies is suggested. ACKOWLEDGEMENTS
The project described in this thesis is part of the
Geochemical Atlas of England and Wales, a programme carried out by the
Applied Geochemistry Research Group, Imperial College of Science and
Technology, London, directed by Professor John S. Webb and financed by
the Wolfson Foundation.
Grateful thanks are given to the Institute de Investigaciones
Geol6gicas, Santiago, Chile, and to the Ministry of Overseas Development
of Great Britain, institutions that provided the author with financial
support.
The writer is especially indebted to Dr. W.T. Meyer, under whose
direct supervision the project was carried out, for his constant
constructive criticism, advice, and encouragement during all the phases
of the research.
Sincere thanks are also given to members of the staff and
students of the A.G.R.G. for their helpfulness throughout the duration of
the project.
Computer time was kindly provided by the Imperial College and
University of London Computer Centres.
• TABLE OF CONTENTS
page
ABSTRACT ACKNOWLEDGEMENTS ii TABLE OF CONTENTS LIST OF FIGURES LIST OF TABLES
CHAPTER 1 - INTRODUCTION 1
1.1 Statement of the problem 2 1.2 Scope of the present research 5 1.3 Limitations 8 1.4 Previous work 12
CHAPTER 2 - GENERAL GEOGRAPHY 19
2.1 Area of study 19 2.2 Climate 20 2.3 Vegetation 20 2.4 Topography 21 2.5 Drainage 23 2.6 Soils 24
CHAPTER 3 - GEOLOGICAL SETTING 26
3.1 Introduction 26 3.2 Stratigraphy 27 3.2.1 Pre-Cambrian Rocks 29 3.2.2 Lower Paleozoic Rocks 30 3.2.3 Upper Paleozoic Rocks 35 3.2.4 Mesozoic Rocks 43 3.2.5 Pleistocene and Recent deposits 45 3.3 Intrusive Rocks 46 3.3.1 Caledonian intrusions 46 3.3.2 Hercynian intrusions 48 3.3.3 Alpine intrusions 49 3.4 Structure 50
O page
CHAPTER 4 - BASE METAL DEPOSITS IN NORTHERN ENGLAND 55
4.1 General considerations 55 4.2 Northern Pennine orefield 56 4.2.1 Introduction 56 4.2.2 Mineral deposits 56 4.2.3 Ore and gangue mineralogy 59 4.2.4 Zoning and wall-rock alteration -60 4.2.5 Controls of the mineralization -63 4.2.6 Age and origin of the mineralization 64 4.2.7 Mining history 67 4.3 Lake District orefield 68 4.3.1 Introduction 68 4.3.2 Mineral deposits -69 4.3.3 Ore and gangue mineralogy 70 4.3.4 Zoning and wall-rock alteration 71 4.3.5 Controls of the mineralization 72 4.3.6 Age and origin of the mineralization 74 4.3.7 Mining history 76
CHAPTER 5 - COMPILATION AND HANDLING OF THE DATA 78
5.1 General considerations 78 5.2 Compilation of the data 79 5.2.1 Geological data 79 5.2.2 Production data 82 5.2.3 Geochemical data 95 5.3 Preliminary handling of the geochemical data 106 5.4 Data handling 108
CHAPTER 6 - REGIONAL GEOCHEMISTRY 110
6.1 Introduction 110 6.2 General spatial distribution of selected trace-elements 112 6.3 Regional geochemical patterns as related to bedrock geology 113 6.3.1 Clays 114 6.3.2 Slate and greywacke 115 - 6.3.3 Friable sandstones 116 6.3.4 ,Massive limestones 117 6.3.5 Mudstones, shales, hard sandstones and massive 118 limestones page
6.3.6 Mudstones, shales and hard sandstones 119 6.3.7 Volcanic rocks 120 6.3.8 Intrusive rocks 121 6.4 Regional geochemical patterns in relation to 122 mineralized areas 6.5 Interpretation of the geochemical data by means of 130 R-mode factor analysis 6.5.1 General considerations and outline of the theory 130 6.5.2 Component analysis of the data 132 6.5.3 Interpretation of factors 135
CHAPTER 7 - FORECAST OF BASE METAL MINERALIZATION 143 IN NORTHERN ENGLAND
7.1 Introduction 143 7.2 Multiple linear regression analysis 144 7.2.1 Outline of the theory 144 7.2.2 Methods of multiple linear regression analysis 152 7.2.3 Multiple linear regression techniques used in 156 the present research 7.3 Forecasting models based on multiple linear regression 158 7.3.1 Generalities 158 7.3.2 Preliminary investigations 160 7.3.3 Forecast of the number of potential deposits per 187 cell 7.3.4 Forecast of the average value of expected reserves 203 per deposit 7.3.5 Combined forecasting models for potential base 216 metal reserves 7.4 Discussion of results 222 7.4.1 General considerations 222 7.4.2 Direct forecast of lead reserves 223 7.4.3 Direct forecast of zinc reserves 224 7.4.4 Direct forecast of copper reserves 226 7.5 Investigations on the design of models for the forecast 229 of combined total and lead-zinc potential reserves 7.5.1 General statement of the problem 229 7.5.2 Forecast of combined total potential reserves 229 7.5.3 Forecast of combined lead-zinc potential reserves , 232 page
CHAPTER 8 - EVALUATION OF REGIONAL STREAM SEDIMENT 234 GEOCHEMISTRY AS A MEANS OF FORECASTING MINERAL POTENTIAL
8.1 Introduction 234 8.2 Other methods of forecasting base metal mineral potential 234 8.2.1 Qualitative estimation of the base metal mineral 234 potential of the area 8.2.2 Forecasts based on the analysis of the frequency 248 -distribution of output values 8.2.3 Quantitative forecasts using a combination of 251 factor and regression analysis 8.3 Evaluation of regional geochemistry in the forecasting 259 of mineral potential 8.3.1 Qualitative-quantitative evaluation of the 259 geochemical models 8.3.2 Evaluation of the geochemical models in terms of 265 their basic statistics 8.3.3 Evaluation of the geochemical models on the basis 268 of multiple discriminant analysis 8.4 Final evaluation of the models designed 278
CHAPTER 9 - FINAL ESTIMATES AND PRELIMINARY GEOCHEMICAL 282 INVESTIGATIONS IN SELECTED AREAS
9.1 Final estimates 282 9.1.1 Lead reserves 283 9.1.2 Zinc reserves 285 9.1.3 Copper reserves 287 9.2 Preliminary survey in cell 15 288 9.2.1 General considerations 288 9.2.2 Geochemical investigations 291 9.2.3 Summary and conclusions 298 9.3 Preliminary investigations in cell 70 299 9.3.1 Generalities 299 9.3.2 Geochemical investigations 302 9.3.3 Summary and conclusions 308 page
9.4 Preliminary investigations in cell 79 311 9.4.1 General considerations 311 9.4.2 Geochemical investigations 313 9.4.3 Summary and conclusions 317
CHAPTER 10 - SUMMARY AND CONCLUSIONS 319
10.1 Regional geochemical reconnaissance survey 319 10.2 Forecast of base metal mineralization in Northern 326 England by multiple linear regression 10.3 Other methods of forecasting base metal reserves 334 10.4 Evaluation of regional stream sediment geochemistry 338 in the forecasting of mineral potential 10.5 Final estimates 342 10.6 Preliminary geochemical investigations in selected areas 344
REFERENCES
APPENDIX I Geological parameters
APPENDIX IIA Allocated output per cell
APPENDIX IIB Number of deposits per cell
APPENDIX IIC Average output per deposit.
APPENDIX III Geochemical scores types A, C, and D.
LIST OF FIGURES
2.1 Location map After page 19 2.2 Main topographic factors of the area 21 2.3 Drainage map 23 2.4 Soils map 24 3.1 Geology of the studied area 27 3.2 Siluro-Ordovician and older stratified rocks in the area 29 3.3 Upper Paleozoic rocks in the studied area 37 3.4 Mesozoic rocks in the studied area 43 3.5 Intrusive rocks in the area 46 3.6 Main structural features of the area 52 4.1 Veins in the Northern Pennine orefield 58 4.2 Base metal deposits in the Lake District orefield 69 5.1 Location of cells 78 5.2a Frequency distribution of the total lead output per cell 93 5.2b Frequency distribution of the total average production 93 per cell 5.3a Frequency distribution of the log-transformed total lead 93 production per cell 5.3b Frequency distribution of the log-transformed total average 93 production per cell 5.4 Frequency distribution of the total number of productive 93 deposits per cell 5.5 Frequency distribution of the log-transformed total number 93 of deposits per cell 5.6 Analytical days for samples of studied area 103 5.7 Percentage relative deviation for selected trace- 103 elements 5.8 Precision control chart for duplicate results (AA) 103 5.9 Frequency distribution of the number of samples collected 104 per cell 6.1 Arsenic-percentile map and histogram 112 6.2 Barium-percentile map and histogram 112 6.3 Cadmium-percentile map and histogram 112 6.4 Cobalt-percentile map and histogram 112 6.5 Copper-percentile map and histogram 112 6.6 Gallium-percentile map and histogram 112 6.7 Iron-percentile map and histogram After page 112 6.8 Lead-percentile map and histogram 112 6.9 Lithium-percentile map and histogram 112 6.10 Manganese-percentile map and histogram 112 6.11 Molybdenum-percentile map and histogram 112 6.12 Nickel-percentile map and histogram 112 6.13 Vanadium-percentile map and histogram 112 6.14 Zinc-percentile map and histogram 112 6.15 Rock-associations in the area 114 A6.16 Potassium-percentile map -128 6.17 Silicon-percentile map 128 6.18 Screegraph of geochemical data 134 6.19 Factor one - percentile map 135 6.20 Factor two - percentile map 135 6.21 Factor three - percentile map 138 6.22 Factor four - percentile map 138 6.23 Factor five - percentile map 140 6.24 Factor six - percentile map 140 7.1 Forecasted number of lead deposits per cell 188 7.2 Forecasted number of zinc deposits per cell 191 7.3 Forecasted number of copper deposits per cell 198 7.4 Forecasted average value of lead reserves per deposit 204 7.5 Forecasted average value of zinc reserves per deposit 207 7.6 Forecasted average value of copper reserves per deposit 211 7.7 Forecasted lead reserves 219 7.8 Forecasted zinc reserves 220 7.9 Forecasted copper reserves 221 7.10 Forecasted total combined reserves 232 7.11 Forecasted lead-zinc combined reserves 232 8.1 Areas favourable for base metal mineralization as 240 selected from geological information 8.2 Frequency distribution of barium 242 8.3 Frequency distribution of cadmium 242 8.4 Frequency distribution of copper 243 8.5 Frequency distribution of iron 243 8.6 Frequency distribution of lead 244 8.7 Frequency distribution of lithium 244 8.8 Frequency distribution of molybdenum 245 8.9 Areas favourable for base metal mineralization, After page 247 as selected by qualitative analyses of regional geochemical data 8.10 Areas favourable for base metal mineralization, as 247 selected by statistical analysis of the frequency distribution of output values 9.1 Cell 15 - geological map 289 9.2 Church Burn-Green Sike area - stream sediment 293 sampling 9.3 Church Burn-Green Sike area - soil traverses 293 9.4 Keenleyfell West-Middle Edge area - stream sediment 295 and soil sampling 9.5 Cell 70 - geological map 300 9.6 Regional stream sediment reconnaissance, cell 70 302 9.7 Birkdale Beck-Great Sledale area - stream sediment 302 sampling 9.8 Birkdale Beck-Great Sledale area - soil traverse 305 9.9 Tan Hill-Keld area - stream sediment sampling 307 9.10 Tan Hill-Keld area - soil traverse 308 9.11 Cell 79 - geological map 312 9.12 Dillican area - stream sediment sampling 315 9.13 Capplethwaite Beck area - stream sediment sampling 315 9.14a Sedbergh area - stream sediment sampling 316 9.14b Sedbergh area - soil traverse 316 LIST OF TABLES
4.1 Distribution of workable lead-zinc veins After page 57 in the Northern Pennine orefield according to their stratigraphic position 4.2 Distribution of flats in the Northern Pennine orefield 57 according to their stratigraphic position 4.3 Model-ages for galenas of the Northern Pennine orefield 65 4.4 Distribution of workable base metal deposits in the 65 Lake District orefield according to their stratigraphic position 4.5 Model-ages for galenas of the Lake District orefield 75 5.1 Basic statistics of geological parameters 80 5.2 Monthly average settlement prices of selected metal 80 during 1971 at the London Metal Exchange 5.3 Distribution of mining districts in Northern England 88 according to their output 5.4 Present value of metal output in Northern England 88 5.5 Basic statistics of output parameters in production cells 88 5.6 Distribution of cells according to the present value of 90 their output 5.7 Distribution of cells according to the average value of 90 their output per deposit 5.8 Distribution of cells according to their number of 90 productive deposits 5.9 Coefficients of correlation between output indexes 90 5.10 Relationship between trace-elements and major interferring 100 elements for A.R.L. 29000B quantometer 5.11 Instrument parameters for atomic absorption spectro- 100 photometry 5.12 Comparison of population mean and analytical variance 102 ratio and precision for stream sediments based on low precision spectrographic analysis 5.13 Comparison of population mean and analytical variance 102 ratio and precision for stream sediments based on atomic absorption spectrophotometric analysis 5.14 Detection limits for selected trace-elements in the 100 A.R.L. 29000B quantometer 5.15 Distribution of cells according to the After page 105 number of samples collected in them 5.16 Distribution of cells according to site geology 105 5-17 Coefficients of correlation between averages of 105 selected trace-elements and number of samples 5.18 Statistical significance of differences between 108 geochemical scores 5.19 Main computer programs used in the present research 109 6.1 Basic statistics of selected trace-elements, Northern 113 England 6.2 Correlation matrix of geochemical elements 132 6.3 Components solution of geochemical data 134 7.1 Coefficients of correlation between geochemical 163 7.2 Standard errors and adjusted multiple correlation 163 coefficients of preliminary geochemical models considering absolute production values 7.3 Coefficients of correlation between geochemical scores 164 and average production values 7.4 Standard errors-and adjusted multiple correlation 164 coefficients of preliminary geochemical models considering average output per deposit 7.5 Coefficients of correlation between geochemical scores 165 and number of mines per cell 7.6 Standard errors and adjusted multiple correlation 165 coefficients of preliminary geochemical models considering number of mines per cell 7.7 Coefficients of correlation between log-transformed 174 geochemical variables and production indexes 7.8 Comparison between geochemical untransformed and 174 logarithmically transformed models 7.9 Comparison between geological untransformed and 174 transformed models 7.10 Forecasted number of deposits per cell, Northern England 187 7.11 Selected equations for the forecast of the number of 188 lead deposits per cell 7.12 Selected equations for the forecast of the number of 191 zinc deposits per cell 7.13 Selected equations for the forecast of the number of 198. 'copper deposits per cell 7.14 Forecasted average value of reserves per After page 203 deposit, Northern England 7.15 Selected equations for the forecast of the average 204 -value of the lead reserves per deposit per cell 7.16 Selected equations for the forecast of the average 207 value of the zinc reserves per depsoit per cell 7.17 Selected equations for the forecast of the average 211 value of the copper reserves per deposit per cell 7.18 Coefficients of correlation between actual output 217 figures and forecasts based on simple multiplication 7.19 Coefficients of correlation between actual output 217 figures and forecasts obtained by multiple regression of estimates of output indexes 7.20 Forecasted base metal potential reserves, Northern England 222 7.21 'Selected equations for the forecast of the total lead 224 reserves 7.22 Comparison between simple and convergent regressions 224 for the forecast of lead reserves 7.23 Selected equations for the forecast of the total zinc 225 reserves 7.24 Comparison between simple and convergent regression for 224 the forecast of zinc reserves 7.25 Selected equations for the forecast of the total 227 copper reserves 7.26 Comparison between simple and convergent regression 224 for the forecast of copper reserves 7.27 Total potential reserves as forecasted by simple and 224 convergent regression means 7.28 Forecasted base metal combined reserves, Northern England 230 8.1 Cells favourable for base metal mineralization, selected 240 according to conventional geological information 8.2 Cells favourable for base metal mineralization, selected 247 by qualitative analysis of regional geochemical data 8.3 Main features of discriminant functions for the 271 classification of production cells into high and low output categories 8.4 Contingency tables of forecasts classified into output 272 categories by multiple discriminant analysis 8.5 Contingency tables of positive forecasts After, page 272 classified into output categories by multiple -discriminant analysis -BA Contingency table of scored forecasts as compared to 275 classification of cells by multiple discriminant analysis 8.7 Contingency tables of scored positive forecasts as 275 compared to classification of cells by multiple discriminant analysis 9.1 Final forecasts - lead reserves 283 9.2 Residual estimates - lead reserves 283 9.3 Final forecasts - zinc reserves 283 9.4 Residual estimates - zinc reserves 285 9.5 Final forecasts - copper reserves 283 9.6 Residual estimates - copper reserves 287 9.7 Main statistics of samples of regional survey - cell 15 291 9.8 Main statistics of smaples of regional survey - cell 70 302 9.9 Main statistics of samples of regional survey - cell 79 314 CHAPTER 1
INTRODUCTION
The present thesis refers to one of the research projects carried out under the direction of Professor John S. Webb at the Applied
Geochemistry Research Group (A.G.R.G.), Imperial College of Science and
Technology, London, on the use of regional geochemistry in mineral exploration.
Originally, geochemical exploration was used-for the preliminary appraisal of the economic possibilities of restricted areas, or to assess the potential of areas in the vicinities of known ore deposits or mining districts. In the mid 1950's, members of the A.G.R.G. performed several surveys in Africa with the purpose of testing the use of these methods under different environmental conditions, and to investigate the use of regional geochemistry, a method of reconnaissance or exploration carried out on the basis of stream-sediments sampling at a low density (e.g. one sample per thirty square miles). These researchs proved to be extremely useful for the delineation of geochemical patterns that could be interpret- ed in relation to bedrock geology and mineralization.
In the 1960's, the use of low density geochemical sampling as a means of revealing the presence in broad regions of geochemical patterns which may be of use in the investigation of several problems (mineral exploration, pollution, etc.), was firmly established. In the British
Isles, the first of such surveys carried out on a large scale was performed in 1965, when stream sediments at an average density of one sample per square mile were collected in Northern Ireland, a province that was used as a test area for the eventual geochemical mapping of the whole United
Kingdom.
In 1969 the Geochemical Atlas of England and Wales started to be compiled by members of the A.G.R.G., when stream-sediments were collected at road-stream intersections in both countries, at an average density similar to the one used in Northern Ireland. In the present research, about 4000 samples collected during that project in north- central and north-west England were used, in an attempt to establish the possible use of regional geochemical data as a means of forecasting the base metal mineral potential of an area.
The area under consideration has been one of the leading lead- zinc producing regions in Britain, and minor amounts of copper were produced there as well. A fairly good account of these outputs is available, dating the mining records in some deposits as far back as the beginning of the eighteenth century. Besides, from the geological point of view, that is one of the best known areas in the world. Therefore it was considered that this was an excellent case on which to build up a statistical model for the forecast of base metal mineralization, on the basis of regional geochemical data, and to test its results by comparison with a similar model designed using conventional geological information.
Taking into account the strictness of the test, due to the optimum geological information available, if the attempt were to be success- ful and the geochemical model designed were to achieve at least similar results to the geological one, it is thought that the scope of regional geochemical surveys within the realm of mineral exploration would be greatly broadened,especially when the results are viewed in light of the difference in costs and the speed involved in obtaining each type of information.
1.1 Statement of the Problem
Among the numerous and complex problems that need to be solved during a mineral exploration program, one of the most important which those concerned are faced with, is to maintain within certain limits the it 4-
3
financial risks involved and to minimise those risks as much as possible
at the lowest possible cost. It is to this aspect of mineral exploration
that the ever increasing expenditure in regional geochemical surveys is
related because these methods allow, at a low cost per unit area, the
delineation of zones with economic possibilities lying within usually
broad regions under investigation.
Probably the most important decision that is taken during any
such program is tackled at the end of the preliminary phase of investiga-
tion, when one of two possible alternatives is decided upon, based on
the results attained during the reconnaissance: either the project is
regarded uneconomic and therefore abandoned, or the performance of more
detailed investigations - usually at a much higher cost - is accorded.
It follows from the outlined and unavoidable pattern, that the acquisition
of any knowledge about the actual economic potential of the favourable
areas, is highly welcome at the latter stage and-even more-highly desirable.
Traditionally, mining concerns have spent a variable proportion
of their resources on exploration in a way that in many respects may be
regarded as gambling on the basis of geological information. This fact
implies that those analysing the information have implicitly given
probabilities to the likelihood of finding resources in an amount such
that they would match the economic targets set by the concern involved.
However, that analysis has in most cases been carried out empirically and
hence those probabilities are seldom - if ever - indicated explicitly.
With the ever-increasing difficulty of discovering economic ore
deposits and the consequent increase in exploration costs, the decisions
taken solely on an empirical basis are encountering difficulties to reach
those in charge of the financial planning, with the result that many
worthwhile opportunities for investment may be lost and - less frequently -
funds may be needlessly allocated to ventures with a very low probability 4 of successful outcome.
Bearing these facts in mind, an ever increasing amount of research has been devoted. since the early 1950's to the resolution of problems dealing with the forecast of mineral potential in areas with economic possibilities or under exploration. These attempts have been concerned with the development or design of statistical models that have a twofold purpose: they are devised firstly, as an assistance to the geologist for the assignation of probabilities to the outcome of an exploration venture, and secondly, as a means of estimating the limits of expenditure that can be allocated to such a venture.
As is obvious, the outcome of such models are of paramount importance, since they would be fundamental in determining the interest that an organization may have in a certain venture and the priority that the venture should have within the scheme of the concern. Regarding the limits of expenditure, it is important to appreciate that not only the maximum limit is of interest, but also the minimum, an amount that in the ideal case ought to be spent before any decision of rejection is considered.
This point is of special interest to the small and medium-size concerns who, according to that limit, need to secure the appropriate financial resources before engaging in the next stages of exploration, since if those resources were to fail before that limit is reached, the whole exercise could be considered a waste.
The problem of forecasting mineral potential involves two main aspects that need to be solved by the model designed, if it is to be considered of real help in mineral exploration: (1) the model should ascertain the probilities that in a certain area one or more ore bodies occur, and (2) it should assess the probable value of the mineral wealth in that area, in terms of present expected value. If both premises are fulfilled by the model and the mineral wealth forecasted for an area is greater or equal to the present expected cost of the next phase of exploration, those in charge of the program should be prepared to proceed with the required investigation.
From the preceding analysis, it may be concluded that the need for a stricter approach for the assignation of proba.lities to the outcome of a mineral exploration program, has become almost a necessity, especially when the large funds involved in those programsoke considered.
1.2 Scope of the Present Research
Several approaches have been followed to deal with the problem of designing a statistical model for the forecast of mineral potential, ranging from those based on the analysis of the distribution of the mineral wealth in known mining districts, to the more sophisticated ones that consider different techniques of multivariate data analysis. In the latter type of approach, the use of Bayesian statistical analysis is favoured by most writers.
By far, most of the models that have been designed to the present are based on the measurement of selected geological parameters in an-area of known (or fairly well-known) mineral wealth. Then, a certain analyt- ical technique is applied to those parameters or indexes to build up a model that expresses the relationship parameters-mineral wealth, and this is used to forecast, by extrapolation, the mineral wealth of areas which possess similar geological characteristics.
The main premise on which the indicated models are based is that the mineral wealth of an area is a functionoEcertain geological character- istics that may be quantified. Therefore, in order to design a model that expresses this relationship, it is necessary to obtain information from a control area of well-known mineral wealth, to manipulate this data, and ultimately obtain the simplest expression possible of the relation-
ship, which is subsequently applied for predicting in areas similar to those used as control. 6
It must be considered in this respect that the requirement
for geological similarity is highly varying in its extent. Strict similarity must be used when the geology of the control and study areas
are not very well known and especially when their size is small. With
larger areas, ever increasing geological heterogeneity must be expected,
as well as an increase in the diversification of the forms of mineral
wealth present; therefore, although individual geological features would
still be important when considering broad areas, the environment contain-
ing and controlling those features is the main target that must be sought
in order to define the mineral wealth in terms of the mutual interaction
of the features rather than on the individual features themselves. Thus,
the use of parameters or indexes that reflect the environment more than
individual characteristics, appears to be highly desirable in this context.
Regional geochemical surveys are almost standard procedure when
broad areas need to be explored at speed and low cost. Until now, most
of these surveys have been used to delineate areas with mineral potential
within a region, aim mainly achieved by the application of several stat-
istical techniques and by the study of regional trends that may be
displayed by selected geochemical indexes (individual elements', combinaT-
tions of these, factors, or others), analysis that in broad terms may be
considered within the realm of pattern recognition.
Considering that the metallogenetic areal units (provinces,
districts, etc.) are one of the manifestations of the geochemical
provinces, and that stream-sediments have been proven as the best sources
of information about geochemical environments, it may be postulated that
the results of regional geochemical surveys based on the sampling of
stream-sediments, may be used to design a model for the forecast of
mineral potential, in the same way that other geological parameters are
used with this purpose, with the advantage that these data more than 7 reflecting individual geological components, would reflect the environment in which those components are contained.
Bearing these facts in mind and accepting the premise indicated above, the results of a stream-sediments regional geochemical survey performed in Northern England at an average density of one sample per square mile, were used in the present research in order to investigate the use of such surveys as a means of forecasting mineral potential. The aims of the research were the following:
(1) To develop a statistical model for the forecast of the base metal
mineral potential of an area covering about 10,000 square kilometres
in Northern England, using as parameters or indexes the values in
106 samples of fourteen selected trace elements normally used in
geochemical exploration.Eachof the samples represent the standard-
ised average of all the stream-sediments collected within an area
of 100 square kilometres.
(2) To evaluate the validity and use of such a statistical model, by
comparison with another model built on the basis of conventional
geological parameters, as measured in the same 106 cells from
available geological maps.
(3) To investigate the possibility of using conventional geological
and regional geochemical information, to design a combined model
that would express the mineral wealth of an area more accurately
than the predictions that could be formulated solely on the basis
of geological data.
Analyzing the different techniques that may be applied for the design of a statistical model for the forecast of mineral wealth, it was considered that the best approach that may be envisaged is the one based on multiple regression analysis. The ultimate advantage of that technique lies in the fact that not only the relationship mineral-wealth parameters 8
may be quantified in terms as strict as the researcher desires, but also
the influence of each parameter in the model may be quantified, and -
what is more important - it takes into account the mutual relationship
existing between the parameters, hence implicitly including in the model
an environmental term.
Several forms of mineral wealth known in the area were regressed
in the present research against geochemical and geological indexes. The
regressions were carried out by standardizing the indexes in several ways
and the best of these was used to build up the statistical model. The
possibility of improving the forecast by the use of factor analysis prior
to the regression was investigated, as well as the,use of a variant of
discriminant analysis for the classification of the samples (cells) in terms of mineral wealth.
Finally, in order to test the validity of the model obtained, a preliminary geochemical reconnaisance was carried out by means of stream- sediments, soils, and rock sampling, in four selected areas which accord- ing to the forecast have important economic possibilities.
1.3 Limitations
During the present research, several factors limiting the full use of the available time and resources, and up to a certain extent the results, were met. The most important of those limiting factors were the following three:
(1) A full account of the production figures for individual deposits in the Northern Pennine and Lake District orefields is lacking. Although a very good record is available for the northern part of the first of those fields, a similar detailed account for the output prior to 1848 is not available for the southern part of that field or for the Lake District.
Since the output of the latter areas by 1848 was declining, accurate figures for the bulk of their output are not available, it being necessary, 9 therefore, to rely on partial figures and estimates obtained from different unofficial sources, values that in many cases may be exaggerated.
In addition, a certain proportion of the production could not be allocated to individual deposits because in the different sources of information those figures are quoted as total production for an area (e.g. Swaledale,
Arkandale, Alston Moor) or even for a whole county.
Furthermore, in the cases of the zinc and copper outputs, the available figures of production sometimes refer to metal, others to concentrate, and others to ore, it being necessary in the latter two cases to use the respective averages for each deposit to convert those values to metal. Unfortunately, the averages were obtained ,sometimes from sources other than the production; thus, the possibility of some inaccuracy in the resultant figure needs to be considered. On the other hand, it must be regarded in this respect, that the zinc productions considered refer to those ores or concentrates that were marketed as such and not to the total production of this type of ore in the area,because in many cases these ores were not sold or beneficiated, or were not included in the out- put figures; this fact is especially important in the case of the deposits in the Lake District where only in the 1890's was it realised that many
"lead" lodes contained sphalerite as their main constituent.
(2) The geochemical data used in the present research, as indicated previously, were obtained at road-stream intersections at an average density of one sample per square mile during the multi-purpose Geochemical
Atlas of England and Wales project. The way in which the sampling was done reflects a compromise that would reconcile the maximum possible productivity in the field at the lowest possible cost,with the different purposes that were served by the survey (mineral exploration, pollution studies, incidence of trace elements distribution in crops and livestock, etc.). 1 0
As is obvious, though the validity of the results is not questioned, this is not the optimum sampling pattern from the mineral exploration point of view. Two main problems arise from this fact:
(a) some areas with poor access, as the higher grounds in the Lake District and in the middle of the Pennines, were not covered to the same sampling density as those low-grounds and valleys that have a good or fair road system, and (b) contamination arising from industrial activities and especially from mine dumps, tailings and smelting sites, though avoided as far as possible during the sampling, was noticed in the preliminary treatment of the data.
The first of the annotated problems was not a serious limitation for the present research, because the values used in the forecast were averages for all the samples lying within cells of 100 square kilmetres in area. The second problem was obviated, as far as possible, by visual examination of all the results and elimination of the most obvious contam- inated samples by a procedure indicated in chapter 5. This painstaking means consumed an important amount of time during the initial phase of the research and by no means eliminated all the possible sources of arti- ficial enhancement of the values. This fact, and a certain amount of subjectivity introduced while selecting the data, could be considered as a limitation of the research; however, in the opinion of the author, these features inherent to data collected wherever mining or industrial activities have taken place, have been largely obviated and their influence strongly diminished, when those contaminated samples that still remained in the set were averaged with a very much larger number of uncontaminated samples taken in the same 100 square kilometres cell.
(3) The geological data used to build up the geological and combined models were compiled from the one inch to the mile maps prepared by the
Geological Survey of England and Wales. Some of the maps used were 11
published in the second half of the last century and others were modified
versions of those published later. It was found during the compilation
that it is sometimes difficult to establish the exact relationship exist-
ing between some levels, mainly because of the different terminology and
way of grouping the main stratrigraphic units used by the different authors
of the maps. This fact is especially evident when comparing the bases
and tops of the main Carboniferous formations in old and relatively recent
sheets. Hence, a subjective criterion needs to be applied in such cases
to define the grouping of certain levels.
In addition, the more recent maps display much more structural
information than the older ones especially with regard to faulting. Since
this feature is one of the most important factors controlling the emplace-
ment of the mineralization in the studied area, the imbalance between
different sheets introduced a certain amount of distortion when the models
that included faulting parameters were built up. To avoid this factor,
extra-manipulation of the data was required to assess its influence in
the final results, with the consequent increase in computing time and
especially in the time spent on the interpretation of such models.
Finally, with regard to the geological data used in the'present
research, it must be considered that Northern England is probably one of
the areas in the world that has been most thoroughly and accurately mapped.
Thus, when comparing the results attained with the geochemical and
geological models, the predictions of the former have an obvious a priori
disadvantage with respect to those of the latter model, a limitation that
is not a shortcoming of the research itself, but a consequence of a clear
case of optimum geological data vs non-optimum geochemical data. This
fact requires special consideration when the results of the research are
viewed in the light of its possible application elsewhere in a more
common and conventional mineral exploration problem, when the geochemical
information would have been specially collected for that purpose and the
M 12 geological information is likely to be reduced or inaccurate.
1.4 Previous Work
The geology of Northern England has attracted the attention of many geologists since the earliest periods of the development of this science. Martin Lister in a communication to the Royal Society in 1684 envisaged what may be considered the first attempt at producing a geolog- ical map. John Michell, a Yorkshire priest who studied the Pennines, was the first to recognise that an orderly succession of newer rocks dip away on either side of a main central axis, and William Smith, who lived in Yorkshire for a long period, prepared the first geological maps of the region in the early nineteenth century. From that time, an ever increas- ing number of researchers have studied the area, the literature dealing with it reaching enormous proportions.
Among the most important contributors to the knowledge of the geology of the area were Sedgwick, illes, and Marr, who studied the pre-
Carboniferous: Harker and Rastall, who studied the igneous rocks in the
Lake District and the Ingletonian Series: Phillips, Garwood, Tait, and
Stanley Smith, who were especially dedicated to the study of the Carbon- iferous Limestone; and Sorby, Gilligan and Bisat, who dealt mainly with the Millstone Grit. Kendall, Gibson and others researched on the strat- igraphy and structure of the Coal Measures; the Permo-Triassic units
(New Red Sandstone) were studied by Murchison, Sedgwick, Hull and others; and the Cenozoic deposits were of special interest to Kendall, Goodchild, and others. Many of these studies may be found in different periodicals, particularly in the Proceedings of the Yorkshire Geological Society,
Geological Magazine, and Quarterly Journal of the Geological Society; others have been published as maps or sheet-memoirs by the Geological
Survey of England and Wales.
The ore deposits of the Pennines have been scientifically studied 13 since the early nineteenth century, though the stratigraphic sequence of the Alston area was well known to the miners of that area before its first serious study by Forster in 1809. Sopwith (1833) gave a general account of the mines in Alston Moor, Weardale and Teesdale; Wallace in the second half of that century (1861, 1890) described the Alston Moor deposits postulating a supergenic origin for them, and Hunt (1884) also described some of those deposits. In that same period, the Geological
Survey of England and Wales started a detailed mapping of the area, including a very accurate mapping of the veins in relation to the outcrops of the rock-units present; unfortunately, only a few descriptive sheet- memoirs accompanying those maps were issued,and of these many engaged in that survey, only De Rance (1873) wrote about the mineral deposits.
During the First World War, all those ore bodies were studied in detail by members of the Geological Survey, the results being published in the Special Reports on Mineral Resources Series (Wilson and others,
1922; Carruthers and Pocock, 1922; Carruthers and Straham, 1923;
Smith, 1923). Other reports dealt with the ferrous-metal deposits and non-metallic deposits. Since the early 1930's, these deposits have been of special interest to K.C. Dunham, who has prepared numerous works in this connection (1934, 1944a, 1944b, 1945, 1952, 1959, 1961, 1965, 1967), culminating his works with the excellent account about the mineralization in the northern part of the Northern Pennine orefield, published as a
Geological Survey Memoir in 1948. Besides, A. Raistrick also devoted a great part of his time to these deposits, either to their geology
(1936b, 1938, 1938b, 1947) or to the history of their exploitation (1936a,
1955, 1965.
Works describing individual deposits or mining districts include those of Nail (1902) about the Alston area; Louis(1917) about the Wear- dale area; Metcalfe (1952) in Swaledale; Varvill (1920) in the Greenhow I. 4 mine area; and numerous others. The possibilities of re-opening some of the mines or of developing new areas within the Northern Pennines were discussed by Jones (1940), Varvill (1954), and Dunham (1959). A brief
account of that field may be found in Schnellmann and Scott (1969).
The previous annotations are just a very brief summary of the
bibliography available on the base metal deposits existing in the Northern
Pennines, and for further information the reader is referred to the
Memoirs of the Geological Survey, especially to that of 1948 by
K.C. Dunham.
In contrast to the Northern Pennines area, the available biblio- graphy dealing with the geology of the base metal deposits of the Lake
District is rather scarce. The oldest published work known to the author about these deposits is the reference to some of them made by
Ward (1876) in the Geological Survey Memoir dealing with the northern part of that district. Later, Kendall (1894) gave a general account of some of the deposits, Postlethwaite (1890) referred to the mineralization
surrounding the Skiddaw Granite, Borlase (1894) described the history and
characteristics of the Greenside deposit, and Collingwood (1912) dealt with some aspects of the mines existing near the town of Keswick.
In 1913, Postlethwaite published what may be the most complete
and detailed account available of the mineral deposits of the district, description that was afterwards complemented in two reports belonging to the series on Special Reports on Mineral Resources published by the
Geological Survey (Eastwood, 1921; Dewey and others, 1925). Since that
time, very little has been published about the ore geology of the district.
Among the few more recent works available are those by Rastall (1942),
dealing with the ore depositis of the Skiddaw district; Trotter (1944),
who analyzed the genesis and general features of the deposits; Eastwood
(1959), who made a summary of the characteristics of the orefield and 15 analyzed its future economic possibilities; Ewart (1962), who described the mineralization associated with the Carrock Fell igeous complex; and the detailed study of the Greenside deposit done by Gough (1962). A general account of the main features of the field is also given by
Schnellmann and Scott(1969) in their summary of the lead-zinc producing areas in the United Kingdom.
Works related to the forecast of mineral potential are not abundant, as could be expected beforehand, because this aspect of the mineral resources is a.relatively new branch of the geological sciences.
The first work known to the author is that of Nolan (1950),who studied mining districts in the Basin and Range Province of U.S.A., concluding that in large areas of a geological province the processes of mineralization introduce roughly constant amounts of ore.
Later, Slichter (1955) analyzed the problem in a general way when dealing with profit-ratios as related to the amount of expenditure in exploration and size of the ore bodies to be sought. The first main work in this context is that of Allais (1957), an author who studied the mineral wealth of the Algerian Sahara by comparing mining statistics of
U.S.A., France, Northern Africa, and general World statistics, concluding that the number of deposits to be found in an area is distributed accord- ing to the Poisson function and that its value follows a log-normal distribution.
In 1959, forecasting methods became common practice in the min- eral industry, mainly as a means of allocating exploration expenditure.
Ellis and Blackwell (1959) reviewed the matter in a general way, paying special attention to the optimization of the number of drills required to explore an area of a certain size and shape. In the same year, Bates related geological feature to the value of the production in mining districts, for the first time. This author used as an evaluation tech- nique the multiple regression of Spearman's Rank Correlation Coefficients 16 of geological factors to predict favourable areas for the existence of
U-V deposits in the Colorado Plateau.
A little later, Slichter (1960) contesaed the hypothesis of
Allais (op.cit.) regarding the distribution of mineable deposits, conclud- ing that the number of mines in an area and the value of their production are better described by means of an exponential function. At the same time, Cobb (1960) and Lacy (1961) advocated that operations-research be established as a formal technique in the mineral industry.
In 1962, two important works concerning the distribution of mineral wealth in known mineralized areas were published: Slichter and co-workers (1962) reviewed the functions proposed until then for that distribution and favoured the exponential one. On the other hand,
Griffiths (1962a, 1962b) introduced discriminant analysis for forecasting purposes and postulated that the distribution of the number of workable deposits in an area follows a negative binomial function, and that their value is perfectly described by the log-normal curve.
Coster and Weiss (1963) reviewed the forecasting problem in general terms and rejected the idea of a Poisson distribution for the number of mines in an area, a criterion that was supported by Ghosh (1965) who studied copper deposits in the Bihar Province, India. A simple way of analyzing the mineral wealth appeared by that time when Ayler (1963) applied frequency distribution analysis to establish guides for the search of veins in the Colorado Mineral Belt.
Again the situation was reviewed in general terms by Weiss (1965) who analyzed the techniques of multivariate data analysis and taxonomy as a means of predicting mineral potential, putting forward several arguments in favour of the latter group of methods. At the same time, Drew and
Griffiths insisted on the value of multivariate statistical techniques when they predicted the number of oil fields to be found in the U.S.A., 17
their distribution and value regarded as following a log-normal function.
The year 1966 was a crucial one regarding the problem under analysis, since three new techniques were used for the first time for this purpose. Whitten employed trend surfaces ( a variety of multiple regression analysis) to predict gold contents in South African deposits, advocating the use of low-variance predictors and of dummies reflecting spatial position, in order to obtain more reliable models. Dowes predicted the occurrence of oil deposits with the aid of Bayesian analysis, and Harris (1966a) used factor analysis combined with multiple regression, as a means of predicting mineralization in Arizona, New Mexico and Texas.
A little later, the latter author (1966b, 1967) employed combinations of those techniques to predict mineral wealth in several areas.
Since then, a series of papers have been published along the lines already defined in the previous years. Simple forecasting models based on the statistical distribution of geological parameters were designed for several areas by Kuntsel and co-workers (1967), Brant(1968),
Beus (1969), O'Brien (1969), De Geoffroy and Wu (1970),Uhler (1970),
Streynina and Yakoblena (1972), Konstantinov and Dmitriyev (1972),,and
Yeremeyev and co-workers (1973).
Principles of game theory were applied by Brooke.(1968) for the optimization of mineral exploration programs. Discriminant analysis combined with Bayesian theory was used by Wignall (1969) to relate data from detailed geochemical surveys to known mineral occurrences in south- eastern Pennsylvania. A similar analysis, but using geological data as parameters, was performed by Harris (1969) to forecast the base and precious metals' potential of Alaska.
Combinations of regression analysis and bayesian theory have been widely used for predictive purposes during.this decade. All the authors that have followed this approach have used lithological and 18 structural factors as parameters for the design of their models; worth mentioning in this respect are the works by De Geoffroy and Wignall (1970a,
1970b, 1971), Smith (1970), and Sinclair and Woodsworth (1970). Character- istic analysis, a relatively new technique for the analysis of binary coded data, has been used for the forecast of porphyry-copper type mineralization in the Cordilleran Belt of America (De Geoffroy and Wignall, 1972).
It is worth mentioning in this context that the forecast of mineral potential has lately changed its main focus. The attention of many researchers is being centred on the estimation of mineral endowment of broad regions, that is of the amount of metals lying in the mineable part of the Earth's crust which are contained in deposits of a grade and tonnage above certain specified limits. This aspect has been mainly dealt with by the use of subjective probabilities (pooling of the opinions of several expert geologists and treating the resulting probabilities by conventional statistical methods) and by Monte Carlo simulations. The main workspublished in this respect are those by Harris and Euresty (1969),
Azis and co-workers (1972),and Harris (1973).
Finally, it needs to be mentioned that the only work concerning the forecast of base metal mineralization in Northern England is that of
Bozdar and Kitchenham (1972), researchers who predicted the lead mineral wealth of the Askrigg Block of the Pennines, on the basis of the analysis of the frequency distribution of deposits in the Alston Block of that area. •
LOCATION MAP ',..
0 Hex h -in s. ...-s"- 4.- ''".
0 CARLISLE
55 0 Stank*. 0 Penrith 0 Coalormouth • Workington 0Mtddlaten 0 h,tehoven . , 50 °Kendal 0 Iverstone 0 25 50 75 loo miles BARROW i 0 IN FURNES 0 Lan star .... .1" 30 0 10 20 30 40 50mdes FIG. 2.1 L 1 19 CHAPTER 2 GENERAL GEOGRAPHY 2.1 AREA OF STUDY The area studied in the present research comprises about 11,500 square kilometres in north-central and north-western England, covering the whole of Westmorland, most of Cumberland, and parts of Durham, Northumber- land, Lancashire,and North Yorkshire (Figure 2.1). The boundaries to the north, south, east and west are the coordinates 570,000]4; 460,000N; 410,000E; and 300,000E of the National Grid Reference System, respectively. The region is mainly rural, the population being mainly restricted to the valleys and'coastal strip. The main populated centres are Carlisle in Edenside and Barrow-in-Furness. Minor towns are Penrith, Lancaster, Kendal, Ulverston, Hexham, and the ports of Workington and Whitehaven. The uplands are almost uninhabited,, though each main valley has a district centre (e.g. Alston, Stanhope, Cockermouth, Middleton-in-Teesdale). The activities that support the population are varied. Mining of fluospar, barite, coal and iron ores takes place in different districts, as well as the quarrying of limestone, sand and ganister. Industry (ship- building, engineering, etc.) is an important activity in the Furness and Lancaster districts, in Carlisle and in the Cumberland coastal towns. Agriculture is practised in the valleys, sheep-farming in the uplands and moors, and some cattle raising in the lowlands and coastal areas of Lancashire and Cumberland. Except for the industrial activities in Lancashire, the remaining districts are not able to support large populations and hence the area is likely to remain essentially rural, if the present trends of development remain. 20 2.2 CLIMATE The climate of the studied area, as could be expected, is not homogeneous, varying according to altitude and longitude. In general, rainfall tends to be seasonal, though no strongly marked wet or dry seasons exist. Nevertheless, the spring months tend to be relatively dry and the autumn months relatively wet, except in the higher tracts of terrain where most of the rainfall occurs in winter. The frequency of rainfall varies between 200 and 225 days per year (Lamb, 1964), and the amount from 850 mm in the western and eastern-most regions, to 2500 mm in the central region; an exception to this is found in the central Lake District where orograph- ical rainfall well exceeding 2500 mm per annum occurs, especially on the eastern slopes of the highest summits. Snow is frequent in the area, with an average of 10-30 days of snowfall per year, though exceeding 50 days in the highest regions.- Temperatures are highly dependent on altitude, the adiabatic lapse being about 2.2°C per thousand feet: Average maximum temperatures vary from 19.5°C in the west to 21°C in the east, and average minimal temperatures from 1.1°C in the west to 0°C in the east. Winds tend to be persistent throughout the year with prevailing south and south-west directions, the latter being more frequent in the winter months. Fog is common in the area and no part of it receives more than 40% of the possible sunshine in the year; there are regions in the Pennines where this figure is reduced to less than 25%. 2.3 VEGETATION The five vegetational formations distinguishable in Britain (Tansley, 1939) are present in the area. Deciduous summer forests are poorly represented and except under specially favourable conditions or on exceptional soils as those on the bottom of river valleys, they are not 21 well developed. Oak is present in the very wet areas of the Lake District and birch in the lowlands of Edenside, where shallow and relatively acid soils are present. The most important forest-forming tree is ash which is specially developed on calcareous soils of the Northern Pennines. The northern coniferous forest is limitedly represented in the area; some pine woods exist in the eastern-most part and in the central Lake District. Members of the heath formation cover large tracts of the country, dwarf undershrubs having developed especially on porous soils of well- drained slopes and plateaux. The most common of these is heather or ling, which extends to altitudes of about 600 ft. Moss or bog formation with sphagnum cotton grass and heath is present on acid, permanently wet soils, which is very common in parts of the Lake District and on most of the Pennines plateau. The arctic-alpine formation is represented in the highest peaks of the Lake District at altitudes greater than 2000 ft, where mountain sorrel, crowberry, bearberry, dwarf willows, and other low-growing perennials grow with mosses and lichens. Finally, it must be mentioned that vast parts of the area are covered by grasslands of the basic type with a dominance of fescue which is accompanied by lady's mantle at higher altitudes. Tracts of the low- lands and coastal regions correspond to agricultural land. 2.4 TOPOGRAPHY The studied area is formed by two main morphological units separated by the lowlands of the Vale of Eden: the Lake District in the west, and the Northern Pennine chain in the centre and east (Figure 2.2). The Northern Pennine chain is a south south-east trending range of hills with an average altitude of 1000 to 2000 ft and generally rounded hilltops that extend southwards from the Cheviots to the Craven District. In general terms it may be considered as a dissected plateau tilted towards MAIN TOPOGRAPHIC FEATURES OFTHE AREA 22 the east. Its western margin is a very abrupt fault-scarp, where the highest peaks of the chain lie (Cross Fell, Little Dun Fell, Great Dun Fell). Its southern and northern margins are also fault-scarps but less marked than the former and its eastern margin is not well defined, gradually descending the hills towards a rugged terrain 500 to 1000 ft high, which in turn grades into the Durham plain. A topographic depression lying within the chain (the Stainmore Gap) divides it into two minor blocks: the Alston Block to the north, and the Askrigg Block to the south. The former is a rugged, highly dissected area with gentle slopes and wide valleys, while the latter presents rocky gorges, steep slopes and cliffs, local presence of karst development and frequent "terraced" topography. A similar relief is present in the Lancaster Fells, isolated group of hills separated from the main chain by the river Ribble. The Lake District is a dome structure with an average altitude of 1500 to 2000 ft, whose topography is strongly dominated by the under- lying rocks. The central part, underlain by volcanics, is a bold, very rugged terrain, with steep slopes and craggy heights that include Helvellyn, the Scafells and Langdales, and the screes of Wastwater, many of which are higher than 3000 ft. This terrain strongly contrasts with the much smoother, less rugged though hilly regions underlain by slate, lying to the north and south of the district. Most of the valleys in this area have been modified by glacial activities; hanging tributaries or side valleys are a common feature of the region. Between both morphological units lie the lowlands of Edenside, extending to the northwest of Stainmore. Towards the north the valley broadens, giving rise in the northwestern-most part of the area to the Carlisle Plain, a low-lying area almost completely covered by glacial drift and with a common "ridge and hollow" drumlin topography. South of Stain- 23 more, the Lake District dome is separated from the Pennines, by"the Howgill Fells, mountainous tracts geologically and topographically very similar to the southern part of the Lake District from which they are separated by the river Lune. 2.5 DRAINAGE The western part of the Northern Pennine range is drained by short, youthful streams with a generally westward flow, which discharge into the River Eden (Figure 2.3). The central and eastern parts of that chain are drained by mature rivers running in a general eastwards direction and flowing towards the North Sea. The three main rivers of north-eastern England (Tyne, Wear and Tees) rise in the vicinities of Cross Fell; the South Tyne and its tributaries flow northwards until they reach the main east-west valley, the Derwent drains to the north-east, the Wear to the east, and the Tees to the south-east. Hence, there is a partial radial drainage centred on the highest peaks of the chain at altitudes of about 2000 ft. South of the Stainmore Gap, the drainage takes place mostly underground along solution-channels. There are many large caves and swallow-holes in that region. The main rivers (Swale, Lune, Wharfe) flow mostly in an eastwards or southwards direction and present very few important tributaries. The drainage of the Lake District is dependent on the domal structure formed in that area during the Tertiary, which imposed a more or less radial drainage that persists to the present days. This feature is best seen from the distribution of the lakes in some of the river valleys which make up a radial pattern in relation to a central point located south of Thilmere. The rivers in that area tend to be youthful short streams that drain into the Irish Sea, the Solway Firth, and the Vale of Eden. Roches · .- i DRAINAGE MAP MAIN BASINS CD Eden Basin @ Wensleydale ® Grizedale @ Tyne Basin o Wharfedale @ Duddon Basin @ Weardale ® Ribblesdale @ Derwent Basin G Teesdale ® Lune Basin @ Swaledale @ Kendal Basin 20 - -- t: FIG.2.3 0114 moutonnees and piles of glacial debris are always present in the bottom of these valleys, many of which show effects of glacial over-deepening. 2.6 SOILS Within the studied area eight main types of soil are present. They may be grouped into three main categories (Agricultural Advisory Council, 1970): (1) Coastal sand and shingle with little soil development; (2) Soils of the drier and sub-humid lowlands with a significant summer moisture deficit; and (3) Soils of the uplands and humid lowlands with no significative summer moisture deficit. Of these soils, those of the latter group are the most widespread, those of the former two groups cover- ing limited areas in the central Lake District, the Solway Basin, and coastal areas in the Furness and Lancaster districts (Figure 2.4). Of the different soil types existing in the area, the most common are acid brown soils, naturally non-calcareous except over limestone. These soils are often shallow and/or stony and very acid, being developed over medium-textured parent materials; their drainage varies according to the site and substratum, but generally only the top few inches are freely-drained. They are found in the lower and middle slopes surround- ing the uplands, on high plateaux, and on upland valleys. Some brown podzolic soils and gley soils are included within this group. Second in importance to the former are gley soils of the uplands found in the high-lying areas of the Pennines, Lake District, Yorkshire Fells and Lancaster Fells. These soils, developed on various parent materials, commonly present strong surface compaction that increases with altitude and determines their having either impeded drainage or excessive surface wetness; gley soils, peat podzols and peat are grouped together with the former. Other important soil types in the studied area are lithosols and shallow podzols, stony and/or peaty soils with much bare rock and scree; SOILS (\J1AP 30 35 o 30 ~ Coastal sand and shingle mrnnnmrn De~p,medium or heavy toxtured in alluvium ti~~J;'@*;] l~cdiut1 or heavy textured ca Lcar-eoun soils ~ Deep,heavy or medium textured soils with impeded drainage ~ Shallow,stony an~or peaty soils of the higher mountains ~ Peaty soils of the uplanda ~ r-:edium textured ::lineral soil~ ~ l-icdiu", or heavy textured non-cakcar-coue soil~ Ln alluvium (After Agricultural Advisor! Council,l970) F1G.2.4 25 occasionally iron podzols on slopes; and warp soils, medium or heavy textured, non-calcareous, locally peaty soils in alluvium, that are present on the coastal plain south of the Solway Firth and on the Furness coast. All the anotated soil groups belong to the third of the categor- ies previously mentioned. To the second category belong three soil types of restricted distribution in the region. In the area around Bassenth- waite and Derwent Water in the Lake District, and west of Lancaster, deep, medium or heavy textured, calcareous or non-calcareous soils are present. These soils are lacustrine silts and clays that tend to be slow draining in the topsoil. In a small area west of Richmond there are calcareous, well drained, medium or heavy textured soils, often.shallow over chalk or limestone; in that area, some brown forest and grey-brown podzols also exist. In the upper River Tees, gley soils of the lowlands are present: they are acid to neutral, heavy or medium textured soils, with very poor impeded drainage; some of them are calcareous gley soils and some grey- brown podzolic soils. The latter generally lie on a sandy or silty clay loam subsoil, and are derived from Carboniferous drift. Finally, on the coast of the Solway Firth around Silloth, and on the Isle of Watney in Furness, coastal sand and shingle is present. In those areas, the development of a soil profile is practically non- existent. 2 6 CHAPTER 3 GEOLOGICAL SETTING 3.1 INTRODUCTION The geology of the studied area is dominated by features formed mostly during Paleozoic times. Little is known about the characteristics of the country before the Ordovician, since only a very small inlier of clastic pre-Ordovician rocks exist in the region. Possibly, these folded and sheared rocks, constituted the basement over which the younger forma- tions were laid down. In the Lower Paleozoic, a geosynclinal basin was developed in the area, leading to the deposition of thick sedimentary sequences and of a volcanic pile representing an important Ordovician magmatism. In the Siluro-Devonian span, those units were affected by the Caledonian orogeny acquiring trends that persist until now and which were important features controlling the later tectonic evolution of the region. Contemporanetly with the orogeny, the emplacement of acidic intrusive bodies happened. Arid conditions existed in the country during the Devonian period when mostly uplift and denudation occurred. In the Lower Carboniferous another marine transgression occurred, but the studied area had partly sub- aerial and partly shelf characteristics, features produced by the Caledon- ian uplift and fault systems and by faulting that developed in the central and eastern regions at the same time as the marine transgression. Only in the north-central and south-central parts, true marine environments existed where thick sedimentary sequences were laid down. Later on, still in the Carboniferous, the prevailing environments were deltaic and gradual uplift led once more to the establishment of arid conditions in most of the region with some local inland seas to the west of the Pennines. 27 During the Late Paleozoic, the Hercynian orogeny affected the area, rejuvenating older Caledonian structures and producing important fault and fold systems. The emplacement of basic sills and dykes occurred 0114/ contemporanexly with the tectonism. At the end of the tectonic cycle, the land gradually started to sink with the final consequence that a new marine basin was established during the Rhaetic. From then onwards, marine deposition continuedfor some time, but the direct record of the deposits formed finishes in the Lower Liassic, the youngest horizons present in the area. Probably, some deposits were laid down in post- Jurassic times, but were eroded during the Tertiary and thus are 'not present., In the Early Tertiary, intense earth movements occurred giving the region its definitive shape. The western part was uplifted to form the Lake District dome and most of the post-Silurian rocks were swept away by erosion, leaving only some in the lowlands which form a rim around the dome. In the Pennines, uplift along normal faults and tilt towards the east happened. The emplacement of some dykes of regional importance took place contemporgWly with the tectonism. Finally, during the"Glacial and Post-Glacial periods, the area was affected by intense glacial erosion and deposition, these aeposioveV.D.E_ s(karge tracts of the country. -More recent changes in the sea- level also contributed the present characteristics to the region. In the following paragraphs, a brief account of the main geological features of the area is given, on the basis of Memoirs of the Geological Survey of England and Wales. 3.2 STRATIGRAPHY As indicated previously, most of the area is covered by Paleozoic sedimentary and volcanic sequences deposited in marine, deltaic and sub- aerial environments (Figure 3.1). Along the coast, at Edenside, and in the Solway Basin, minor outcrops of Triassic sedimentary deposits laid M r O 0 ILIASSIC CARBONIFEROUS LIMESTONE VOLCANICS MAIN INTRUSIV0 BODIES 1°00.1 KEUPER BASAL CONGLOMERATES I: BUNTER SILURIAN SILLS AND DYKES PERMIAN I" 1 ASPIGILLIAN COAL MEASURES SKKIDDAW SLATES MILLSTONE GRIT INGLETONIAN 0 10 20 30 40 50 miles —12MAINISIESM FIG.3.1 44'''Al 8 down under sub-aerial conditions or in inland seas are present. As well, very small patches of pre-Cambrian and Liassic sedimentary rocks are also known along the Craven fault system and in the Solway Basin, respectively. The geological sequence that can be distinguished is the following: CENOZOIC QUARTERNARY Alluvium, peat, boulder clays, morraines, submerged forest, etc. MESOZOIC JURASSIC Liassic shales and limestones TRIASSIC Keuper Marl and Stanwix Shales St. Bees Sandstone PALEOZOIC PERMIAN Magnesian Limestone St. Bees Shale Hilton Plant Beds Penrith Sandstone CARBONIFEROUS Coal Measures Millstone Grit Series Carboniferous Limestone Series Basal Conglomerates-Cockermouth Lavas SILURIAN Ludlow Series Wenlock Series Llandovery Series ORDOVICIAN Ashgill Series Coniston Limestone Series Borrowdale Volcanic Series Skiddaw Slates Series PROTEROZOIC Ingletonian Series The main characteristics displayed by these stratigraphic units follow. 3.2.1 Pre-Cambrian Rocks This terrain is represented in two very small outcrops lying in the vicinities of Ingleton (Figure 3.2). They consist of slates with grit bands and coarse arkoses or conglomerates with a total thickness amounting to 2,500 ft. These rocks were assigned by Rastall (1906) to the Pre-Cambrian due to a somewhat greater degree of folding, metamorphism and dyke injection than that in the neighbouring Lower Paleozoic formations. Since the nearest proven Pre-Cambrian rocks (Longmyndian of Shropshire) are geographically and structurally separated from these no clear comparison may be made and hence the Ingletonian Series are considered to be of possible but not proven Pre-Cambrian age. The low grade of metamorphism probably suggests a late Pre-Cambrian age as the most probable, though lately O'Nions and co-workers (1973) have argued in favour of a Cambrian or early Ordovician age on the basis of radiometric ages (Rb-Sr and K-Ar) SILURO·ORDOVICIAN AND OLDER STRATIFIED ROCKS IN THE AREA ~9Ie'on , d-&_ '--~ ~~ 30 40 SILURIAN PRECAMBRIAN (?) @~W L1andovery,Wenlock and Ludlow series fY,::\~:tmllngletoni3n Series ORDOVICIAN n: ::0) Coniston Limestone and Ashgill series illTIlIllIJ] Borrowda le VoIcanir Series 1::;'<>1 Sklddaw Slates Series o 10 20 30 __==:1----=,50 miles r:=::==---t--. . _.~. _ .__ 1_. FIG.3.2 3 0 determined in slates of this series. In addition , the gravity and magnetic surveys carried out in the Askrigg Block of the Pennines have demonstrated the presence in the subsurface of a belt of highly magnetic rocks extending between Wensley- dale and the Craven and Dent fault-lines. This belt has been interpreted as a series of Pre-Cambrian rocks older than the Ingletonian and to contain metamorphic rocks as well as lavas (Bott, 1961); pebbles and fragments of such rocks are present in some coarse grits of the Ingletonian. Apparently, these compacted, folded and sheared rocks form the basement for the whole region over which the younger Paleozoic materials were deposited. 3.2.2 Lower Paleozoic Rocks Sedimentary and volcanic Lower Paleozoic rocks are abundant in the Lake District and are also found forming minor inliers in the central and south-central zones of the area, at Cross Fell, west of the Burtreeford Disturbance,and north of the North Craven Fault near Ingleton (Figure 3.2). 3.2.2.1 Cambrian System Cambrian rocks have not been indicated to exist in Northern England, though Eastwood (1946) suggests that probably the bottom-most part of the Ordovician Skiddaw Slates may be of this age. The nearest Cambrian levels recognized have been found in a borehole at Eakring (Nottinghamshire) where phyllitic mudstones and quartzites probably representing this system were found at a depth of 7,200 ft (Edwards and Trotter, 1954). Apparently rocks of this system are not present in Northern England, at least not east of the Lake District. 3.2.2.2 Ordovician System This system is widely represented in the western part of the • 1 studied area where the following four main units may be distinguished: (1) Skiddaw Slate Series This marine sedimentary unit crops out mainly in the Lake District where it covers an area of approximately 200 square miles. Other isolated outcrops are found in the Cross Fell Inlier and at Cronkley in Upper Teesdale (Figure 3.2). The series is formed by shales, siltstones, sand- stones and grits, horizons that display a distinctive rhythmic alternation in most cases. Spotted mudstones and stripped shales are also locally common (Eastwood and others, 1968). The base of the sequence is unknown and intense folding and contortion impedes an accurate estimation of its thickness. Rose (1954) indicates a minimum thickness of 6,500 ft for the section in the Keswick- Buttermere area, Eastwood and others (op.cit.) a thickness of 4,600 ft for the exposures at Skiddaw, and Rayner (1967) considers a probable total thickness of 7,000ft. Several attempts have been made to subdivide this series into units of regional importance, but apparently each of the recognized successions is only of local use due to frequent mergings and lateral gradations. The most important works in this field are those of Ward (1876) and Dixon (1925, 1931). Elles (1933) on the basis of faunal zonation considered that the age of the series ranges from Tremadocian to Lower Llanvirn, an idea that was challenged by Hollingworth (1954) and Rose (op.cit.). Lately, Eastwood and co-workers (1968) postulated that these beds are essentially Arenigian in age, just ranging into the Llanvirnian. Very different interpretations have been given to the relation- ship existing between this series and the overlying Borrowdale Volcanics. Among the hypothesis, the most important suggest that the junction is a normal fault, a thrust fault, or that there is a gradual passage from rjo • / • 4., one series into the other. Apparently, each of those relationships is present at some place of the juncture, but as a whole it appears that both series lie conformably. In the upper mudstones of the Skiddaw Slates there are intercalations of volcanic tuffs and lavas which increase upwards in proportion until the sediments are excluded from the sequence (Mitchell, 1956). (2) Borrowdale Volcanics This unit outcrops mainly in the central part of the Lake District and at Caldbeck Fells in the northern part of that area. Minor outcrops are found in the Cross Fell Inlier and in the Furness District, (Figure 3.2). The series comprises an alternate succession of pyro- clastic rocks and lavas more than 12,000 ft thick. The lavas are mainly andesites though ranges in composition from basalts to rhyolites are known. The pyroclastic rocks range from fine-grained tuffs to coarse agglomerates and breccias; dynamic metamorphism has transformed part of them into slates, particularly in the Borrowdale and Coniston areas. Numerous authors have subdivided this unit into regional form- ations, but detailed works have demonstrated that great variations occur from place to place as can be expected from the lithology of the series. No fossils have been found in the very minor sedimentary horizons present at the base of this unit which is considered to represent the span Upper Llanvirn-Llandeilo (Hollingworth, op.cit.) due to its stratigraphic relationships. As indicated previously, this unit originally overlaid conform- ably the Skiddaw Slates though at present their juncture is mostly tectonic. Its top underlies unconformably the Coniston Limestone Series which trans- gresses more than 8,000 ft of volcanic rocks between Kentmere and Duddon Bridge, resting near Dalton-in-Furness over Skiddaw Slates. Therefore, it is clear that after this huge Ordovician volcanism, there was a period 3, 3 of important tectonic movements and severe erosion probably during Llandeilo times (pre-Bala tectonism). (3) Coniston Limestone Series This marine unit outcrops in the central part of the Lake District as a narrow north-east trending strip that extends from Millom to the vicinities of Shap. Other isolated outcrops are known to the north of Dalton-in-Furness and at Kirsley,in the Cross Fell Inlier (Figure 3.2). It consists of less than 1,000 ft of interstratifield limestones and cal- careous sediments with intercalations of conglomerates and rhyolites. Two stages are usually recognized within this unit whose fossils indicate a Caradocian age. As indicated previously, this sequence overlies unconformably the Borrowdale Volcanics and overlies conformably the sediments of the Ashgill Series. An unconformity existing within the sequence indicates that during the deposition of its lower part minor tectonic movements were taking place in the area, probably as a very late manifestation of the pre-Bala movements. (4) Ashgill Series This unit is a thin marine sedimentary sequence that conformably overlies the latter series along the whole of its outcrop. Minor isolated outcrops are also known to the north of the North Craven Fault and west of the Dent Fault (Figure 3.2). It consists of a basal lime- stone succeeded by shales, mudstones and calcareous sediments, totalling a thickness of about 100 ft. Three subdivisions are recognized within this sequence (Marc, 1916), their fossils indicating an Ashgillian age (King and Williams, 1948). Worth mentioning is the presence in this unit of ashy beds which represent the late manifestations of the Ordovician volcanism which previously affected the area. The stratigraphic relations of the series are clear, resting n conformably between the Coniston Limestone Series and the Silurian Stock- dale Shales, at its base and top respectively. 3.2.2.3 Silurian System Silurian rocks cover considerable areas in the southern part of the Lake District and adjacent fells to the east, and also constitute the bulk of the Lower Paleozoic rocks of the Horton Outlier in the northern side of the North Craven Fault (Figure 3.2). On the whole, these rocks are coarser-grained and more arenaceous than the underlying sediments and are characterized by an abundant fauna. Three of the four main subdivisions of the British Silurian are represented in the studied area, the uppermost Downtown Series being absent. The main features of the existing units are the following, from bottom to top: (1) Llandovery or Valentian Series This series is represented by the Stockdale Shales sequence of dark shales and some grits, with thin intercalations of limestone and calcareous sediments. Pyrite and carbonaceous matter are common in these levels. Its thickness is about 250 ft, its outcrop following closely those of the Coniston Limestone Series. (2) Wenlock Series This series is represented by the Lower Coniston or Brathay Flags, a sequence 1,000 ft thick of laminated mudstones and grits which appears to have been deposited in shallower waters than the first. It passes gradually downwards into gritty Valentian beds and its top is marked by the appearance of coarse sandstones for the first time within the Silurian sequence. (3) Ludlow Series This series, about 12,000 ft thick, constitutes the top of the ..i 5 Silurian in Northern England. Its base (Coniston Flags or Coldwell Beds) is formed by mudstones and grits, on top of which lie coarse grits with bands of flaggy mudstones (Coniston Grits) that are frequently faulted against the underlying horizons. The sequence grades upwards into a series of sandy mudstones with thin beds of sandstone and occasional grits (Bannisdale Slates), which are strongly cleaved rocks comparable to flysch deposits. Overlying the latest sequence there is a group of flags with some gritty beds (Kirkby Moor Flags), which include some calcareous horizons. With these horizons the Silurian ends in Northern England, a great gap existing over them in the stratigraphic succession since neither Downtown- ian nor Devonian rocks outcrop in the region unless some of the conglomerates found beneath the Carboniferous Limestone Series at some localities, such as Mell Fell, Millom, etc., were representative of the Devonian. Whether rocks were laid down in this part of England after the Ludlowlian cannot be ascertained since the Caledonian orogeny commenced in,the Downtownian and continued during most of the Devonian period, provoking important structural changes and the uplift of the whole region with the concomittant intense denudation of the contemporaneous and older rocks. 3.2.3 Upper Paleozoic Rocks Sedimentary Upper Paleozoic rocks are by far the most abundant in the studied area, covering most of the eastern and southern regions and forming a rim around most of the Lower Paleozoic rocks of the Lake District. Some minor volcanic horizons of this age are also known in the area north of Cockermouth. The main features of the stratigraphic units that can be distinguished within the Upper Paleozoic sequence of Northern England are the following: a 3.2.3.1 Carboniferous System The transgression of the Carboniferous sea over pre-existing units is one of the main features of the geological evolution of Northern England, resting the deP'Osits accumulated during this period over various members of the Ordovician and Silurian Systems, and to the north of the studied area over Devonian lavas. A threefold division of this system is normally done on the basis of lithology: the basal unit (Carboniferous Limestone Series) contains massive limestones as its most conspicuous rock type, being succeeded by an essentially clastic formation (Millstone Grit Series) and this in turn by a similar though less arenaceous sequence with numerous coal seams (Coal Measures). These major division3represent phases of deposition in an irregularly subsidizing area, in which s idence and sedimentation kept a rough pace. Clear-water conditions were initially dominant giving rise to the limestones; later, uplift of the neighbouring terrain produced recurrent deltaic sedimentation, generating sandstones and mudstones with coal layers interbedded. It is worth noting that there is no sharp separation between the major stratigraphic units since pelitic sedimentary rocks and coal'seams can be found in the mainly calcareous basal beds, limestone persists into the rhythmic succession of the Millstone Grit and marine facies can be locally recognized high in the sequence of the Coal Measures. Moreover, since the transgression was not simultaneous in the whole region, rocks of similar nature that are found in different areas need not represent the same event. This fact is especially important when considering the early part of the period. It is therefore very difficult to indicate a litholog- ical sequence applicable to the whole area. Considering that the present research is more concerned with rock-types than with stratigraphic units sensu stricto the following division n 7 of the system was regarded suitable for the intended purpose: (1) Basal Conglomerates; (2) Cockermouth Lavas; (3) Carboniferous Limestone Series; (4) Millstone Grit Series; and (5) Coal Measures. (1) Basal Conglomerates In many parts of Northern England there are conglomerates at the base of the Carboniferous sequence, their most important outcrops lying in the periphery of the Lake District and in valleys cut into the Pennines Escarpment (Figure 3.3). Minor outcrops are present in the southern Lake District north of Kendal, north of Dalton-in-Furness, and around Kirkby Longsdale. The rocks grouped within this unit are conglomerates, sand- stones and shales, with some minor intercalations of argillaceous limestone. Its thickness varies from 10 to 1,000 ft, and probably fills broad hollows existing on the basement of the area. In the Pennines there are usually two and even three conglomer- ates, the uppermost of which has calcareous materials that link it to the overlying limestone. The one at the bottom (Polygenetic Conglomerate) is reddish and contains a high proportion of pebbles foreign to the region; this has induced some writers to consider it as belonging to the Old Red Sandstone. The intermediate conglomerate is also reddish but contains few foreign pebbles; together with intercalated sandstones and shales it forms the Roman Fell Beds for which a definite Carboniferous age has been proven by Shotton (1935). Definite evidence about the age of most of these beds is lacking. The red colour shown by several horizons must be considered indicative of conditions of deposition and not of age and therefore they may be regarded as Early Carboniferous deposits of rock waste accumulated in the Late Devonian, a feature known in other parts of Britain such as North Wales. (2) Cockermouth Lavas This unit constitutes a narrow strip, almost eight miles long, UPPER PALEOZOIC STRATIRED ROCKS INTHE STUDIEDAREA 30 40 PERMIAN CARBONIFEROUS Fi-~':~:~q Magnesian Limestone o Coal Measures L- -J Penrith Sandstone-St.Bees Shale-Brockram GIillIill Millstone Grit ~ Carboniferous Limestone [~ili~,tJ Cockermouth Lavas 10 20 3,0 y------_._-- L:- ! FIG.3.3 1^1 0 Li CI in the north-western margin of the Lake District (Figure 3.3). It is formed by fine-grained olivine basalts that occur in several flows, four or five of which are exposed near Cockermouth, totalling a thickness of over 300 ft. Lenticular masses of green marl ("bole") have been noticed between two of these flows (Eastwood, 1928). The occurrence of the basalts as flows with slaggy tops and bases, and the, absence of pillows and ashes, suggest a quiet sub-aerial extrusion. The presence of "bole" suggests that the volcanism took place intermittently. Most of the outcrops of these lavas overlie Basal Conglomerates and are succeeded by the Carboniferous Limestone with which they agree in general attitude. Therefore, these rocks are of Lower Carboniferous age, being equivalent to the volcanics of Kershope Foot (Cumberland-Dumfriesshire) and also similar to those existing in Shropshire and near Bristol (Pocock, 1926; Morgan and Reynolds, 1904). (3) Carboniferous Limestone Series This stratigraphic unit is the most important for the purposes of the present research since most of the ore deposits existing in Northern England occur in country rocks of this series. Four major groups have been distinguished within this unit in the present work, totalling a thickness of about 5,000 ft and representing the Dinantian or Tournasian- Visgan span. (A) Cementstone, Fell Sandstone, Craighill Sandstone,and Birdoswald Limestone Groups: These groups constitute minor outcrops in the northern- most part of the studied area where they represent the base of the Carbon- iferous. They consist of shales and sandstones with thin intercalations of impure limestone, increasing the amount of calcareous material towards the top, which is formed by limestones and sandstones that in places display the typical "rhythm" of the Carboniferous sequences of Northern England. :3 9 (B) Lower Limestone Group: This unit outcrops in the western margin of the Pennines, and in some main valleys that cut across the Carboniferous sequence. It extends vertically to the base of the Smiddy Limestone with a fairly constant thickness of about 220 ft, except to the south of the Swindale Beck Fault where its thickness is almost doubled. The lower part consists of pale-grey or grey massive limestones and thin marl beds interbedded. The upper part consists of alternating shales, sandstone and limestones, the latter including the Robinson Lime- stone that is intermediate between these pale rocks and the dark ones of the succeeding unit. The group ends in an alternation of sandstone and shales. (C) Middle Limestone Group: The outcrops of this group are widely scattered throughout the studied area, constituting large portions of the Pennines and also the rim that surrounds the Lake District. The rhythmic deposition that started in Lower Limestone times is typical of this unit which is composed of at least eleven cyclothems formed by the following strata in upwards succession (Hudson, 1924; Brough, 1929): dark limestone, calcareous shale, ferruginous shale, sandy shale, sandstone, ganister or underclay, and coal. Small breaks in the succession may be found due to minor erosive episodes that occurred during this time. The group comprises the beds lying between the Smiddy and Great limestones,totalling a maximum thickness of 1,000 ft and a minimum of about 600 ft, according to sections selected by Dunham (1948). An increase in the thickness of the group is noticeable towards the east. (D) Upper Limestone Group: This unit outcrops in large tracts of the studied area covering almost one fifth of it. It includes the beds that lie between the bases of the Great Limestone and of the Millstone Grit Series, its thickness being highly varied throughout the region. A minimum of 570 ft and a maximum of 950 ft can be estimated for the whole sequence. x0 The rhythmic sedimentation characteristic of the previous unit is still present in this group, but a gradual change in lithology is noticeable. Coarse grits appear a short distance from the base, and the marine beds are very thin limestones, shales and shaly sandstones; in much of it, shales are the predominant rock-type though in some belts thick sandstones or grits are developed to the exclusion of shales. (4) Millstone Grit Series This series outcrops mainly in the eastern part of the area between the Carboniferous Limestone and the coalfields extending beyong the Pennines,and in the south in the Lancaster Fells (Figure 3.3). Minor outcrops are found capping the most important hills, of the Yorkshire Fells, and in the southeastern corner of the area, near Richmond. The outcrops lying north of the Craven Fault system are not strictly comparable to those typical of the series in Lancashire, Yorkshire and Derbyshire. They consist of coarse grits and sandstones with inter- calations of shale, ganister, marine bands and thin impersistent coal layers, the sequence varying in thickness from 250 to 375 ft. Its base is considered to be an important grit layer lying above the "Grindstone Sill", a layer which is apparently hig.her in the stratigraphic succession than the one regarded as base of the unit in the Middle Pennines. Therefore, it is possible that part of what is considered as Upper Limestone, in the present research are rocks belonging to the lower portion of this series. South of the Craven Fault, the series attains its main develop- ment, though in the studied area it is not very well represented, especially the upper levels which have been eroded. Characteristically, in that region there is a rhythmic succession containing coal, fossiliferous mud- stone, barren mudstone, very thick coarse-grained sandstone, and seatearth. The thickness of the sequence in that area is about 1,000 ft. The Millstone Grit would be the representative of th'a Namurian 41 in the studied area. (5) Coal Measures This unit outcrops mainly in the north-east and north-west of the area, in the coalfields of Durham, Northumberland and Cumberland. Minor patches are found in the north-central and south-central regions, near Halwhistle and Ingleborough, respectively. The outcrops of Durham- Northumberland include a basal sequence, 2oo ft thick, of shales and shaly sandstones with minor coal seams which are conformably succeeded by about 2,000 ft of alternating shales, sandy-shales, sandstones, fireclays and coal seams. The upper portion of the series has been eroded. In the West Cumberland Coalfield the whole unit is present. The lower and middle parts of it, which contain the workable coal layers, are mainly argillaceous, but include several thick lenticular arenaceous beds, totalling a thickness of about 1,000 ft. Over those beds lie up to 1,000 ft of red and purple shales, sandstones and mudstones, with few coal seams and two thin limestones in the southern outcrops. The presence of fossils in the shales and mudstones above the coal layers assigns this unit to the Westphalian. Apparently, during its deposition deltaic conditions predominated over the whole area, but periodical silting-up determined the formation of short-lasting but extensive flats at sea-level, where vegetation proliferated until renewed subsidence drowned the forests and covered them with fresh mud deposits. The environmental conditions changed during the Late Carboniferous when the deltaic deposits rarely reached the sea-level. Thus, the higher horizons of this series display strong predominance of clastic materials and only occasional coal seams and local freshwater limestones. Later, the region was folded, tilted and uplifted, and the upper horizons were mostly eroded. Therefore, the outcrops of the series are separated by large tracts of older rocks and the correlation between the different coal- 42 fields can only be made on broad terms. 3.2.3.2 Permian System At the end of the Carboniferous, the Hercynian tectonisms faulted, flexed and uplifted the area, with the consequent erosion of important thicknesses of Carboniferous and older rocks. During the Permian new marine transgressions occurred giving rise to small basins partly or wholly cut-off from the open sea. These basins were separated by Hercynian uplifts, the most important of which was the Pennine massif. The nature of the rocks accumulated during this period indicate that inter- mittent arid conditions prevailed during much of that time in the region. In the studied area, Permian rocks outcrop mainly along the Vale of Eden where they constitute a south-east trending strip about 35 Miles long. Minor isolated outcrops occur east of Whitehaven, north-west of Ingleton, south of Grange, and around Barrow-in-Furness (Figure 3.3). At Edenside two main units may be distinguished within this system which unconformably overlies the Carboniferous Limestone and is in turn conformably overlain by Triassic rocks. The lower series is the Penrith Sandstone, a largely aeolian deposit comprising up to 1,500 ft of coarse sandstones, with sedimentary breccias ("brockrams") at its base and towards its top. Near Appleby this unit is succeeded by dolomitic shales, marls and sandstones (Hilton Flat Beds) and by a thin dolomitic limestone equiValent to the Magnesian Limestone of north-east England; elsewhere, it grades upwards into 150 to 300 ft of alternating shales, mudstones, and gypsum layers, a sequence known as St. Bees Shales. Near Whitehaven a coarse breccia, local equivalent of the former series, unconformably overlies Upper Carboniferous rocks. Above it, rocks belonging to the Magnesian Limestone and St. Bees Shales outcrop. To the east of that area only the breccias are present in a sequence that in places reaches hundreds of feet representing the whole Permian and part of 43 the Triassic. In the Furness district, the base of the Permian is formed by 63 ft of Magnesian Limestone, a unit that is succeeded by "brockram" beds and St. Bees Shales; near Ingleton, the system is represented by sandstones similar to those of the Penrith Sandstone. Apparently, most of the coarser rocks included in the foregoing units represent torrential deposits of neighbouring valleys which origin- ally formed gravel fans that intermingled in the lower grounds. Where these gravels reached small lagoons, dolomitic limestones, gypsum layers and shales were interbedded with them. 3.2.4 Mesozoic Rocks These rocks are not abundant in the studied area, corresponding to sedimentary deposits that crop out in the Solway Basin, Edenside and along the coast between St. Bees Head and the Furness district. The Triassic and Jurassic systems are represented in those outcrops, the former being the most important. The main features of those Mesozoic deposits may be summarized as follows: 3.2.4.1 Triassic System As indicated previously, when this period began many areas of Northern England were submerged and the group of marine sediments known as St. Bees Shales was being deposited in an inland basin wholly or partially cut off from open sea. These conditions of deposition persisted throughout the period. The rocks representative of this system outcrop in two main regions of the studied area: In a north-west trending strip at the Vale of Eden that broadens at the Solway Basin to cover most of the country around Carlisle,and in a coastal strip extending from St. Bees Head to the vicinities of Heysham (Figure (3.4). Minor outcrops are found to the south-east of Grange. MESOZOIC ROCKS IN THESTUDIED AREA G 30 35 40 JURASSIC ~ Lower liassic TRIASSIC _ Keuper Marl g Keuper and Bunter Sandstones 30 40 r I FIG.3.4 44 All these deposits may be subdivided into two main groups: (1) Bunter Deposits These deposits constitute most of the Triassic rocks in the studied area. They are mainly shales, marls, and sandstones, with minor intercalations of conglomerates and gypsum. The basal unit is mainly argillaceous, being formed by 150 to 300 ft of red shales and marls with occasional gypsum layers. Succeeding that sequence there is a series of red sandstones with subordinate shales, a group that reaches a thickness of 1,700 ft. Overlying the last sequence there are 250 to 300 ft of wholly arenaceous deposits, a unit especially well developed around Carlisle (Dixon and others, 1926). (2) Keuper Deposits These deposits are much more restricted than the former, being found along the coastal strip of outcrops and to the west of Carlisle where they form a big outlier. They are formed by silty or sandy shales with thin dolomitic and sandy beds interbedded in a sequence totalling about 1,000 ft thick in its best development. This unit is known locally as Stanwix Shales and is considered to be equivalent to the Keuper Marl of the Midlands. 3.2.4.2 Jurassic System The only rocks known in the studied area to belong to this system lie west of Carlisle, where they constitute an irregular patch conformably overlying the Stanwix Shales. No Rhaetic beds are known in Northern England, but it may be assumed that at the end of the Keuper widespread marine submersion took place leading to the deposition of marine sediments of which the only known remnant is centred around Great Orton. This outlier is formed by about 200 ft of dark shales with several intercalations of argillaceous limestone. The sequence is in general poorly exposed, but is sufficiently known at old wells to be definitely 45 regarded as of Lower Liassic age (Dixon and other, op.cit.). 3.2.5 Pleistocene and Recent Deposits Within this heading those deposits referred to as the Glacial (Pleistocene) and Post-Glacial (Recent) periods are included. During the Glacial period, enormous ice-sheets spread over the area from the north, generating important topographic features by erosion and/or deposition. Glacial sediments include boulder clay, sands and gravels which were deposited during two main events separated by an inter-glacial span. The oldest deposits (Older Drift) correspond mainly to boulder clays formed when ice arising from south-west Scotland invaded the region and later retreated. The Newer Drift was deposited in two stages by ice arising not only from the north-west, but also by local ice-sheets formed in the Cheviots, Lake District and Pennines. After the main glaciation, a period mild enough to allow the accumulation of peat occurred, but renewal of cold conditions led to another invasion of Cumberland by ice coming from Scotland (Scottish Readvance). This event took place mainly between the foothills and the sea, modifying only slightly the older features. The Post-Glacial deposits in the area are hard to separate from the Glacial ones. Along the coast they include the Submerged Forest (peaty deposits with trunks and stools of different kinds of tree), the Raised Beach (beach gravels and silty clays lying 25 ft above the present sea-level), and sand dunes, all of them revealing important changes in the sea-level that have occurred recently. Inland, these deposits are mainly screes in the hills, alluvium along the valleys, and peat bogs or mosses in the lowlands. 46 3.3 INTRUSIVE ROCKS The three main orogenies that affected the area were accompanied by the emplacement of intrusive bodies of various nature, shape and size, which are scattered throughout the region. In the Lake District, large areas are occupied by intrusive rocks which constitute several bosses of predominantly acidic composition and other minor bodies as sills and dykes. Contrasting with that area the central and eastern regions are almost devoid of outcropping intrusive rocks, although important intrusive masses have been proven to exist beneath the Carboniferous country-rocks around Weardale and Wensleydale. According to their age of emplacement, the intrusions of Northern England may be divided into Caledonian, Hercynian and Alpine. The main characteristics of the bodies comprised in each group follow: 3.3.1 Caledonian Intrusions Intrusive rocks of Caledonian age are found cropping out in the western part of the studied area forming an important proportion of the Lake District and beneath the CarbOniferous rocks around Weardale and Wensleydale (Figure 3.5). In the Lake District, the intrusions are confined to Ordovician country-rocks, but geological evidence of their age is only conclusive in the case of the Shap Granite which intrudes Ludlow levels and whose erosion has provided feldspars found in the basal Carboniferous conglomerates. In that area the most common rock-types are acidic in nature, but intermediate, basic and ultra-basic rocks are also present. The shape of the bodies tend to be irregular, though most of them may be classified as stocks with the exception of the Threlkeld Microgranite that constitutes a laccolith (Marr, 1916). Dykes and sills are also common. The main granitic bodies are those at Eskdale, Shap, Skiddaw, INTRUSIVE ROCKS IN THE AREA ... , 0 - c 0., . : .. . I. Gill 1' . Carrock fell IMEttk Gree will deb .4 ■ IP 4 e"-.5lacklow , Ettersgoll 6 y. i 70 Threlkeld 4° 66" -I, — .. . v .,., - A ',—.- • 4 /O. "tba•-• ' ‘ % ''.1. ... rs 1'/4/ ar „ [newel& tt ; ,itr• • e shop )- \ ? , _./ 4 ,.. i $ „• , 30 33 40 Basalt ,dolerite,camptonite , etc. ----,- Gra nite, s yenite, etc. illin Gabbro I /7 1 Porphyrite, felsite, etc. o 10 , 20 30 40 50mi les i 1 1 FIG.3.5 47 and Threlkeld, presenting normally suites of pegmatitic and aplitic dykes. Granophyres are found at Ennerdale, Embleton and Carrock Fell, though the latter is mainly a basic complex formed by different types of gabbro, felsite and diabase. Other rock-types occasionally found include lampro- phyres (minette), dolerites, and picrite. All these intrusions have thermally metamorphosed their host-rocks to varying degrees, a feature that is especially evident in the case of the Shap and Skiddaw granites, which also include late pneumatolytic and hydrothermal phases, modifying even more by metasomatism their surrounding country-rocks. The available radiometric age determinations indicate that these bodies were mainly emplaced in the Early Devonian.' Brown and co-workers (1964) determined an age of 339 my for the Skiddaw Granite, and Kulp and co-workers (1960) indicate a weighted average age of 391 my (K-Ar) or 381, my (Rb-Sr) for the -Shap Granite. Gravimetric investigations performed in the Northern Pennines (Bott and Masson-Smith, 1953, 1957) revealed in the Weardale area the presence of an important negative gravity anomaly trending east-northeast. This feature was interpreted as the result of a granitic batholith with cupolas("Weardale Granite") lying beneath the exposed Carboniferous rocks, a hypothesis that was demonstrated in a borehole done at Rookhope which entered an intrusive body at a depth of about 1,300 ft (Dunham and others, 1961, 1965). This intrusion is a granite containing abundant muscovite and biotite with a low-dipping foliation in the upper part. Aplitic and pegmatitic materials are common among the rock-types found within the body. Radiometric age determinations in samples of that granite (Dodson and Moorbath, 1961) indicated that it was emplaced during the Middle-Late Devonian (weighted average age of 362/6 my), during a magmatic episode somewhat more recent than that of the Lake District. In addition, in the Wensleydale area a similar anomaly was 48 discovered in the late 1950's. Bott (1961) interpreted this feature, which also bears a positive magnetic effect,as a result of a granitic batholith somewhat smaller than the former one and probably of grano- dioritic or tonalitic composition. No proof of this hypothesis is avail- able; it is probable that,as suggested by Bott (1967), its age could be Pre-Cambrian and not Devonian. 3.3.a Hercynian Intrusions During the Late Paleozoic, sills and dykes which intrude Carbon- iferous rocks were emplaced in Northern England. The most important of these is a series of related sills or phacoliths of quartz-dolerite that crop out at intervals in Northumberland and in the Teesdale area (Figure 3.5). They are collectively known as the Whin Sill and are regarded as the product of a single intrusion due to their similar composition and structure throughout the region. Petrographically, four types of dolerite are included in these bodies: (1) Tachylitic marginal phases; (2) Fine-grained dolerite; (3) Medium-grained dolerite (mottled); and (4) Grey and pink dolerite- pegmatites (Holmes and Harwood, 1928). Of these types, (3) and (4) are generally found in the thickest bodies. Their emplacement produced thermal metamorphism and metasomatism in their host-rocks with the development of "baking",spotted slates, marbles, calc-silicate rocks, etc. The effects of this metamorphism may may be noticed up to 100 ft (stratigraphically) from the quartz-dolerite bodies. The thickness of the Whin Sill reaches to a maximum of 240 ft at several places (e.g. Ettersgill prospect, Greenhurth mine) but on average it is 80 to 100 ft. Along broad stretches of land these intrusions occupy a constant position within the sequence; the position changing along definite lines or belts, a few of which coincide with major faults. Normally 49 these bodies are found between the lower levels of the Lower Limestone group and the upper levels of the Middle Limestone group, though in places they have been found to intrude the Upper Limestone group and even the middle Coal Measures. Other intrusive bodies that were emplaced during this period correspond to dykes trending between north-east and east north-east. They are formed by fine-grained dolerites with common chilled (tachylitic) margins. Among them, the most important are the Haydon Bridge, Loo Gill and Hett dykes. The age of the emplacement of the Whin Sill and other dykes can be considered to be Late Carboniferous-Early Permian since they intrude Carboniferous but not Permian rocks. Besides, pebbles of quartz-dolerite have been found in basal Permian conglomerates (Holmes and Harwood, op.cit.; Dunham, 1932), supporting the pre-Permian age of emplacement. Radiometric age determinations (K-Ar) of the sills crossed at the Rookhope borehole, indicate an average age of 281 my (Late Carboniferous), thus coinciding with the geological evidence (Miller and Mussett, 1963). 3.3.3 Alpine Intrusions The only post-Paleozoic intrusive rocks known in the area are the west north-west trending echelon of dykes that constitutes the Cleve- land-Armathwaite system, a group of tholeiites or augite andesites that outcrop intermittently from the vicinities of Carlisle to the vicinities of Middleton-in-Teesdale (Figure 3.5). To the west, this system of dykes is supposed to extend beneath the glacial drift west of Carlisle linking up with dykes lying across the Solway Firth in Scotland. To the east, the system links up with the Cleveland Dyke of east Yorkshire. The eastern outcrops cut across the Liassic rocks of north-east Yorkshire and the western outcrops intrude on Permo-Triassic rocks in the Vale of Eden. These-rocks, and other similar dykes existing in Durham 50 and Northumberland to the north-east of the studied area, are of undoubted Tertiary age and are believed to be part of the swarm of basic dykes of the Mull Complex. Evans and co-workers (1973) lately obtained on three samples of the echelon K-Ar ages ranging from 55.3 to 58.7 my; the average age of 58.4±1.1 my (Paleocene) is considered to be a close minimum age for the intrusion of these bodies. 3.4 STRUCTURE Four tectonic periods are distinguishable in the geological evolution of Northern England, each of which imposed in the country-rocks particular structural features that were more or less modified later by subsequent orogenies. The oldest of these tectonisms probably occurred during the Pre-Cambrian, affecting the formations that are believed to form the basement of the southeastern and south-central regions of the studied area. The characteristics of this cycle are little known, but in general terms it may be stated that its main result was the moderate to strong folding and shearing of the Ingletonian Series. In the Lower Paleozoic, intense tectonic movements occurred affecting the basement of most of Northern England. These eartIP-movements started with minor disturbances during the Llandeilo, which were responsible for the unconformity that separates the Borrowdale Volcanic from the Coniston Limestone series and for minor folding along north-east trends (Mitchell, 1929). Slight tectonic activity succeeded the initial stage until the Downtownian, when the main orogenic cycle started lasting probably during most of the Devonian and not occurring as a single tectonism but rather as a series of movements (Helm and others, 1963; Mitchell, 1967). The main stresses were related to intense compression along south south-•east and north north-west lines. The fold axes formed are arcuate, changing their strike from north-east- in the west to a more 51 easterly direction in the east (Figure 3.6). The principal trend of these axes as a whole is east north-east. The main structure that may be recognized in relation with this tectonism is a broad anticline passing through Skiddaw and a complementary syncline passing through Sca Fell. Another main anticline of this age is found in the southern Lake District extending from the Duddon estuary in the west to beyond Staveley in the east. Numerous minor folds of similar trend were also developed though appreciable divergences in strike have been noticed. The difference is competence between the various rock-types existing in the area is reflected in the type of structure developed in each of them. The softer Skiddaw Slates show tight folds and are severely crumpled with minor folds frequently overturned and isoclinal; associated thrusting is also common, as well as lag and normal faults (Eastwood and others, 1931; Trotter and others, 1937; Rose, 1955). The more competent Borrowdale Volcanics are as a rule more gently folded, displaying broad open folds; in places tight folding is evident as well as tear-faults and thrusts, the latter occurring mainly along bedding planes. The Silurian rocks present considerable crumpling and are frequently traversed by tear- faults and thrusts, though these features are diminished towards the top of the succession (LudIowlian) which is not so tightly folded; the most important structure developed in these rocks is a great strike-fault, which is either a lag or a thrust occurring between the Ordovician Ashgill Shale and the Silurian Stockdale Shale. Jointing is a conspicuous feature in the Lake District. Most writers recognize two types of joints: (1) Low-angle joints frequently coinciding with the bedding, and (2) Steeply dipping joints trending between NW-SE and NE-SW. Apparently, all these sets were developed as a result of the NNW-SSE Caledonian compression though some of the former ones may be the result of tensional effects. Joints produced by the subsequent orogenies are undoubtedly present in that area, but are difficult to separate from the former and hence all the jointing is considered as if it were Caledonian. Outside the Lake District, the Lower Paleozoic rocks show in general similar trends to those of the main outcrops. At the Cross Fell Inlier, the trends in the Skiddaw Slates are dominantly ENE(Shotton, 1935), a situation similar to that in the Teesdale area. An exception is found in the outcrops north of the Craven Fault whose structures trend south-east; possibly, this trend is a continuation of the swing on the strike occurring in the eastern part of the Lake District, but a later origin for this feature cannot be dismissed. Apparently, the rocks that constitute the basement of most of the central and eastern regions of the studied area have a Caledonian grain that affected the way in which the younger rocks responded to the later tectonic movements (Dunham, 1948). During the Upper Paleozoic numerous tectonic movements affected the region. In the western part they reactivated and modified some of the Caledonian structures and gently folded the Carboniferous rocks of West Cumberland which show open broad folds trending NE-SW; these folds are roughly parallel to the Caledonian ones, probably being strongly controlled by them. The main effects of the Hercynian orogeny may be observed in the central and eastern parts of the studied area. This region, since the Early Paleozoic, constituted a shelf separated by the Stublick and Craven fault systems from troughs existing both to the north and south (Figure 3.6). Its western margin was defined at the end of the Carboniferous when two groups of faults were developed to the east of the Vale of Eden: (1) The Inner Pennine Fault, a structure trending NNW and dipping towards the east, and (2) A series of thrusts along which the overthrusting was directed ENE. The latter group and the Burtreeford Disturbance, an east facing Main Structural Features of the Area 30 40 50nules Syncline el" Anticline 00000# Deep-seated fault Normal fault Monocline Low-angle thrust Wrench fault Dome FIG.3.6 monocline extending southwards from Swindale Beck, are considered by Turner (1935) as the northwards continuation of the Dent system of over- folds and reverse faults. Once the Pennine fault-block was established regular systems of joints oriented NNW and ENE appeared. Later, in the Carboniferous-Permian interval, gentle distortion of the Carboniferous rocks into an asymmetric dome occurred and the important Cotherstone or Stainmore Syncline was formed in a former trough of sedimentation. This syncline constitutes a structural and topographic depression that divides the Pennines into two minor blocks: the Alston Block to the north and the Askrigg Block to the south. Simult- aneously with the former processes, intense tension and compression affect- ed the area generating systems of normal faults with dominant NW and E-W directions and displacements of up to 330 ft; feeble ENE faulting and some structures trending north-south were also produced. Among the most important of these are the Teesdale-Harwood-Sir John's-Park Fell Cross- Faugh Cleugh system and the Great Sulphur Vein. During the late Hercynian, torsion due to gentle domal uplift occurred and the formation of conjugate systems of vein-fissures took place. These systems trend NNW, ENE and E-W to WNW, being normal faults sometimes accompanied by minor shear folds. Typically, these fissures show refraction effects and their displacement is small, in the range of up to 20 ft, though throws of up to 140 ft occur. To the west and south of the rigid Pennine block, other important structures were developed during the Hercynian. Among the most important of these are the dome-like Howgill Fells Anticline, and WSW-trending syn- clines that are part of the great Ribblesdale Fold Belt formed south of the Craven Fault. The age of the tectonisms that happened in the area after the Hercynian is difficult to determine with precision because the stratigraphic record finishes with Lower Liassic levels. These movements very probably occurred during the Tertiary. In the west they produced uplifting, tilting and gentle warping of the country-rocks, generating the present Lake District dome. A broad east-west anticline that extends through Harrington, and other minor folds trending NE and NW, are considered by Mitchell (1956) to be the results of those movements in that area; besides, faults trending NNW and NW were formed in the periphery of the dome, structures that are very conspicous where they break the Carboniferous Limestone bordering the Skiddaw Slates. It is probable that some of the big shatter-belts that cross the Lake District in a NNW direction (e.g. those at Esk House and at Dunmail Rise), may have had some displacement during this tectonic cycle, even if they were the result of previous orogenies. In the Pennine region, the Alpine Orogeny gently tilted the rocks towards the east and the whole block was uplifted along normal faults trending NNW and E-W. Of these faults, some were produced during the Hercynian (e.g. the Stublick and Lunedale-Butterknowle systems), but others, as the Outer Pennine Fault, were formed during this cycle. Preceding or following the uplift, compressive stresses in a N-S direction produced, near the southern margin of the block, some folds trending east-west. Finally, minor lateral movements up to 10 ft happened in the Hercynian fissure-veins generating striated slickensides. e-5 CHAPTER 4 BASE METAL DEPOSITS IN NORTHERN ENGLAND 4.1 GENERAL CONSIDERATIONS Numerous base metal deposits are known in the studied area many of which have been intermittently worked since Roman times. There are records of production in 258 of them. As it can be expected from such a large number of ore deposits, their economic importance has been varied; generally they constituted small operations when mined and only two of them (Greenside and Allenheads) rendered more than 200,000 tons of lead concen- trate during their operational lifetime. These deposits form two of the nine areas of base metal mineral- ization that can be distinguished in Great Britain: The Northern Pennine and the Lake District orefields, a distinction that does not only represent a geographic grouping of separate mining districts, but reflects contrasting geological and metallogenetic settings, each of the orefields being a metallogenetic district as defined by Petraschek (1965). The importance that these deposits have had as producers of base metals, can be visualized by considering that they produced about 4,230,000 tons of lead concentrate and 300,000 tons of zinc concentrate, figures that represent 49% and 24% of the total production that has been raised in the United Kingdom, respectively (Schnellman and Scott, 1969). In addition, minor amounts of copper ore have also been mined in both fields totalling an output of about 5,650 tons Cu metal. In the following paragraphs a brief account of the main characteristics displayed by the deposits existing in each field is given. The Northern Pennine area is described on the basis of the excellent account given by Dunham (1948), and the description of the Lake District 5s is based mainly on works by Postlethwaite (1913), Eastwood (1921, 1929), Dewey and Eastwood (1925) and Gough (1962). 4.2 NORTHERN PENNINE OREFIELD 4.2.1 Introduction This field covers approximately 1500 square miles in the counties of Cumberland, Westmorland, Northumberland, Durham and Yorkshire, where it forms a single physiographic unit that may be described as a plateau uplifted along its margins and slightly tilted towards the east. Its western margin is the Pennine Escarpment which separates it from the low- lands of Edenside; its eastern margin is not well defined, merging into the Durham Coalfield. To the north the field ends some five miles south of the Tyne Valley, but usually deposits found between that valley and the Roman Wall are included with those of the field itself. To the south, the Northern Pennines extend to the Craven district, separated by the Stainmore Gap into two sub-areas: The Alston Block to the north and the Askrigg Block to the south. Numerous base metal deposits have been worked in the area, 239 of which record output. The region has been the largest lead-zinc productive area of the United Kingdom, with a total production of about 3,110,000 tons Pb metal; 17,200,000 oz. of silver; and 147,000 tons Zn metal. The main period of production was between 1805 and 1880, although the mining records go back to the 12th century and activities were main- tained until the late 1940's. The size and consequently the production of the deposits is obviously widely varying. One mine (Allenheads) produced more than 250,000 tons Pb concentrate, the second Most important producer of Great Britain; ten other mines produced over 100,000 tons, and five produced in the range 50,000 - 100,000 tons. 4.2.2 Mineral Deposits The ore deposits of the field may be grouped into two categories: P' 7 (1) Veins emplaced along fissures that generally dip more than 70° where mineralized, and (2) Flats developed by metasomatic replacement in sub- horizontal limestone beds. Both groups are spatially related. The flats are always associated with fissures along which the mineralizing fluids reached the limestones, although the fissures themselves may not carry mineralization in the vicinities of the flats. Obviously, the fissures are not mineralized along their whole extension, some of them carrying more than one oreshoot or more than one flat. (a) Veins The orefield has a conjugate pattern of vein fissures, with a main ENE trend of the productive veins, set that is traversed by seldom mineralized cross-veins trending N20°-35°W and by a minor set trending o o N45 -50 W . A second set of main veins (the so called "Quarter Point Veins") trend from E-W to N65°W. Individual fissures may be traced for long distances,as the Old Fall-Scarsyke-Boltsburn Vein that can be followed for 7.5 miles and the Slitt Vein which is 14 miles long. The productive veins typically show small displacement, a feature that tends to produce clear-cut fissures free of gouge; the main faults are seldom mineralized, probably because at the time of mineral- ization they were filled with gouge from dragged-in shales. Dipwise refraction of the fissures is common, the dip being diminished where soft rocks,such as shale, are crossed; hence it is in the hard rocks of the sequence, such as limestone, dolerite, and hard sandstone, where the main oreshoots are developed. The distribution of the workable oreshoots according to their position in the stratigraphic sequence is summarized in table 4.1, where it can be seen that there is a great concentration of deposits in the Upper Limestone Group; and within it the greatest concentration being in and near the Great Limestone, whose deposits ate the most important TABLE 4.1 Distribution of workable lead-zinc veins in the Northern Pennine orefield according to their stratigraphic position (modified after Dunham, 1948) Horizon No. of oreshoots Coal Measures 11 Millstone Grit Series 17 Upper Limestone Group 233 (except Great Limestone) Great Limestone Bed 245 Middle Limestone Group 219 Lower Limestone Group 26' ' Whin Sill System 18 TABLE 4.2 Distribution of flats in the Northern Pennine orefield according to their stratigraphic position (after Dunham, 1948) Horizon No. of flats Upper Limestone Group 9 (excluding Great Limestone) Great Limestone Bed 87 Middle Limestone Group 25 Lower Limestone Group 5 ; 8 of the field, with the exception of those lying in the Whin Sill and in the Grit Sills. Figure 4.1 displays the spatial distribution of the ore bodies worked in the field, showing the uneven distribution of the mineralized fractures in the region where zones of similar lithology to that of the main mineralized areas are almost devoided of known ore deposits. The most important trends of the mineralized structures (ENE, WNW, and NNE) may be noticed, as well as a pronounced concentration of ENE-WSW veins in the Grassington-Greenhow area. Also worth noting is the predominance of NNW veins on the southern and northern sides of Swaledale and Wensleydale, respectively. (b) Flats These ore deposits have been found in nine horizons of the succession (table 4.2), again the Great Limestone being the most important ore-bearing level. They are found in connection with veins that are associated with numerous diverging or sub-parallel minor fissures ("leaders"), or lie in the vicinities of vein-intersections, where highly mineralized irregular masses of ore are commonly present (Varvill, 1930; Dunham, 1957). Although the reasons for the formation of flats in preference to vein-oreshoots are not fully understood, there is evidence suggesting that they were formed where the formation of veins was inhibited for some reason. Dunham (1948) points out the case of the Boltsburn mines in this connection. There, veins were formed where the sandstone and underlying limestone are thick and flats developed in the limestone where a thick shale appeared between both rocks causing the thinning of the sandstone. Similar cases are known at the Rotherhope Fell Mine and in the Barneycraig-Rampgill system. It is worth noting that some flats occur in gentle anticlines, the most important case of this feature being that of St. Peter's deposit where the flats lie partially in a small dome. - At the Rotherhope mine the flats also occur in a flat-topped anticline. This feature is not Veins in the Northern Pennine Orefield ells ‘gstones .e , I- 56 Ourtr•eford Dseurbonce ••• ••-- ,,,,,-, N : - -7, - -- -' St Pet''■ V...\•-, Ix ...' ‘., INNER . • '1. LIMIT OF L 1 ;Ie.. - Jr' 1 :BARITE ZONE „.\:: ), ,,--- , .."--. • 4: • Isburn % ‘ 1/ ,eelling ... Al ....•■ : \ / G el l ''. / - „ \ \ 1 .=-•. . ‘ \ .. /".= . ■ . #71 -% .!-. r ? „ „ -___(--4- , o ...,yf , / . ., . i• . , / g I , ..\¢-' ,:".•/ Et ...." ...... "\LIMIT OF FLUO- RITE ZONE ) ' t .7...... ' . XIZ ' \. I I. '.• •re . 52 -4.--- 51 .... ir • 4 9 i , ; N. ,"\ 4. •.%,, ‘'',. \ \-. No .....c— i \ \ I N, 1‘ ‘ I — \ I - ‘ _ II ,tk 4 ■‘ - --, .,. ,,..k,. . 47 -/- e i ■.----- t------ I-N, ‘ A \ % / ...•'", \ Gro*ungtcn j (.._... -- I, j .• % , _, 37 38 _ 39_ \ 0 -'-"-'-'" FigAl common to all deposits, being absent in many of the most important'flat- bearing ore bodies, for example those at the Boltsburn mine. Finally, it must be considered that workable flats are not necess- arily adjacent to the veins to which they relate, but may be separated from them by several feet of sterile or little mineralized rock. Examples of this feature are found at Boltsburn mine where the flats are separated from the main vein by 25 ft. of ankeritised limestone, and at Rotherhope Fell mine, where silicified and ankeritized limestone separates the flats from the veins. 4.2.3 Ore and gangue mineralogy Galena is the main lead ore occurring as bands in the veins and as disseminations in the flats; silver is present 'in solid solution within it, in amounts ranging normally from 4 to 8 oz/ton concentrate, the average content being about 3.5 oz/ton (Raistrick, 1936a; Dunham, 1944, 1948). Exceptional veins in this respect are Stow Crag and Sir John's, which rendered on average 40 oz. Ag/ton." Sphalerite is the only primary zinc mineral present in the field, occurring usually as bands in veins, and flats. It contains important amounts of Fe (Dunham, 1948), ap well as Cd, Cu, Ga, and Ge, and minor amounts of Bi and Ag (El Shazly and others, 1957). Chalcopyrite and chalcocite are the main copper ores; they are present in almost all the veins in small quantities, and locally in amounts that permitted their economic exploitation rendering ores with 20-30% Cu (Raistrick, 1936b). Subordinate sulphides present are pyrrhotite, pyrite and marcasite, all important constituents of the Great Sulphur Vein. Covellite and bornite occur in minor amounts in the copper veins. Rare sulphides reported include ullmanite and niccolite. Minor amounts of gold have been reported at Greenhow mine (Dunham and Stubblefield, 1945). Secondary metallic minerals common in the area are cerussite and anglesite (both 60 mined at Middle Fell near Alston), hemimorphite, hydrozincite, malachite, azurite, native copper (Smith, 1973), goethite, erythrite, and greenockite. Pyromorphite and smithsonite are very abundant in some areas, such as Malham Moor where they have been economically recovered. The gangue accompanying the ore varies from place to place due to the lateral zoning in the field. Fluorite is the main gangue in the central part of the most important mineralized areas. Barite constitutes the predominant gangue in the periphery of the main districts, and silica (quartz or more rarely chalcedony) is abundant in the northern (Alston) part of the field. Dolomite, ankerite and chalybite are also abundant in the Alston Block. Calcite is not abundant but is always present in small amounts in the deposits. Witherite and barytocalcite, minerals rather uncommon, are frequent in the field, especially in the northern part where witherite constitutes the main gangue in several deposits (e.g. Settlingstones, Fallowfield, Cragside, etc.). Aragonite is present in some cases in small amounts, strontianite has been reported at Settlingstones and Greenlaws mines, and prehnite has been indicated as a gangue constituent at Kilnsey Moor. Finally, the presence in witherite veins of hydrocarbons (complex paraffins or olefines or a mixture of both) has been indicated.' The generation of supergenic gangue minerals is common in the field. Barite occurs as ill-formed crystals and incrustations associated with limonite. Gypsum has been recorded at Hilton mines as a product of alteration of pyrite and in several other deposits as efflorescence. Epsomite, melanterite, and goslarite have been locally reported. 4.2.4 Zoning and wall-rock alteration The ore deposits of the field present a wide variation in mineral composition, ranging from deposits formed mainly by fluorite to bodies where barite and witherite constitute the bulk of the mineralization, 81 ranging through those where metallic sulphides are the most important components. Transitions between these types are common. Detailed studies performed in this respect showed that a clear lateral zoning related to a number of centres exists in the field (Figure 4.1) and that the following sequence of mineral zones can be recognized from those centres outwards (Dunham, 1934, 1948, 1967): Zone 1: Quartz-fluorite-pyrrhotite-chalcopyrite (galena-marcasite) Zone 2: Galena-sphalerite-fluorite (quartz-siderite) Zone 3: Galena-sphalerite (quartz-siderite) Zone 4: Galena-sphalerite-barite-witherite Zone 5: Barite-witherite (aragonite-barytocalcite-minor sulphides) According to Dunhams's zoning, the centres are formed by deposits composed almost exclusively by fluorite and quartz, with only small amounts of sulphides, except where the presence of chalcopyrite is important. Galena becomes important in the outer part of the fluorite zone, where the biggest lead-producing deposits lie. Sphalerite is almost absent where fluorite is present, except in the outermost part of that zone where it starts to increase, reaching a maximum in the intermediate zone (zone 3) and promptly decreasing until it almost disappears in the inner part of the barite zone. As well, for a long time it has been noticed that sphalerite in economic quantities is restricted, in the Alston Block to the area west of the Burtreeford Disturbance. Once the barite zone is reached, galena also starts to diminish until it becomes very subordinate or disappears altogether. Finally, an outer copper-bearing zone is present in some areas (Dunham, 1934, 1959). In addition to the lateral zoning, a vertical one, corresponding to the former,has also been noticed in some'parts of the field. Thus, among the gangue minerals, fluorite gives way upwards to barite and down- wards to quartz, marcasite and pyrrhotite. Among the ore minerals, chalcopyrite is succeeded upwards by galena, and in many instances 62 sphalerite is far more common than galena in the lower levels of the lead- zinc deposits. Wall-rock alteration, though very common in the area, seldom extends beyond a few feet from the mineralized fissures, its effects obviously depending on the type of rock present. Along the veins, the limestones were transformed into an ankerite-rock with varying amounts of chalybite and chalcedonic silica. Also, preferential metasomatic replace- ment took place extensively along some horizons where the limestone was replaced by ore minerals and locally by sericite and chlorite. The quartz-dolerites that form the Whin Sill were always affected by hydrothermal alteration in the vicinities of the, veins, where they were transformed into a white, light rock composed of secondary carbonates, kaolinite, micaceous clay minerals, anatase orleucoxene, and residual quartz and apatite. Locally, substantial amounts of fluorite, pyrite and quartz were introduced in these rocks. A complete account of this alter- ation is given by Wager (1929); it is worth mentioning that the solutions introduced carbon dioxide, potash and water into these rocks, plus silica and iron in the central part of the main mineralized area; materials removed include iron, magnesia, soda, and in almost all cases, silica. The sandstones existing in the area have not been markedly altered. Their replacement by galena, fluorite, barite and quartz has been noticed in places, as well as intense silicification in the vicinities of the Great Sulphur Vein. Pyrite is commonly found replacing sandstones, though its origin cannot be related for sure to the mineralizing processes. The shales of the area display silicification as their most common alteration, the silica being mainly in the form of chalcedony. Locally, the addition of chlorite and sericite, besides silica, has been indicated, as well as the development of galena, ankerite, and sphalerite in some horizons. 83 4.2.5 Controls of the mineralization The emplacement of the mineralization in the field was controlled by structural, stratigraphical and metallogenetic factors. The main structural control in the area is the faulting developed during the Hercynian, which originated several systems of faults in which the mineral- ization was deposited. Of the existing sets, those trending ENE, WNW and, to a lesser extent, east-west, were the most favourable for the emplacement of mineralization probably because at that time they were affect- ed by tensional stresses. The important NNW-trending system is seldom mineralized, probably because during that period it was under compressive effects. Besides, oreshoots tend to terminate and commence where the favourable fracture systems cross the NNW one, and therefore within a single fracture several oreshoots may exist separated by barren rocks bounded by cross-faults. The stratigraphic control is manifested on the refraction effects produced in the ore-bearing fractures when passing from one lithological type to another. Where the wall-rock is hard, the dip increases and oreshoots are preferably formed , while where the wall-rocks are soft, the dip diminishes, collapse effects occur, and the fractures are closed or barren. In addition, the stratigraphy influences the shape of the deposits which in longitudinal section are ribbon-shaped due to the relative small thickness of the favourable beds (there are numerous cases of deposits 400 ft. long by 60 ft. high). It must also be taken into account, that the presence of lime- stones in the sequence has favoured the formation of valuable flats by metasomatic replacement along preferential horizons. No explanation is available regarding the tendency of the metasomatism to replace certain definite levels in the sequence, though the existence of closely-spaced fractures in the limestones is known to be a favourable feature, even 64 when it tends to produce wide vertical bodies rather than horizontal ore- shoots. The metallogenetic controls of the mineralization are still not well understood because the source of the mineralizing fluids is not clear. Apparently, the fluids rose along favourable structures that spatially coincide with the highest parts of the pre-Carboniferous basement (Dunham, 1967a; 1967b). When they reached the favourable highly fractured and gently domed limestones, they started to migrate mainly laterally, deposit- ing their metallic load under conditions strongly controlled by temperature. Thus, the central and lower parts of the main districts are almost barren, containing some minor copper mineralization; the intermediate parts present the important lead-zinc deposits; and the outer and upper parts of the districts are barren, except for the local presence of some copper ore. 4.2.6 Age and origin of the mineralization The available geological evidence regarding the age of the ore deposits is not conclusive, though they may be considered to represent a single metallogenetic event. Since the ore bodies cut.all the Carbon- iferous levels and the Whin Sill, they must be post-Carboniferous; hence, if they are related to igneous activities, their age must be Hercynian or Tertiary. Several arguments have been put forward by different writers in favour of one or other age. Among these arguments, the most important that would confirm an Hercynian age are: (1) The presence of detrital fluorite and barite in basal Permian beds; (2) The similarity between these deposits and those of Cornwall and others of undoubted Hercynian•age in Europe; (3) The lack of similar deposits in post-CarboniferouS rocks; (4) The association of some deposits to the Whin Sill but not to the similar, but Tertiary, Cleveland Dyke, which cuts through veins near Tynehead. On the other hand, the writers favouring a Tertiary age argue that: (1) Lead, zinc, and copper minerals occur as dissemination in the 65 Magnesian Limestone Series; (2) Fluorite forms strikes and nucleii inooliths of the same series; (3) The ore minerals are fresh and unbroken when occurring in cavities, suggesting very little or no post-mineralization tectonic effects; (4) A member of the Cleveland Dyke system shows sericitization near the Lodgsike Vein (Coldberry Gutter); (5) No fluorite has been found in the Permian of county Durham; and (6) There is no relation between the mineralization and the major Hercynian folds (Bew- castle and Middleton Tyas Anticlines), as could be expected if the ore deposits were Hercynian. A careful consideration of the different arguments (Dunham, 1934, 1953, 1959) seems to favour an Hercynian age, which appears to be supported by model lead-ages determined by Moorbath (1959, 1962) table 4.3, deter- minations that rendered a Permian average age (284/40 my). In this respect it must be considered that these ages only indicate the approximate date of separation of the lead from an homogeneous source, and hence they need not indicate the time of deposition in its present location. Bowie (in Dunham and others, 1965) considering this fact and the similarity with other orefields, suggested the possibility that all the apparent contrasting geological evidence may be correct and that the deposits were forthed during a long span extending from the Carboniferous to the Tertiary. This hypothesis has been lately supported by Dunham and co-workers (1968), on 40 39 the basis of Ar /Ar age determinations on the White Whin, which indicate recurrent mineralization starting 234 ± 40 my ago and subsequent maxima occurring at intervals (two of these have been recognised at 230"my and 170 my). These ore deposits are of undoubted epigenetic origin, a feature that was already distinguished by Wallace (1861) and which has been accepted by all the authors that have dealt with them. Unfortunately, the origin of the mineralizing fluids is not yet clear. Some writers advocate a TABLE 4. Model-ages for galenas of the Northern Pennine orefield (after Moorbath, 1962) Deposit Model-age Barbary 280/80 My Sedling 310/50 Rotherhope Fell 260/60 Settlingstones 270/60 TABLE 4.4 Distribution of workable base metal deposits in the Lake District orefield according to their stratigraphic position Horizon No. of veins Carrock Complex 5 Borrowdale Volcanics 32 Skiddaw Slates 35 66 supergenic origin, others consider these fluids as purely hydrothermal solutions, and others consider that they were mostly connate waters. Studies of fluid inclusions in minerals of the fields (Sawkins,. 1966), the very clear lateral zoning present, and other geological features suggest that the depositS were formed by hot fluids at about 1.5 km depth and temperatures ranging from 100° to 200°C in the fluorite zone, falling to less than 50°C in the barite zone. Moreover, the metasomatism produced by the fluids in the Whin Sill would suggest that they must have been rich in potassium and capable of transporting silica and metal components; this hypotheis was confirmed by the studies of Sawkins (a. cit.) who demonstrated that the fluids were brines bearing a K / Na ratio inconsistent with their being considered as pure sea water or connate waters. All these facts suggest that the ore deposits were formed by brines, at least partly juvenile, carrying important amounts of potassium, metals, fluorine and probably barium. These brines mixed with connate waters existing in the sediments probably around the margins of the fluorite zone. The _relation of the main mineralized districts to elevated parts of the basement which were possibly connected to crustal or sub- crustal magmatic'activities (Dunham, 1967a; 1967b), may indicate that-the juvenile components originated from the magmatism whose main superficial expression in the region is the Whin Sill. Besides, the very well defined lateral zoning present suggests that the fluids rose at a few well defined centres and that on reaching favourable horizons their movement became mainly lateral, though some upwards migration still occurred. In this connection is it probably that, at least in the Alston Block, those centres of ascent were in some way related to the presence in the basement of Lower Paleozoic intrusive bodies, whose cupolas acted as structural channels permitting the migration of the fluids through the fairly 6 7 impervious rocks that constitute the basement of the region (Dunham and others, 1965). 4.2.7 Mining History The ore deposits of the Northern Pennines have been worked since Roman times. Although the presence of very rich untouched veins in the vicinities of some Roman' camps suggest that the Alston ore bodies were not mined during that period (Wallace, 1890), there is evidence that lead was mined by the Romans in several mines in Yorkshire, such as Greenhow and Hurst (Varvill, 1920; Raistrick, 1955). Of the lapse between the annotated works and the 12th century nothing is known. The first recorded production in the Alston area goes back to 1130 (Wallace, 1890) and in the Yorkshire area to 1225 (Mac Quoid, 1883). The mining epoch spanning from that time to the 18th century has been described in detail by Raistrick (1936a, 1936b, 1938b, 1947, 1955), Raistrick and Jennings (1965), Wallace (1891, 1890), Smith (1923) and others. Very little is known of the period between the early medieval activities and the early 1600's. Mining activities on a big scale started in the late 17th century, mainly because of the formation of the two big concerns that dominated the lead mining in Northern England during the two following centuries: The London Lead Co. and the Blackett-Beaumont Co. The industry reached its peak in the 1790-1880 span, when both concerns produced more than 20,000 tons of lead concentrate per year. During those years, stable economic conditions prevailed in the region, mainly as a result of a few large operations and numerous small workings which were partly subsidized by the earnings of the large mines. As indication of the importance of the activities during that time, it is noted that 28 lead.smelt-mills operated simultaneously in the Alston area only. The Yorkshire operations started to decline in the second half &Q of the last century due to a rapid fall in the price of lead. This situation affected the Alston works a little later, and in the early 1880's both concerns surrendered their main leases. From then on mining was reduced to deposits lying in the Alston Block of the field. In 1884 the Weardale Lead Co. was formed taking over the leases in Weardale where it operated until 1931, mainly because of the great success achieved at the Boltsburn mine. The Alston Moor leases were taken initially by the Nenthead and Tynehead Zinc Co., and later by the Vieille Montagne Zinc Co. which operated old lead workings and developed the small but rich deposit at Nentsberry. Later, this company worked for zinc some deposits in West Allendale, its operations lasting until 1947 due to productive flats discovered at the Rotherhope Fell mine. In Teesdale, the London Lead Co. wound up its operations in 1905. Shortly before the Second World War, a consortium of London-based companies (English Lead Mines Ltd),developed the small lead deposit at Coldberry, but they did not exploit it. During that war, the Ministry of Supply developed the small zinc orebody which is still in site at Ettersgill and recovered zinc and some lead by treating tailing dumps at Nenthead (Dawson, 1947). Finally, during the late 1940's and the 1950's, the Coldberry Mines Ltd worked the Coldberry orebody at Teesdale and the Weardale Lead Co. raised some galena at the Barbary mine, bringing to an end the base metal mining in Northern England. 4.3 LAKE DISTRICT OREFIELD 4.3.1 Introduction The Lake District orefield comprises about 250 square miles in north-west England, in the counties of Cumberland, Westmorland and Lancashire. Although 46 base metal deposits are known in the area, most of them are of very small size, and hence only a few deposits record G9 production of some kind. The situation is so marked that about 90% of the total lead output of the field has come from only one mine (Greenside). For descriptive purposes the field may be subdivided into three main districts (figure 4.3): Caldbeck Fells District, an area covering approximately 10 square miles north of a line drawn from Cockermouth to Penrith (north of latitude 54040'N); Keswick District, lying in a radius of eight miles from the town of Keswick; and Coniston District, in the southern part of the area north of the Coniston Water. The first two districts have produced lead, zinc and copper ores, whilst the last one has only yielded copper production. 4.3.2 Mineral Deposits The base metal deposits of the area are lead-zinc and lead- copper fissure-filling veins. The bodies were traditionally classified as "lead" or "copper" veins, depending on the dominant constituent; only in comparatively recent times was it realized that many of the so called "lead" veins have sphalerite as their main ore .mineral. The lead-zinc, veins trend between north-west and north-east, dipping towards the east; on the contrary, the copper veins trend mostly east-west and dip northwards, being in many cases shifted by north-south trending lead veins. The veins are steeply dipping or vertical, presenting lodes controlled by variations in the strike and dip. They tend to be square in longitudinal section or even to have greater vertical extent than length. The largest known structure in the field is that at Greenside which has a strike length of 1700 ft. and a down-dip extension of 1350 ft. It is noteworthy that the veins have not been displaced by post-mineral faults. In the Coniston District, the veins are restricted to levels of the Borrowdale Volcanics. The deposits in the Keswick District are emplaced in two types of rock; the bodies lying west and north-east of BASE METAL DEPOSITS IN THE LAKE DISTRICT OREFIELD 3200 3300 3400 3500 I _._: 1. moll Retoghton6111 .1 CALREZELIS, / \ 5300 c-z- 1,\ Thre:1",[ , 5:1 1, iten Derwent - , st. ycro , -"° Water '--, .„. josce.C”iw \ 5200 \ ' I..'" ■ tel 2 \ •'' 71 • DISTR1 — ` r Gold yewr :4, Greenstde — ------.- 1/ 1\ N'e&,/: \- , Ivellyn /ESgie /` ) ----- '1;4.99 I 0 , .,- 'N -7- \ , _ o 5100 -% 1` r \ 0 ,-- \...., CS '' )j l' J--"--- ,, V7--- 1_ NW ,--1,_\____ -"r-- \,., `SNP ) 4900 0 5 10 20 30Km FIG.4.2 7 0 the Derwent Water (Goldscope, Stoneycroft, Threlkeld and others), fill fractures that cut across sedimentary rocks of the Skiddaw Slates Series and have rendered mainly lead and zinc ores with subordinate amounts of copper. The deposits lying in the Helvellyn area between the Thilmere and Ullswater lakes (Greenside, Helvellyn, Eagle Cragg), lie in levels of the Borrowdale Volcanics Series pierced by minor acidic intrusions; these orebodies have rendered mainly lead ores. The Caldbeck Fells District presents the greatest variety of country-rocks of them all: Copper, lead and Zinc ores have been mined in that area from veins emplaced in the Skiddaw Slates, Borrowdale Volcanics, and Carrock gabbro-granophyre complex. Table 4.4 shows the distribution of the,deposits of the field according to the stratigraphic level where they lie. Two aspects of the ore field are worth mentioning. Firstly, no base metal deposits have been found in the large acidic intrusions existing in the area, and secondly, at the Drygill mine ore was raised from levels assigned to the Coniston Limestone Series, constituting the only known case in Northern England of productive veins emplaced in rocks older than the Carboniferous Limestone Series and younger than the Borrowdale Volcanic Series. 4.3.3 Ore and Gangue Mineralogy In the lead-zinc deposits of the field the main ore is galena, mineral that is markedly argentiferous (the average content is about 16 oz Ag/ton lead concentrate). This silver content appears to have some relation with the amount of barite present in the deposits, since veins with little barite, as Threlkeld and Thornthwaite, bear not more than 10 oz Ag/ton, whilst barite-bearing veins as Force Cragg and Driggith have seldom less than 30 oz/ton (Eastwood, 1921). Sphalerite is the only zinc ore in the field, usually bearing up to 1% Cu and 0.3% Cd (El Shazly and others, 1957). Chalcopyrite is the only copper ore present, rendering products with 5-15% Cu once dressed (Dewey and Eastwood, 1925). Minor amounts of gold have been reported from the deposits worked at Brandlehow and Goldscope (Postlethwaite, 1913). Supergenic minerals common in the field include cerussite, pyromorphite, mimetite, kampilite, and alteration products of chalcopyrite. Anglesite is seldom found and in places the presence of smithsonite, aurichalcite and hydrozincite has been reported. Accessory minerals in the deposits are pyrite, limonite, psilomelane, chalybite, marcasite, tetrhadrite, antimonite, bournonite, stolzite, leadhillite, caledonite, linarite and johnstonite. In some deposits, magnetite, cobalt-nickel sulphides, olivenite, brewsterite, arsenopyrite, chessylite, and melaconite are found. The main gangue in the lead-zinc deposits is quartz. Barite and witherite are in places important (e.g. Greenside, Blencathra, Force Cragg; Wilson and others, 1922). Calcite is rather uncommon, being present at Greenside and Roughtengill mines. Dolomite is a common, though accessory, mineral, and ankerite, chlorite, and fluorite have been reported. The copper deposits that do not bear lead have quartz as their chief gangue accompanied in many cases by calcite and dolomite. Those deposits that in addition to copper bear some lead, present - besides quartz - important amounts of barite. In all these deposits, rock debris is normally abundant in the veins, as well as fault breccia and gouge. 4.3.4 Zoning and Wall-Rock Alteration Zoning of minerals is not clear in the Lake District orefield contrasting with the Northern Pennines. No lateral zoning has been found but a rough vertical change in the type of ore present in the veins may be noticed. Galena, sphalerite and chalcopyrite are in most cases abundant in the lower levels of the veins, giving way upwards to the association barite-dolomite and this, in turn, to the pyrite-psilomelane association 73 that commonly predominates in the upper levels of the deposits. The ratio galena:sphalerite and the amount of silver present in the galenas do not change systematically. The information available in this respect is conflictive since Eastwood (1921) reports an increase, with depth of galena with respect to sphalerite at Force Cragg mine, and a slight increase with depth of the silver content of the galenas at Thorn- thwaite mine. On the other hand, Gough (1962) indicates that at Greenside mine the silver values decrease with depth and that sphalerite is relative- ly abundant in the lower levels of that mine. Further studies in this respect are wanting. Very little information is available regarding the wall-rock alteration present in the field and apparently this is not a widespread phenomenon. At dreenside the alteration includes silicification, sericitization, carbonitization, and weak chloritization. The final effect is the bleaching of the volcanic wall-rock. Silica, potash, carbon dioxide, water, lead and zinc were introducted, and iron, lime and magnesia were redistributed; soda and titania were removed. This alteration is somewhat similar to the one affecting the quartz-dolerites of the Whin Sill in the central part of the main mineralized area of the Northern Pennine orefield. Ewart (1962) indicates that a strong hydrothermal alteration may be noticed in the complex tungsten-lead-copper veins of the Carrock Fells - District. The final product of the alteration was greissen with abundant pyrite and arsenopyrite. No information regarding other deposits is available. 4.3.5 Controls of the Mineralization In general, very little is known about the factors that controlled the emplacement of the ore deposits with the exception of Greenside. Refraction of the fissures in which the ore deposits lie is one of the 3 factors known to affect the generation of lodes. Rich lodes are formed o where the veins dip 70 or more, while where the dip decreases to less o than 50 the fissures are practically barren. Changes in the strike of the fissures also control the formation of enriched lodes. In this respect, the type of movement that took place in the fault was important: favourable openings were formed where the fractures differ mostly from their strike-slip direction and therefore the net slip in each fissure has been a critical factor controlling the formation of lodes. The nature of the wall-rock, obviously, had a degree of control over the emplacement of orebodies. Soft rocks (shale, slate) are generally unfavourable in this respect, partly because of their low primary permeabil- ity, but mainly because the dip of the fissures tend to decrease in these rocks and collapse effects occur if favourable openings were to be formed. Hence, moderately brittle rocks appear to be the best ore-bearers of the orefield. The chemical nature of the wall-rock appears to have little effect in controlling the importance of the orebodies developed, with the exception of the Carrock igneous complex where sub-basic and basic rock- types seem to favour the enrichment of the veins that traverse them, a feature noticed at the Threlkeld, Brandlehow, and Roughtengill mines. With regard to the more acidic intrusive rocks, such as the quartz-porphyry dyke existing at the Greenside mine, the evidence is not conclusive because in places an enrichment is noticeable, but in other parts - where the dyke forms both walls of the vein - the fissure is barren. The latter situation must be considered with extreme care because it may be possible that the impoverishment or enrichment of the deposit could be related to changes in strike and/or dip occurring where the fissure meets the dyke, hence being independent of the chemical nature of the dyke itself. In common with other regions, enrichment often happens in the 74 deposits at the intersection of veins, especially if their ores are of different type (e.g. great enrichment at Goldscope mine in the intersection of "lead" with "copper" veins). No explanation has been offered for this phenomenon but it may tentatively be assumed that it probably reflects different ages of mineralization and removalization during a later stage. A final factor controlling the formation and richness of the lodes in the field is the presence of pre-mineralization cross-faults. In most cases, the deposits die when reaching cross-faults or their width tends to be greatly diminished. Although no satisfactory explanation has been put forward for this effect, it may probably be related to changes in strike, dip and amount of down-throw in the mineralized fractures at either side of the fault. 4.3.6 Origin and Age of the Mineralization The origin of the deposits is undoubtedly hydrothermal. The mineralogy and vein-structure of the copper veins (chalcopyrite-pyrite- quartz veins) suggest that they were formed at a somewhat higher temperature than the lead-zinc deposits and that they may be regarded as mesothermal. In those bodies, dolomite and pyrite started the sequence of deposition followed by the main sulphide mineralization and finally by barite. Quartz must have been deposited during the entire mineralizing process. The mineralogy of the lead-zinc deposits (galena-sphalerite- chalcopyrite-quartz-barite veins) and their common crustified, vuggy structure suggest that they may be regarded as epithermal (leptothermal according to Gough, 1962). In this case the paragenesis started with carbonates (dolomite and ankerite) followed by pyrite, sulphides and barite (Where present). A late period of pyrite deposition is common, frequently accompanied by the deposition of psilomelane. Quartz appears at any stage of the paragenesis And its deposition normally occurred before, during and-after the main mineralization stage. 75 There is no agreement between the different writers regarding the age of the deposits. Eastwood (1921), on the basis of geological evidence, suggests that at least two and perhaps three periods of mineral- ization took place. The same author (1958) suggests a general Caledonian age for the main mineralization period and a later recrudescence, perhaps as late as Tertiary. Moorbath (1962) determined model lead-ages for the galenas of several deposits in the orefield, obtaining values ranging from 370/60 my to 170/80 my (table 4.5). All except the galenas from Buttermere, which appear to be pre-Caledonian, the model-ages give a mean of 280 my. The galenas connected to the Shap Granite give an age that closely follows the weighted average ages for the intrusive body itself; Kulp and co- workers (1960)obtained a K-Ar age of 391/7 my and a Rb-Sr age of 381/7 my and thus these veins appear to be Caledonian. Because the values cluster around 210 and 320 my, Moorbath (op. cit.) suggested that two periods of mineralization occurred in the field; one in the Lower or Middle Carboniferous and the other possibly in the Upper Triassic. Gough (op.cit.) contested that hypothesis, postulating that all the bodies had a common and simultaneous Hercynian origin, with the exception of those deposits associated with the Shap Granite. Contam- ination and regeneration of galenas would in this case account for the younger ages obtained for some deposits. The copper deposits of the field are considered by Gough as Caledonian, because they are in some places displaced by lead-bearing veins and because some pre-mineralization faults at the Greenside mine have copper ores filling them. Dunham (1952) suggested that the intersection of copper veins by lead veins could possibly represent successive stages of a single Hercynian mineralization epoch, as in the case of South-West England where the lead-zinc, veins cut across tin veins. The absence of TABLE 4.5 Model-ages for galenas of the Lake District orefield (after Moorbath, 1962) De2osit Model-age Greenside 330/90 My Eagle Cragg 170/80 Hartsop Hall 210/70 Myers Head 31000 Carrock Fell (lead vein) 340/70 Wooded Vein (Threlkeld) 210/70 Roughtengill 220/40 Driggith 280/90 Barrow 300/80 Buttermere 470/50 Goldscope (lead vein) 310/80 Shap Blue Rock (Quarry 1) 370/60 id (Quarry 2) 360/80 Henshingham (borehole) 320/70 76 transitional characteristics in both types of deposit, a feature commonly present in South-West England, and the absence of similar copper veins in the Pennines, appear to contradict the idea of Dunham and support a Caledonian age for these copper ores. Nevertheless, it should be mentioned here that the copper veins appear to be unrelated to the Caledonian intrusions of the Lake District which are persistently barren. If the veins were Caledonian, this apparent disconnection with the intrusive bodies of a similar age could probably be explained by the fact that the granitoids and their capping rocks have been deeply eroded and therefore the mesothermal veins that may have existed in the upper parts of the intrusives and in the metamorphic aureole were possibly swept away by denudation in post-Caledonian times, as has happened with most of the post-Silurian rocks in the area. 4.3.7 Mining History There is good reason to believe that mining has been carried on actively for about two thousand years in the Lake District, much of the history of the region being related to its mines. Although no written records are available, many of the oldest mines give evidence of works performed in very ancient time, some of which was undoubtedly done by the Romans. It is also conceivable that part of those ancient works might have been done before by native Britons. In 1561 the Company of Mines Royal was established with the purpose of working Goldscope and Dale Head mines, a concern which in 1564 was in full operation (Collingwood, 1912). Later, other mines started to be worked (Grassmere, Newlands, Buttermere, etc.) and smelting works were established at Keswick in 1565. These works, which at the time were the largest in Britain and probably in Europe, continued in active operation until 1651. At the end of the 17th century, the smelters were rebuilt and 77 since then intermittent working took place until the late 1700's. In that period, lead mining began on a very small scale in the district, but the combined output was kept low until the early part of the 19th century when the Coniston copper mines were developed on a large scale and lead operations started to expand all over the field. The situation was maintained until the 1870's when most of the copper mines were forced to close, changing the regions into a lead- producing field mainly due to works carried out at the Greenside mine which worked almost continously until 1920. At the same time, other minor workings operated intermittently in other parts of the field, especially in those cases where lead veins were found to carry important concentrations of silver. The post-1920 mining history of the area is very brief. Several trials were made on small deposits but the production arose almost exclusively from the Greenside operation which worked from 1923 to 1927 and from 1936 until 1961 when the last ton of ore raised in the district was mined. 7 8 CHAPTER 5 COMPILATION AND HANDLING OF THE DATA 5.1 GENERAL CONSIDERATIONS As indicated previously, the present research was based on the statistical analysis of 106 samples or observations of north-central and north-west England, each of which represents an area of 100 square kilometres bounded by a 10 kilometre square grid coinciding with the main coordinates of the National Grid Reference System. The location of the samples or cells, as they will be referred to henceforth, is indicated in Figure 5.1. It may be seen in that figure that of the 121 cells enclosed between coordinates 300,000E; 410,000E; 460,000N; and 570,000N, only 106 were used in the statistical analysis, the remaining 15 cells corresponding to areas mainly covered by the Irish Sea. It is worth noting too that 10 of the cells included in the research (cells 1, 9, 29, 62, 73, 84, 85, 86, 87 and 94) contain a variable proportion of sea in them, but their use was considered justified because their known geological features are simple enough as to allow their extrapolation to those parts of the cells submerged. Therefore, care must be taken when analyzing the results of the forecasting models that include geological terms in them, when applied to those areas. In the following paragraphs, a brief description of the sources of the data employed is given, as well as an indication of the manipulations performed on them prior to the forecasting analysis. For the sake of brevity, whenever it is possible, the reader is referred to other works that deal exhaustively with some of the topics considered in the present chapter, especially when those topics are not of paramount importance to the results of the research. LOCATION OF CELLS 5700 N 7 8. PIIIIP e 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 9 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 2 4 9 0 51 52 53 54 55 56 57 58 59 60' 61 i E0 E 62 63 64 65 66 67 68 69 70 71 72 7 '' 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 ) 94 95 96 97 98 99 100 101 102 103 104 105 106 4600 N 0 10 20 30 40 50meles FIG. 5.1 79 5.2 COMPILATION OF THE DATA As indicated, when the scope of the present work was stated, three different models for the forecast of base metal mineralization in Northern England were designed and tested: Geochemical, Geological, and Combined geochemical-geological models. While building up each of them, the relationship between base metal production values and selected geochemical and conventional geological parameters measured in each of the 106 cells used as population, was examined. Therefore,.three different types of data needed to be compiled and handled for this purpose. As is obvious, their sources varied in each case regarding their precision and accuracy. Thus, in order to diminish the risks of inaccuracy, especially important in the case of the production figures, the selection of the data was done from official figures whenever possible. A description of these sources, the methods employed to obtain the data, and the values attained by the different variables in each cell, follows. 5.2.1 Geological Data While building up the geological and combined forecasting models, two types of conventional geological parameters were used: (1) Stratigraphic parameters, and (2) Indexes related to faulting. The selection of these parameters as variables was based on the prior knowledge about the factors that controlled the emplacement of the known ore bodies in the area. Eighteen parameters or indexes representing the main units that compose the stratigraphic sequence of Northern England were chosen, as well as four indexes connected to faulting. These indexes were measured for each cell on the one inch to the mile geological maps prepared by the Geological Survey of England and Wales, as percentages of total area covered by the outcrops or suboutcrops of each stratigraphic unit, or as absolute values or length in miles, in the case'of the faulting indexes. 80 The l"/lm geological maps used for this purpose were the following: Old Series sheets Haltwhistle (96NE), Newcastle (105SW), Penrith (102NW), Durham Coalfield (1O3NW), Keswick (1O1SE), Appleby (1O2SW), Brough and Stainmore (1O2SE), Ambleside (98NW), Kendal (98NE), Kirkby Stephen (97NW), Bootle (99SE), Ulverston (98NW), Grange (98SE), Whernside (97SW), Bedale Masham (97SE), Furness Abbey (91NW), Lancaster (91NE), Settle (92NW), and Pateley Bridge (92NE), and New Series sheets Bewcastle (12), Longtown (11), Morpeth (14), Silloth (16), Carlisle (17), Brampton (18), Hexham (19), Maryport (22), Cockermouth (23), Alston (25), Whitehaven (28), Barnard Castle (32), Gosforth (37), and Richmond (41). The values attained by the different variables in each cell are given in Appendix I. The average value of the geological parameters in the 106 cells considered in the statistical analysis are given in Table 5.1, together with their variances and standard deviations. As can be seen from the listing of the selected stratigraphic parameters, they do not always coincide with stratigraphic formations or members, but have been chosen to correspond to homogeneous lithological assemblages that represent conditions of deposition and environments, as well as age and origin. Regarding the stratigraphic indexes, it is worth noting that due to the fact that in the Old and New series of geological maps the grouping of horizons. into stratigraphic units do not correspond.exactly, it was necessary to adopt several conventions while measuring them. These conventions were the following: (1) The Stanwix Shales were considered as Keuper beds; the Kirklinton' and St. Bees sandstones as Bunter beds, and the Penrith sandstone, St. Bees Shales, and Brockram as Permian horizons. (2) The base of the Millstone Grit Series in the eastern region was considered to be the first coal layer appearing in the sequence above the Upper Felitop Limestone, or a thick sandstone bed lying above the so-called Grindstone Sill. In the western region, the base of the Henshingham Group TABLE 5.1 BASIC STATISTICS OF GEOLOGICAL PARAMETERS (N = 106) MEAN VARIANCE STD DEV LIAS 0.385 9.027 3.004 KEUPER 3.310 213.215 14.602 BUNTER 7.370 360.069 18.975 PERmIN 3.925 167.323 12.935 COALMS 4.238 160.838 12.682 MILSTN 10.714 342.294 18.501 LOWLST 5.927 193.861 13.923 MIOLST 18.975 530.306 23.028 UPPLST 17.380 575.203 23.983 BASEBD 1.126 25.363 5.036 SILURN 9.665 621.495 24.930 ASHGIL 0.229 0.425 0.652 BORROW 8.389 468.471 21.644 SKIDAW 5.598 299.592 17.309 INTRUS 2.158 69.263 8.322 COCKER 0.038 0.136 0.369 FAULTS 33.642 638.594 25.270 INTERS 22.377 519.266 22.787 LENGTH 32.730 440.375 20.985 FLTCNT 27.434 806.762 5.690 TUEDIN 1.046 32.382 5.690 PRECAM 0.042 0.102 0.319 MONTH LEAD ZINC COPPER SILVER January 109.37 118.55 420.95 67.9635 February 110.90 113.38 434.85 66.0950 March 111.46 118.24 476.78 68.7696 April 111.66 118.15 521.50 74.4400 May 110.21 120.00 464.38 71.9075 June 110.56 128.61 447.52 66.2455 July 109.13 132.35 464.75 65.2136 August 106.18 132.55 451.24 65.4667 September 96.83 125.60 427.80 59.8114 October 92.10 135.12 417.98 55.1310 November 88.93 138.14 406.70 52.6682 December 91.48 142.11 410.93 55.0091 Average 104.07 126.90 445.95 64.0602 TABLE 5.2 MONTHLY AVERAGE SETTLEMENT PRICES OF SELECTED METALS DURING 1971 AT THE LONDON METAL EXCHANGE (VALUES IN STERLING POUNDS PER LONG TON OR TROY OZ.) 81 was taken as the base of the series. (3) Following relatively recent mapping performed in the Alston area of the Pennines (Geological Survey of England and Wales, Sheet 25,1965), the horizons comprised between the bases of the Millstone Grit Series and the Great or Main Limestone, were considered to represent the Upper Limestone Group. As Middle Limestone Group were taken all those levels lying between the bases of the Smiddy and Great limestones. The Lower Limestone Group was considered to be formed by those beds lying above the Basal Conglomerates and below the Smiddy Limestone. (4) The intrusive rocks assigned to the basic category are those of the Carrock Fell complex, Whin Sill, and minor bodies of basaltic, dolerite, dioritic and lamprophyric composition. Those intrusive rocks assigned to the acidic group correspond to the main acidic intrusive bodies of the Lake District, and to minor bodies (mainly dykes) of felsitic, keratophyric, and granophyric composition. (5) The remaining stratigraphic units were measured as they appear in the different geological maps used and no sujective criterion of grouping was required in those cases. With regard to the structural parameters used in the statistical analysis, it must be considered that of the several structural features that may be obtained from a conventional geologidal map,those related to faulting are the most important in controlling the emplacement of the mineralization in the present case. Other parameters that could have been used were not taken into account, either because of the lack of detailed information in the ifi/lm maps (as is the case of folding) or to their lack of ,importance as metallogenetic factors (as is the case of unconformities). The only unorthodox parameter considered in this case was the number of fault-contact intersections present in a cell, an index that was measured with the purpose of getting a more clear picture of the distribution of 82 flats, deposits whose presence in certain preferential horizons is not completely clear. As in the case of the stratigraphic indexes, some conventions needed to be established for the quantification of the structural parameters. The two conventions followed were: (1) The number and length of faults considered for each cell, relates to all the faults shown in the 1"/lm geological maps, disregarding their size, amount of displacement, barren or mineralized nature, etc. (2) The number of intersections between faults and between faults and contacts, was increased by two whenever two of these features cross each other and by one whenever one of them is cut by the other. Finally, it is worth mentioning with respect to the geological' data that the only manipulation performed on them prior to the statistical analysis was the times 10 multiplication of the stratigraphic parameters and of the length of faults. This procedure, rather than standardization, was chosen in order to increase the contrasting variances of the different indexes. 5.2.2 Production Data 5.2.2.1 General Considerations As indicated earlier on, the design of forecasting models for the estimation of mineral potential is based on the analysis of the relationship that might exist between the economic features of the mineral deposits of an area and its geological characteristics, the latter being represented by selected parameters of various kind, and the former by economic indexes chosen in accordance with the problem under consideration. Therefore, it is obvious that as important as obtaining the best possible geological information, so it is to obtain similarly accurate and significative' economic data. Several economic indexes have been used for the purpose of 83 building up forecasting models. The most common are: average production per unit area as determined from the statistical distribution of the production figures; actual production figures in terms of tons of ore, concentrate or metal; tons of reserves, weighting in a certain pre- -accorded way the different categories into which the reserves may be sub- divided; and present expected value of production. Analyzing the different possible economic parameters that may be used, it was considered that the most suitable index for the purposes pursued was the present value of production. This value was obtained for each cell by adding the base metal production figures and reserves (if any) of all the mines lying within it, and weighting that figure by the average settlement price attained by each metal during 1971 in the London Metal Exchange (LME). The LME monthly average prices for lead, zinc, silver and copper,metalsproduced in the area,are given in Table 5.2. The selection of current price values as weights was done because the mining companies evaluate mineral deposits in terms of present day economics, a gross value term being most meaningful as an indication of mineral wealth when expressed in current figures, since it allows the precise understanding of its importance on the face of present costs and prices. Besides, this type of weighting was used because the production for the different mining districts was raised over a long period and hence if the prices that prevailed during each year of production were used, a volume of output for one district may have a quite different meaning than a similar volume mined at another district during a different time. An objection that can be raised to the use of current prices is that these weights disregard the effect that price changes have had on the quantity of each metal produced. As is obvious, if present day economics would have prevailed during the whole inception of the output, a different pattern oiproduction would have been obtained. However, it is difficult M. 84 to assess the effect that this would have had on the amount of metal that was eventually produced at each site. On one hand, present-day technology would very likely have caused the mining of ores that were uneconomic in the past and a more efficient recovery of metals at smelters and of the marketable ore lying in situ. On the other hand, the high present cost of labour would have rendered uneconomic the exploitation of small high- grade ore bodies with no fringe additional low-grade ores, for the mining of these deposits still needs to be done by hand methods. The consideration of all the aspects of this problem is certainly beyond the scope of the present research, as is the detailed analysis that this problem would require in consistency with the accuracy of the other data used. Considering all these aspects, it is believed that the method employed is justified. The output figures for the different base metal deposits existing in the studied area were mainly obtained from the Mineral Statistics of the U.K., published as memoirs of the Geological Survey of England and Wales for the period 1848-1881,and by the Home Office for the span 1882-1919. The figures for the period 1920-1938 were obtained from -Mine and Quarries: General Reports with Statistics, Mines Department, and those for 1845-1848 from the compilation of data done by Hunt (1848a, 1848b). All these publications contain the official output figures from 1845 onwards. Other output data not available in the mentioned reports were obtained from the following sources: Allenheads MSS, 1723-1826, a manu- script that includes the mines worked by the Blackett-Beaumont Co.. Bell MSS No. 1362 942-32664, a manuscript dealing with the mines owned by the Greenwich Hospital; Dodd and Stagg (1820), a manuscript referring to mines worked by the London Lead Co. during 1806-1820. Data for some mines in the Alston Moor area were obtained from Forster (1821), Locker (1823), Wallace (1890) and Nall (1902). Some S 5 mines in the Lake District are referred to by Postlethwaite (1913), Collingwood (1912), Trotter (1951), Eastwood (1958), Gough (1962), and Clutterbuck (1967), the latter referring only to copper ore production. Some output figures for the mines in the Alston Block of the Northern Pennines were obtained from Dunham (1944, 1948, 1952); Dunham and Dines (1945); De Rance (1873); Hunt (1884); and Louis (1917, 1930). The mines in Swaledale are considered by Metcalfe (1952) and Raistrick (1955a), and those at Malham Moor by Raistrick (1947). The output from the treatment of dumps at Nenthead was obtained from Dawson (1947) and finally some figures of production for the present century were obtained from Varvill (1954). In order to attain the best possible explanation of the relation- ship existing between the geological and geochemical indexes and the production of the different deposits worked in the area, three types of economic indexes were considered for each cell: total production; average value of the production per deposit; and number of deposits worked. At this point, it is worth noting that henceforth the term deposit will refer to one or more ore bodies amenable to exploitation from a single mine. The three production indexes were quantified for all the cells that have recorded output, according to the following conventions: (1) Every mine with recorded production was included in the analysis, regardless of the size of that output. (2) The production for each cell was calculated in terms of present value of the output plus reserves (if any) of the deposits contained in it, a figure that was expressed in thousands of sterling pounds. Those cells with very small value of output, were assigned a total value of £1,000 in order to differentiate them from those cells with no recorded output or with no known deposits. 86 (3) Whenever a mine or mines worked a deposit extending through more than one cell - as it is the case of Brandlehow, Sunnyside, Harehdpe Gill, and other deposits - the available output figures were allocated on the basis of an equal share to each cell containing the deposit in question. (4) The transformation into present value of the production figures quoted as tons of concentrate or ore was done on the following basis: the lead concentrates produced in the area were considered to contain 70% lead on average. The zinc concentrates of the Northern Pennine orefields were assigned an average 40% zinc, and those of the Lake District orefield an average of 48% zinc. Whenever silver output figures were not quoted, their value was calculated considering that their content in the lead concentrates of the Alston Block of the Pennines was on average 3.5 oz/ton; in the case of deposits lying in the Askrigg Block, the average was taken as 5 oz/ton, and in the case of the ore bodies of the Lake District as 7 oz/ton. The lead and zinc ores of the Northern Pennines were considered to bear on average 14% Pb and 10.5% Zn, respectively, and the copper ores ofthe Lake District to bear 3% Cu (15% when dressed). No need to convert into metal values the copper ores of the Pennines or the lead and zinc ores of the Lake District arose. (5) The output figures quoted in several sources as belonging to counties, areas, or mining districts, were allocated to particular cells only when they referred to restricted areas lying on the whole within one or, at the most, two cells, as is the case of figures quoted for Arkandale (cell 71), Wharfedale(cell 99), Grassington (cell 106), etc. In the cases of areas covering two cells, the allocation of that output was done according to the procedure indicated in (3).. (6) The present value allocated to each deposit must be considered to represent the minimum that may be assigned to it, since no production prior to 1729 was considered in the present researchland in some cases 87 output data for several years are lacking. The latter is the case of the .deposits in the Derwent area of the Pennines for which no output prior to 1845 is available, and the case of the deposits in the Haydon Bridge and Teesdale areas, for which no output figures are available for the years prior to 1848 and 1816, respectively. Besides, in the case of the mines in Yorkshire and the Lake District, very little information is available with respect to their production prior to the publication of the official statistics in 1845, and hence most of the output gained before that time had not been included in this analysis. Nevertheless, in the opinion of the author, the output figures with which it was dealt are fully significant since most of the mines in Northern England reached their main productive capacity in the period considered and in most cases there was little serious mining before that epoch. 5.2.2.2 Indexes of Production As indicated previously, three parameters related to production were selected in the present research for the design of the different forecasting models. Those parameters were: total production, average value of the production per deposit, and number of deposits per cell, the first two expressed as present value and the latter as absolute value. The first and last indexes are economic parameters normally used in this type of analysis, but the second one is a rather unorthodox index that to the best knowledge of the author has not been used previously. The selection of this parameter was done taking into account the convenience of introducing in the forecasting models as many "local" economic indexes as possible. That is, it was intended that, the models designed reflect areal tendencies in the best possible way, rather than purely reflecting broad regional patterns which might be distorted by local environmental conditions when applied to individual cells. 88 The general features of the different output indexes measured were the following: (A) Total Production Of the numerous mines and prospects known in the studied area, 264 have a recorded output, totalling since 1729 a production of 3,109,848 tons of lead metal; 17,187,481 oz of silver; 146,727 tons of zinc metal; and 5,644 tons of copper metal. This output has a present global value of about £317m at the metal prices previously indicated. Of the total present value, only £279m could be allocated to individual deposits, the remaining £38m corresponding to undifferentiated production recorded in Weardale (£33.5m), Alston Moor (£2.6), Teesdale (£1.9m) and Arkandale (£3,700). The distribution of the output according to production categories is given in Table 5.3, where it may be seen that most of the operations in the area were of small to medium size, producing on average less than 5,000 tons of lead metal; 1,000 tons of zinc metal; 50,000 oz of silver, and only marginal amounts of copper during their productive life. - The productive deposits are contained in 39 of the 106 cells into which the area was subdivided. In Appendix IIA the values of the allocated outputs for each cell are given, figures that give a total average product- ion. of £7,154,000 for the productive cells. The lead and zinc productions of the area arose from 255 mines, which raised 2,392,411 tons of lead metal and 146,727 tons of zinc metal: of those deposits only 35 have recorded output of zinc ores. The combined output has a present value of £341,996,000 and the respective individual outputs, £323,377,000 in the case of lead and £18,619,000 in the case of zinc. Of those figures only £304,665,000 could be allocated to individual deposits, of which £286,046,000 correspond TABLE 5.3 DISTRIBUTION OF MINING DISTRICTS IN NORTHERN ENGLAND ACCORDING TO THEIR OUTPUT (VALUES IN LONG TONS OF METAL OR TROY OUNCES) Lead Zinc Copper OVER 100,001_ TONS 6 - - OVER 500,000 oz. 100,000-50,001 4 - - 500,000-250,000 50,000-20,001 10 1 - 250,000-100,000 20,000-10,001 15 2 - 100,000-50,000 10,000-5,001 23 2 - 50,000-10,000 5,000-1,001 52 5 1 10,000-1,000 LESS THAN 1,000 142 25 20 TABLE 5.4 PRESENT VALUE OF METAL OUTPUT IN NORTHERN ENGLAND (VALUES IN POUNDS x 1,000) TOTAL LEAD ZINC COPPER SILVER TOTAL VALUE 317,082 286,046 18,723 2,513 9,993 TOTAL ALLOCATED VALUE 279,015 249,041 18,723 2,511 9,188 NO. OF PRODUCTIVE CELLS 39 38 13 11 38 AVERAGE VALUE/CELL* 7154.74 6553.71 1440.15 228.27 241.79 NO. OF MINES 264 252 35 21 252 AVERAGE VALUE/MINE* 1056.87 988.26 534.94 119.57 36.46 * Refers to allocated output TABLE 5.5 BASIC STATISTICS OF ECONOMIC INDEXES IN PRODUCTIVE CELLS (VALUES IN POUNDS x 1000) TOTAL VALUE NO. OF DEPOSITS/CELL AVERAGE VALUE/DEPOSIT/CEL 0.05 0.05 0.05 X S confidence X S confidence R S confidence interval interval interval TOTAL 7154.74 15086 2419-11,890 6.61 9.5 3.6- 9.5 747.4 1166.7 381-1023 OUTPUT LEAD 6553.71 14675 1887-11,220 6.55 11.0 3.0-10.0 663.1 1264.6 261-1061 ZINC 1440.15 3203 0- 3,455 2.53 3.5 0.3- 4.7 422.3 754.7 0- 897 COPPER 228.27 646 0- 683 1.63 1.8 0.3- 2.8 111.5 322.4 0- 337 SILVER 230.81 476 79- 382 6.55 11.8 3.0-10.0 26.9 68.6 46- 80 * Confidence intervals calculated from normal curve, except for copper and zinc outputs which are calculated from Student's t curve 89 to lead production (2,751,135 tons) and £18,619,000 to zinc production (146,727 tons). The lead and zinc output in the area came from 38 cells, with an average combined presentvalue of £7,102,000 per cell and an average lead output value of £6,553,000. The zinc production arose from 13 cells which produced on average £1,440,000. Copper was produced, according to the records, in only 21 mines with a total value of their output of £2,513,000. The allocated production has a present value of £2,508,000, representing 5,633 tons of copper metal. The productive deposits are scattered in 11 cells, with an average present value of £228,000 per cell. The total production figures in the five output categories distinguished in the present research are summarized in Tables 5.4 and 5.5; the distribution of these values in the productive cells of the area is given in Table 5.6. (B) Average Value of the Production per Deposit This economic index was obtained for each cell by dividing the total figures of production allocated to that cell by the total number of deposits that have a recorded output within it. Following the general pattern, this parameter was also subdivided into five output categories that were independently quantified and analyzed: Total, lead-zinc, lead, zinc and copper. The values allocated to each cell that have recorded output are indicated in Appendix IIB. The 264 productive mines existing in the area have, according to the annotated way of estimating, a total average present value of production of £747,448. The 255 deposits that produced lead and/or zinc have a present average value of their output of £715,205; of these deposits, 252 produced lead ores with an average value of £663,110 and 35 rendered zinc ores with an average value of £422,343. The 21 deposits that produced copper ores in the area rendered on average £111,574. 90 If the above average figures are compared in each case with those given in Table 5.5, which were taken from the simple ratio present value/ total number of productive mines, it may be seen that they are markedly lower. The explanation for this apparent contradiction lies in the fact that when averaging, the present value of the output of small deposits is greatly increased if there are deposits with a much larger present value of their output within the same cell (obviously these, in turn, will see their present value strongly diminished). Since averaging is done first for each cell and then for the total area, the effect of this weighting is enhanced twice to the detriment of the larger producing' mines or cells. Besides, whenever a single deposit was worked from more than one site, the average for the cell will also be diminished. In the opinion of the author, the rather low figures of average value of the output used are much more realistic than those obtained from the simple ratio since they do not only consider local characteristics as size and grade of the deposits existing in each cell, but also include economic conditions that prevailed in each area during the time of the exploitation of the ore bodies, as well as amenability of these to mining and other features that are not revealed if a grand average is used. The average value of the production obtained for the five output categories distinguished are summarized in Table 5.5, and their distribution is given in Table 5.7. (C) Total number of deposits per cell The third economic parameter considered was the number of prod- uctive deposits or mines existing in each cell. The usage of number of mines instead of number of ore bodies was chosen because although almost all the mines worked a single ore body, some of them worked veins and flats that may be considered as separate ore bodies, or even worked several separated veins. Besides, some of the big mineralized structures in the TABLE 5.6 DISTRIBUTION OF CELLS ACCORDING TO THE PRESENT VALUE OF THEIR OUTPUT (VALUES IN POUNDS x 1000) TOTAL LEAD ZINC COPPER SILVER GREATER THAN 50,001 2 2 50,000-25,001 25,000-15,001 32 3 15,000-10,001 4 4 1 10,000- 5,001 2 1 5,000- 1,001 9 9 3 1 3 1,000- 501 5 4 1 500- 101 2 2 2 2 11 LESS THAN 100 12 13 7 8 23 TABLE 5.7 DISTRIBUTION OF CELLS ACCORDING TO THE AVERAGE VALUE OF THEIR OUTPUT PER DEPOSIT (VALUES IN POUNDS x 1000) TOTAL LEAD ZINC COPPER SILVER 1 OVER 2501 2 2 2500-1501 1 1 - 3 1 1500- 501 11 10 11 2 2 500- 101 12 LESS THAN 100 13 14 7 10 36 TABLE 5.8 DISTRIBUTION OF CELLS ACCORDING TO THEIR NUMBER OF PRODUCTIVE DEPOSITS TOTAL LEAD ZINC COPPER SILVER OVER 25 2 2 - - 2 25 - 16 1 1 - - 1 15 - 11 4 4 1 1 4 10 - 6 4 5 - - 5 5 - 2 19 18 5 5 18 1 9 9 7 6 9 TABLE 5.9 COEFFICIENTS OF CORRELATION BETWEEN OUTPUT INDEXES TOTAL OUTPUT LEAD OUTPUT TOTAL AVERAGE/ NO.DEPOSITS/ TOTAL AVERAGE/ NO.DEPOSITS/ VALUE- DEPOSIT CELL VALUE DEPOSIT CELL 0.720* 1.000 0.630* 0.765* TOTAL VALUE 1.000 0.593* 0.204 1.000 0.230 AVERAGE/DEPOSIT 1.000 NO.DEPOSITS/CELL 1.000 1.000 ZINC OU,TPUT COPPER OUTPUT TOTAL AVERAGE/ NO.DEPOSITS/ TOTAL AVERAGE/ NO.DEPOSITS/ VALUE DEPOSIT CELL VALUE DEPOSIT CELL 0.952* 1.000 0.226 0.999* TOTAL VALUE 1.000 0.408 0.150 1.000 0.196 AVERAGE/DEPOSIT 1.000 No.DEPOSITS/CELL 1.000 1.000 * Significant at the 0.01 level • 91 area were mined from several sites, features of the activities that render it very difficult to determine the precise number of productive ore deposits existing in each cell and even more difficult to assess their individual outputs. The 264 mines that produced ores of different kinds in the area are distributed in 39 cells, giving an average of 6.61 deposits per cell. The average number of mines per cell that register lead and/or zinc output is 6.57, these deposits being scattered through 38 cells. Those 38 cells that had lead output have on average 6.55 deposits and the 13 cells that register zinc output have an average of 2.53 operations per cell. The 11 copper-producing cells in the area have on average 1.63 deposits that produced copper ore at one or other time. The number Of productive deposits existing in each cell is indicated in Appendix IIC, where the different categories of output distinguished are listed. As may be seen in that appendix, the productive cells had in general less than 5 deposits in them, which confirms the fact that most of the deposits were mined from a single operation. The only areas with a large number of mines are those of cells 25 and 36, which cover the Alston Moor area, and cells 26, 27, 37, and 38 which cover most of the Weardale area. The average value and standard deviations of "thenumber of deposits per cell for the five output categories considered are given in Table 5.5 and the distribution of these values in the productive cells in Table 5.8 5.2.2.3 Distribution of the base metal production in Northern England and the relation between the economic indexes of the area The distribution of the mineral wealth of an area is a subject of controversy among authors who have dealt with this problem. In general, three main theoretical models of distribution have been postulated for the different output parameters that may be considered: Poisson, Log-normal, and Negative Binomial distributions. Allais (1957) in his classical study about the distribution of the mineral wealth in mining districts of France, U.S.A. and other areas concluded that the number of mineral deposits in an area follows the Poisson function. Slichter and co-workers (1962), when dealing with the calculation of the optimum size of a unit cell for the solution of mineral wealth problems, contested Allais' criterion, proposing that the number of deposits in an area follows an exponential or log-normal function. Coster and Weiss (1963), counting the number of mines existing in the Western United States observed that their distribution failed to follow the Poisson law and followed more closely the log-normal one. Griffiths (1962) found that the data used by Slichter and co- workers (op.cit.) was better described by the negative binomial distribution, criterion followed by De Geoffroy and Wu (1970) when dealing with the mineral occurrences in the Greenstone Belt of the Canadian Shield;, De Geoffroys and Wignall (1970, 1971) have applied a similar criterion when dealing with the mineral wealth of several areas, and Bozdar and Kitchenham (1972) also considered this model as the most suitable to explain the number of mines existing in the Alston Block of the Northern Pennines. It is worth noting at this point, that most of the authors that have postulated negative binomial distributions have done so when applying Bayesian stat- istics, when the probability of existence of a mineable deposit was classified as success or failure (or presence or absence) and when it was found that the variance of the number of mines counted in an area was very big. It must also be considered that most authors followed Bliss and Fischer (1953) in this respect, investigators who demonstrated that when k (one of the parameters that define the negative binomial distribution) is small and no zero values are considered (as in the present case), that distribution is similar to a log-normal one. 93 The distribution of the output values considered in the present research showed a marked positive skewness and strong kurtosis, as indicated in Figure 5.2, where the distribution of the value of the lead output in the area and of the average value of the total production per cell are given as examples. If those values are logarithmically transformed the skewness and kurtosis are drastically reduced (Figure 5.3) and the distributions acquire values of the non-parametric Kolmogorow-Smirnov test (Keeping, 1962; Miller and Kahn, 1962; Mitchell, 1971) significative at the 0.01%confidence level when compared with a normal distribution. Hence, in agreement with what has'been found elsewhere, the value of the base metal output of Northern England may be regarded as log-normally distributed, if it is considered either as absolute figures or as average per deposit per cell. With regard to the number of mines per cell, it may be seen from Table 5.4 that the Poisson law may be disregarded for this index since the values of the mean and variance for each case are widely diverging, conditions that contravene that law which requires the mean of a variable to be equal to its variance. The distribution of this parameter, as those of the output values, presents a strong positive skewness and kurtosis, as indicated in Figure 5.4, where the histogram for the total number of mines existing in the productive cells is shown. Transforming these values logarithmically,the skewness and kurtosis are strongly diminished (Figure 5.5), and the Kolmogorov- Smirnov statistic obtained allow a comparison between this distribution with the normal one at the 0.01% confidence level. This conclusion is in apparent contradiction with the one obtained by Bozdar and Kitchenham (op.cit.), but it must be considered that those authors did not fit a log-normal function to their data, deciding that since the fit obtained with the negative binomial distribution was more • FREQUENCY DISTRIBUTION OF THE TOTAL LEAD OUTPUT FREQUENCY DISTRIBUTION OF THE TOTAL AVER :GE PRODUCTION PER CELL PER CELL XXXXXXXXXXKXXXXXXX * 35.53 XXXXXXXXXXXXXXX 4 30.77 0.161E+04 * 0.164E+03 * XXXXXXXXXXXXXXXXXX * 35.53 • XXXXXXXXXXXXXXX * 30.77 0.452E+04 * 00459E+03 * XX 3.95 xxxx • 7.69 0.803E+04 * 0.515E4-03 * XX * 3.95 XX'(X 7.89 0.112E+05 * 0.114E+04* XXX 6.58 XXXX * 7.r.9 0.145E+05 * 0.147E+04 * XXX * 6.58 xxxx 7.69 0,177E+05 * 0.179E+04 * X " 1.32 1.2 0.209E+05 * 0.2126+04 * X * 1.32 X 1.25 0.241E+05 * 0.244E+04 * * 0.00 * 0.00 0.2736+05 * 0.277E+04 * * 0.00 4 0.70 0.305E+05 * 0030 96 +04 * 0.00 • 0.'30 0.337E+05 * 0. 3426 +04 • 0.00 6.00 0.370E+05 * 0.375E+04 * " 0.00 X * 1.28 0.402E+05 * 00407E+04 * 0.00 X ' 0.434Q+05 * 0.440E+04 * 0.00 0.00 0.466E+05 * 0.472E+04 * 0.00 * u.30 0.490E+05 * 0.5056+04 * X * 2.63 * 1.23 0.530E+05 * 0.537E+04 * X 2.63 X * 1.2,1 4 A 4 4' 0 2') 40 60 80 100 0 20 40 60 80 100 PERCENT PERCENT NUULF OF SAMPLES = 35 N1.143E,i OF SAmPLES = 39 MEAN = 6553.711' MEAN = 747.451 VARIANCE. = *0750.759 VARIANCE = '6131.602 STANOARJ DEVIATION = 13306.560 STANDARD DEVIATION = 1166.754 SKLW 2.85 SK:W KLI1TOSIS 2.761 5.346 KURTOSIS • 3.452 CHI SCUARE • 937074 CHI SCUARF = 1211.60 D-GREES OF FR:EDOM • 6 45. DEGREES OF F(':FOOM • 6 F14 2a FIG.5.2b FREQUENCY DISTRIBUTION OF THE LOG-TRANSFORMED TOTAL FREQUENCY DISTRIBUTION OF THE LOG-TRRNSPORAED TOTAL LEAD PRODUCTION PER ORM AVERAGE PRODUCTION PER C7T,T, HISTOGRAM INTERVALS AZT LOGARITHHT3 97c.TOKM INTERVALS ARE LOGA=ITP4IC 4 4 4 XXXX * 7.59 XXX * 5.13 0.136E+01 * 0.127E+01 * * 0.00 0.00 0.2496+01 * 0.206E+01 * XXX * 5.26 0.00 0.459E+01 0.334E+01 * X * 2.63 XXXX 7.65 0.8436+01 * 0.540E+01 * X 2.63 X 2.56 0.155E+02 * 0.875E+01 * XXX * 5.26 X 2.5t 0.285E+02 * 0.142E+02 * XXXX * 7.39 XXX r 5.4 3 0.5246+02 * 0.229E+02 * X * 2.63 XXXX 7.69 0.964E+02 * 0.372E+02 * * 0.00 r 0.30 0.177E+03 0.602E+02 * * 2.63 X 2.56 0.3266+03 * 0.974E+02 * XXX 5.26 XXXX 7.69 0.600E+03 0.158E+03 * XXXXX * 10.53 X 2..56 0.110E+04 * 0.256E+03 * XXXX * 7.09 XXXXXX * 12.32 0.203E+04 0.414E+03 * XXX k 5.26 XXXX 7."-9 0.373E+04 * 0.670E+03 * XXXXX * 10.53 XXXXXX '1 9.32 0.6e66+04 * 0.109E+04 * XXXX * 7.89 XXXXXXXX 4 15.35 0.1266r05 * 0.176E+04 * XXXXX * 10.53 X 2.56 0.232E+05 * 0.285L+04 * XXX 4 5.26 XXX 5.13 4 X M 6 W 0 20 40 60 BO 0 20 40 60 59 10C' PERCENT 9ERCEIT I NUMBER OF SAMPLES = 30 I 'NUMBER OF SAII9L,I.S = 39 MEAN = 459.132 "TAN = 164.733 VARIANCE = 2.027 VARIANCE = 1.021 STANDARD DEVIATION = 1.424 STANDARD DEVIATION = 1.010 SKEW = -0.445 SKEW = -0.627 KURTOSIS = -1.067 KURTOSIS = -0.744 CHI SC OA RE = 27.56 CHI SOUAIr = 33.23 DEGREES OF mxipam = 15 DLGREtS OF FUEDOM = 15 FIa.5.3a FIG.5.3b FREQUEli CY DI &TRIBU T ION OF THE LOG-TRABSb 0 TOTAL FREQUENCY DISTRIBUTION OF THE TOTAL NUMBER OF PRODUCTIVE 02 IDPOSITE 21L.1 DEPOSITS PER CELL HT STr1GRA V INTERVALS ARE L OGAR1 T HAT; 4 4 XXXX XX xXXXXX XXXXX X I 35.913 0.242E+01 XXXX XXXXXXXX * L3. 05 XXXX XXXXXXXXXXXXXX * 35.90 0.1i2E+01 0.52 5E+01 * 0.00 XXX * 5.13 0. 239E+01 4 0. 80 5E +01 * n.00 XXX * 5.13 0.173E+01 4 0.109E +02 * XXXX X XXX 15.36 XXX 5.13 0.216E +01 4 0.137E+02 * " 0.9n XXX * 5.13 0.269E+01 4 0.166E+02 * XXXXXX 4' 12. A2 * 0.00 0.334E+01 0.194E+02 XXXX X 10.2 0.00 0.417E+01 4. 0.222E+02 * XXXX X * 10, 2f * 2.56 0.519E+01 0.251E+02 * XXX * 5.13 • 2.56 0.646E+01 0.2796 +02 * u 0.10 .1* 0.00 0. 805E+01 4 0.307E+02 * XXX A 0.13 0.00 0. 10 0E+02 00336E+02 * * 2.05 0.00 0.125E+02 4 0.164E +02 * xxxx . 09 0.00 0.155E +02 0. 19 2E+02 * 0.10 0.00 0.194E +02 0.421x0+02 * X 2.E6 0.00 0.241E +02 0.449E+02 * X 2. 5F1 X 1.28 0.300E+02 0.477E+02 * 0.00 X 1.28 0.374E+02 * X 4 4 * 2.56 0 20 40 60 80 100 V PERCENT 0 20 40 60 60 100 PERCENT NUMBER OF SAMPLES = 39 MEAN = 5.615 NUME:R OF VIMPLLs = 39 VARIANCE 93.359 MEAN = 3.,043 STANDARD DEVIATION = 9.316 VARIANCE = 0,205 SKEW = 3.103 STANDARD DEVIATION = 0.453 KURTOSIS = 11.011 SKEW = 0.523 KURTOSIS = -0.475 CHI SCUARF = 5119.20 OEGREES OF FR...room, = 6 CHI SCUA RE = 59.38 FIG.5.4 DEGREES OF FREFOCM = 15 :10.5.5 9 4 than adequate, no need to analyze any other distribution existed. In the opinion of the author,a log-normal distribution is much more logical to accept than a negative binomial or other complex mathematical function since the latter may be very convenient expressions for certain purposes (e.g. Bayesian analysis), but very difficult to explain in terms of geolog- ical or other natural parameters, which is not the case with the log-normal function which may indicate exponential relations between the number of ore bodies present in an area and some controlling feature of their emplacement (see Chapter 7). The relation existing between the different production parameters measured in the studied area is, as can be expected,, varying. The coeffic- ients of correlation between those parameters are indicated in Table 5.9, where the three types of index measured for each category of production are listed. It may be seen in that table that in all cases the present value of the output of a cell is significantly correlated to the number of deposits worked in that cell and that only in the case of the production figures dominated by lead output is the present value significantly correlated to the average value of that output per deposit. In the case of the copper and zinc production, it is possible that the lack of correla- tion obtained could reflect the fact that the small number of cells which have recorded output of such metals is probably insufficient to reflect a relation that might probably exist between the parameters, but which is not so marked as the one existing between the indexes mentioned before. As may also be noticed, there is no significant correlation between the number of deposits existing in a cell and the average value of their production. A possible explanation for this lack of correlation may be that it reflects the general nature of the mining activities in Northern England, characterized by'the existence of very few big mines and a great 95- number of small to medium sized operations, the latter usually established in the same districts as the former, and being partly subsidized by the earnings of those. Those small mines were only able to operate thanks to the existence of facilities constructed when the main ventures were installed. Finally, it is worth mentioning that the annotated lack of correlation may also be a consequence of two other more speculative aspects of the industry. Firstly, the way in which mining concessions have been traditionally granted, authorizing the exploitation of a prism of land and not of a mineral deposit, has in many cases had as a consequence several ventures widely differing in size established in the same huge mineralized structure or body, often resulting in very contrasting outputs that mainly reflect the differences in investment allocated in each case. In this way, no clear relationship between the number of deposits working in a district and their average output exists, varying the proportion between both para- meters to a certain extent at random. Secondly, this fact may reflect the different quality, mining or geological intuition, or even luck of the technicians and miners working at neighbouring mines. For instance, in many operations the discovery of rich flats - which were not always adjacent to the main veins - was of paramount importance regarding the output and revenue obtained. It is possible that in many cases, these mineralized structures might have been missed if they were separated from the veins by barren or semi-barren rocks, hence changing the whole outcome of the operation and distorting the relation- ship between the different economic parameters of the area. 5.2.3 Geochemical Data 5.2.3.1 General Considerations The stream-sediments analysis that constituted the basis of the geochemical data used in the present research were obtained by members of the A.G.R.G. while compiling the Geochemical Atlas of England and Wales, 6 a project that comprised the regional sampling of active stream-sediments throughout both countries, their analysis for six major and twenty-five trace elements, and the production of geochemical maps where the distribution of those elements was shown. The validity of the sampling methods and of the spatial density of sampling used, as well as the analytical techniques employed in that main task, have been reviewed and assessed by Nichol and co-workers (1970), Young (1971), Davis (1971) and Urquidi (1973). During the present research, once the statistical models for the forecast of base metal mineralization in Northern England were designed, several anomalies detected during the regional survey were followed up in selected areas in order to perform a preliminary appraisal of the forecasts obtained with the models. These detailed surveys were carried out by means of stream-sediment, soil, and rock sampling, the samples being analyzed in most cases in a similar fashion to those of the regional reconnaissance. 5.2.3.2 Sampling Methods More than 10,000 stream-sediments were collected at stream-road intersections in Northern England during the summer 1969, by nine two-man teams who gathered by hand duplicate samples at each site, covering the whole region at an average density of 1 sample per square mile. Only active sediments were collected and special emphasis was placed on avoiding contamination, collapsed bank materials, and organic litter and residues. The samples were placed in pre-numbered Kraft paper bags holding about 250 grams of sediment. The sampling sites were plotted in 1"/1m Ordnance Survey maps and their coordinates referred to the National Grid Reference System and were entered in field-sheets specially designed, together with other characteristics of the site. The field observations included: mechanical composition of the sediment, presence or absence of organic matter, rate of flow of the stream, width and depth of the stream, presence of Mn-Fe 97 oxide coatings on stream pebbles, sources of contamination (if present), nature of local topography and lithological characteristics of the bedrock. During the detailed surveys performed, stream-sediment samples were collected as above, at regular intervals (150-200m) along selected streams and at critical points of the drainage system. A total of 210 samples were collected in this manner though duplicate sampling was not performed. As well, in selected areas, soil profiles were sampled with "a one inch screw auger at intervals varying between 100 and 200m. In all sites the samples were collected from the sub-soil at 12" depth and in selected profiles every three sites a top-soil sample was also gathered. As with the stream-sediments, the samples were placed in pre-numbered Kraft paper bags. Notes recorded in the field while performing that sampling included depth, colour, texture, moisture, and organic content of the soils. In this way, 269 soil samples were collected. Twenty three rock samples were collected during the detailed surveys. Altered and meteorized rocks were avoided as far as possible, most of the samples being gathered at quarries and valley-bottoms. In addition, six mines were visited where samples of the ore, gangue and wall- rock were obtained. All the sampling sites visited during the detailed reconnaissance of selected areas were recorded in the 21/2 inches to the mile Ordnance Survey maps Nos. NY75, SD69, NY8O, and SD27. 5.2.3.3 Sample Preparation The preparation of the samples for analysis was carried out in two steps. Firstly, the samples were dried and sieved, and secondly, they were chemically attacked or ignited and mixed with buffer, depending on the type of analysis performed. Stream-sediment and soil samples were dried overnight at 600 C • '98 in an electrically heated drying cabinet. The dried materials were gently disaggregated in a porcelain mortar and sieved through an 80-mesh (nominal aperture of 0.204mm) nylon bolting cloth mounted on an acrylic (Perspex) frame. The minus 80-mesh fraction was retained for analysis and placed in appropriately numbered paper bags. Rock samples were dried, hammered to gravel size and reduced to minus 1/4" chips in a jaw-crusher. The chips and pulverized material obtained were quartered, two portions were ground to minus 80-mesh size on an agate mortar and sieved similarly to the sediment and soil samples. The fine (minus 80-mesh) fraction recovered,was further prepared according to the type of analysis required. Of the portion used for spectrographic analysis, ten grams were ignited for 3 hours at 450°C inn order to remove moisture and oxidize the organic matter that.might have existed in them, and then the samples were thoroughly mixed at a 2:3 ratio with a buffer consisting of a mixture (1:2) of sodium fluoride and carbon powder. The resulting mixture was packed into a pre-drilled carbon electrode, by tamping it into the powder, thus analyzing a constant volume in each case; a small hole was made down the centre of the packed electrode to prevent spitting of the sample during arcing. The portion of the samples that was analyzed by means of atomic - absorption spectrophotometry was taken into solution through acid digestion, with nitric acid in the case of the samples of the reconnaissance survey, and with a mixture (4:1) of nitric and perchloric acids in the case of the samples of the detailed surveys. The part of the samples determined colorimetrically was attacked by means of acid fusion with potassium bi- sulphate. A comprehensive account of the decomposition methods used in this research is given by Stanton (1966). 69 5.2.3.4 Analytical Techniques The analytical techniques used are standard methods of analysis employed in the A.G.R.G., where these techniques are used for the rapid routine analysis of geochemical samples. These methods compromise, up to a certain extent, accuracy and precision for high productivity, a feature that is a requirement of any survey that deals with the production of more than 1,200,000 determinations, such as the Geochemical Atlas of England and Wales. The samples collected during the regional reconnaissance and detailed surveys were analyzed for six major and twenty three trace elements using a direct-reading emission spectrometer (Quantometer). In addition, those samples were analyzed for Zn and Cd by means of atomic absorption. spectrophotometry, and colorimetrically for As and Mo. Of all the elements analyzed, it was considered in the present research that 14 of them would be suitable for the design of the fore- casting models since they are those that most probably relate to mineral- ization. These elements are: Ba, Cd, Co, Cu, Fe, Ga, Li, Mn, Mo, Ni, Pb, V and Zn. Besides, the regional patterns of-distribution of Si, Ti, Al, K and Mg, were analyzed in order to determine their possible relation to hydrothermal alteration. (A) Emission Spectrography As stated, the basis for the present research was the analytical determinations performed by emission spectrography in an A.R.L.29000B direct-reader spectrometer (Quantometer). The use of this technique in geochemistry has been reviewed by many authors as Cameron and Horton (1967), Crufts and Giles (1968), and Tenat and Sewell (1969), all of whom were especially interested in obtaining highly precise and accurate results, thus analyzing small batches of samples per day. The instrument and method used in the A.G.R.G., which considers the analysis of 200 samples per day, have • 1 0 0 been thoroughly reviewed by Norman and Foster(1968) and Young (1971). In the present case, the arcing conditions were 9.5 amps, 3mm of electrode gap and integrated time of 90 seconds. To overcome the major disadvantage that quantometers pose, which is the need for background corrections due to the enhancement or depletion of some elements as a result of the matrix composition of the samples, the spectrometer was fitted with two channels (4116 and 2008 R) to check possible fluctuations. Calibration was performed with synthetic standards resembling an igneous rock of inter- mediate composition with various levels of trace elements included. The corrections for background allowed to determine that the principal elements causing interference in the trace-elements values are: Ca, Si, Al, Fe and Mg (in order of importance). Regression lines were calculated for these interferences and a computer program working in three stages was designed to evaluate the necessary corrections. Initially, corrections for bias in calibration were performed, then corrections for background and arc effect, and finally corrections for line interference. Table 5.10 shows the relation existing between the trace elements used in the present research and the major interfering elements. (B) Atomic Absorption Spectrophotometry The samples collected in the regional and detailed surveys were analyzed for Cd and Zn in a 403 Perkin Elmer atomic absorption spectro- photometer. This double-beam instrument is connected to a high dispersion Czerny-Turner grating system with ultraviolet dispersion of 6.5 R per milli- metre and visual dispersion of about 13.0 R per millimetre. Its minimum spectral band-width is about 0.2 R(UV) and about 0.4 R(V). In all cases the flame used was a lean oxidizing one with acetylene as fuel gas. A detailed account of the technique and of the characteristics of the instrument may be found in Elwell and Gidley (1967) and in Ramirez Munoz (1968). TABLE 5.10 RELATIONSHIP BETWEEN TRACE ELEMENTS AND MAJOR INTERFERING ELEMENTS FOR A.R.L. 29000B QUANTOMETER (Background and arc effect corrections) BA = BA/(1.0 - 0.001(AL - 85) + 0.0003(CA - 550) CO = CO - 0.11(CA - 550) - 0.1(MG - 270) CU = CU - 0.004(CA - 550) GA = GA - 0.01NI LI = (LI + 0.07(AL - 8s) - 0.048(CA - 550) + 0.01(SI 2800))/1 - 0.0001(51 - 2800) MN = MN/1 - 0.0002(CA - 550) - 0.00015(FE - 580) NI = NI - 0.014 (CA - 550) V = V + 1 - 0.001(AL - 85) - 0.0003(CA - 550) - 0.00015(FE - 580) TABLE 5.11 INSTRUMENT PARAMETERS FOR ATOMIC ABSORPTION SPECTROPHOTOMETRY Maximum Element Wavelength (R) Sensitivity (1.1g/m1) Monocromator Band Pass(R) Cd 2280.0 0.03 10 Zn 2138.6 0.03 50 TABLE 5.14 DETECTION LIMITS FOR SELECTED TRACE-ELEMENTS IN THE QUANTOMETER (in ppm except Fe which is indicated in percentage)* Element Minimum Maximum Ba 20 10,000 Co 2 1,000 Cu 5' 1,200 Fe 0.1 20.0 Ga 1 100 Li 15 10,000 Mn 25 10,000 Ni 5 10,000 Pb 5 1,500 V 10 10,000 * After Dr. M. Thompson (1972, pers.comm.) 40, 4 '0 Ic The main interferences dealt with during the present analysis was the "non-atomic absorption effect" (molecular absorption plus light scattering), which increases with decreasing wave-length of the resonance lines used and with increasing amounts of Ca, Na and Fe in the sample. Since the elements analyzed by this means are especially sensitive to this interference because their most sensitive lines lie below 2500 R, a deuterium background corrector emitting a continuous radiation in the 2000-2700 R region was used,automatically correcting this effect. In Table 5.11 the operating conditions of the instrument are given for both elements analyzed by this means. (C) Calorimetric Analysis This means of analysis was used in the present research for the determination of As and Mo. Arsenic was determined by the so-called Gutzeit Method described by Stanton (1964) which ultimately is based on the reaction of arsine with mercuric chloride paper giving a confined spot that is compared with artificial standards. Molybdenum was determined by the method described by North (1956) and Stanton (1966) in which the element in state of molybdate is complexed with 1% dithiol solution, the green complex being extracted on a layer of amyl acetate and compared with artificial standards. As indicated previously, both elements were determined after acid digestion of the sample by fusion with potassium bisulphate and hydrochloric leaching. 5.2.3.5 Sampling variability, analytical control and precision The major sources of geochemical sampling error have been discussed by Miesch (1967). The majority of them are usually unavoidable and their individual magnitudes can seldom be determined, though sound planning in the design of the sampling pattern should greatly reduce their effects. 1 0 2 Several authors as Hawkes, Bloom and Riddell (1957); Govett (1958); and James (1965) have suggested that the stream-sediment sampling error is small as compared to the analytical precision of the methods employed. This criterion was contended by Khaleelee (1969) who, studying spectrographic analysis of stream-sediments in the United Kingdom, concluded that for a wide range of elements the sampling error was at least similar to the analytical one. The incidence of sampling variability in routine stream-sediment- reconnaissance in England and Wales, as compared to the analytical precision of the A.R.L. 29000B quantometer, has been assessed by Howarth and Lowen- stein (1971). These authors concluded that for most elements the sampling error is less than the low precision spectrographic analytical error and that only in cases of mineralization or contamination the ratio sampling variance:analytical variance exceeded a factor of about three (Table 5.12). Besides, it was observed that with analytical precisions under 20% (such as those normally obtained with atomic absorption spectrophotometry), the sampling error is greatly in excess of the analytical error in most cases (Table 5.13). For the purposes of the present research, where each statistical sample represents the average of all the geochemical samples collected in an area of 100 square kilometres, the smoothing effect of averaging is thought to reduce the adverse effect of sampling variability in the case of those elements determined by high-precision analytical techniques. Analytical control was maintained in three ways during the auto- mated spectrographic analysis: (1) Eight standard samples of stream-sediments were analyzed every day as well as two synthetic standards with high and low trace-elements which were repeatedly analyzed. Precision, mean zero point offset, absolute zero point change, and correlations, were calculated daily, all the analysis TABLES 5.12 and 5.13(After Howarth and Lowenstein.1971) Comparison of population mean and analytical variance ratio (r) and precision (10 for stream sediments based on low-precision spectrographic analyses Element Sandstones Sandstone^ Shales Shales Limestones Basic igneous Basic igneouss Granite^ i Granite' Detection r 4' 4, r 16 r r r* 4 r r't 9S limits/ Al 29 (2 •0) 26 30 30 22 39 39 10 - 30 3.1 - 18 0.15% Ca 101 38 - 38 109 (2.9) 45 (1.5) 49 49 - - 109 - - 164 0.2% Fe 44 20 (1.2) 17 48 21 35 35 - - 48 - 32 36 0.1% K 24 (1-7) 14 (2.0) 12 (1 •5) 27 14 58 58 3.9 (2.3) 27 (1.1) 7.2 30 0401% Si 35 - 15 15 40 11 20 20 - - 40 - - 26 0.5% Ba 32 4.5 40 2.0 23 28 31 38 38 - 28 - - 68 10 Co 75 21 5.0 10 51 n.d. n d. 47 47 - - 51 20 279 20 3 Cr 246 62 - 67 85 73 43 43 - - 85 n d. n d. n.d. 10 Cu 32 27 (2.0) - 120 44 n.d. n.d. 63 631 63 (2.6) - 44 16 76 16 3 Ga 46 47 - ' 30 40 n.d. n.d. 32 32 2.0 (2.0) 40 - 6.0 40 1 Li 38 45 - 32 80 39 86 2.3 86 - - 80 - 2.3 27 5 Mn (3.9) 42 (1-3) 25 2.0 34 56 6.0 17 56 56 56 - 35 17 5 Ni 88 61 2.3 17 (1 -7) 50 n d. n d. 24 24 n.d n d. n.d. n.d. n d. n.d. 6 22 Pb 68 2.5 17 - 30 n.d. n.d. 52 19 52 - - 30 10 30 21 3 a 29 48 72 24 (1.2) 53 - 53 1.8 - 70 - - 57 2 Sn 65 641 186 299 26 652 n.d. n d. 228 140 1.8 151 548 151 120 158 1540 - - 224 5 Sr 46 (2.2) 37 32 1.5 50 33 35 35 (1.4) - 50 - - 49 6 n.d. n d. - 48 V 39 71 n.d. n.d. 52 52 - 71 nd. nd nd 10 20 20 18 21 21 8 12 30 8 10 5 Comparison of population mean and analytical variance ratio (r) and precision (0) for stream sediments based on atomic absorption analyses Detection Element Sandstones Sandstonet Shale= Shale' Limestone* Basic igneous7 Granite^ Granite' limits' rr 4, Or if # Cu 6.8 5 13 5 6.7 16 3.5 9 39 17 6996 14 1875 11 639 4 2 Ni 7.1 8 (3.5) 14 3.5 12 6.0 5 8.2 14 - 6 n.d. n.d. 85 14 10 Mn 92 14 7.9 12 22 7 17 6 34 7 5434 5 (8) 16 1214 3 3 Fe 49 4 33 3 15 5 2711 3 14 5 120 5 33 6 127 4 5 Co (2.2)18 13 (2.1) 17 (1.5) 9 143 0 18 11 n.d. n.d. 233 5 5 Zn 37 6 16 4 51 4 5.4 3 21 5 10 633 5 421 7 267 4 1 Pb n d. n.d. 7.4 5 n.d. n.d. 2.0 6 n.d. n d. n.d. n.d. n.d. n.d. 187 5 18 n 20 20 18 21 21 12 30 10 • . Ratio of population mean/analytical variance. r is less than 1 : 3, r when within-site ° Limestone. South Cadbury. Somerset (36311248). random error component differs from zero at 0-05 level of significance. (3 ), r when f Basic igneous, Cudlipptown. Devon (25210/88). within-site random error component is not different from zero at the 0.05 level of g Basic igneous (with possible contamination from adjacent mine dumps). Zoar. near significance. 4,. analytical precision (--L- 4, per cent), based on 10 replicate analyses n d.. Horndon. Devon (25270808). Population mean below detection limit, n, number of localities sampled in duplicate ° Granite, Devon (25640917) ° Permo-Triassic sandstone. Copptestone, Devon (Nat. Grid ref. 27621019). Granite (with trace-element enhancement caused by secondary environment controlled b New Red Sandstone, Osmaston, Derbyshire (41913434). manganese-iron precipitation), northwest Dartmoor. Devon (26080891) Shale. Upper Cotton, Staffordshire (40583475) Detection limits after Dr M Thompson (personal communication. 1971); values in Shale (known to have high trace-element values). Onecote Grange. Derbyshire ppm unless stated otherwise (40473558) k Bulk samples 1 0 3 being repeated if the results of any one day were not considered satisfactory. Analytical precisions were calculated as twice the coefficient of variation expressed as percentage (P=200s/m, where s is sample standard deviation and m its arithmetic mean). Detection limits were estimated as the concentration at which the precision equals 100, that is when m=2s (Thompson and Howarth, 1973). Table 5.14 gives the detection limits calculated by Dr. M. Thompson, senior analyst of the A.G.R.G. for the stream- sediment standards used as control. (2) The among-days analytical variation was controlled by the use of daily map plots of Ge, an element that was used as an internal standard at a 1000ppm concentration, which was compared with map plots of the different elements analyzed. Thus, poor analytical days were easily spotted and the analysis for those days were repeated. Figure 5.6 shows the plots of the analytical days corresponding to those days when the samples used in the present research were analyzed. (3) Finally, a graphical method was used as further control of possible variations among days. ThiS method consisted of the plot of the Percentage Relative Deviation (PRD) for each element at one standard deviation versus the number of the analytical day. The PRD were calculated according to the following equation: X - X . max min PRD - x 100 1.96m whereXmax isthemaximumregisteredvalueofthestandard,Xnan the minimum registered value of the standard, and m the arithmetic mean. Figure 5.7 indicates the resultant graphs for the analytical days corresponding to the present research. From the statistical and graphical analytical controls, it may be concluded that, as can be expected if large productivity is chosen as the main target, the automated spectrographic method of analysis is a low- ' ... Analytical Days for Samples ofStudied Area Fig.5.6 Percentage Relative Deviation for Selected Trace-Elements (values in standard deviation units) S ®Cu 0Ga +2.0— o Mn a ONi +1.5— a a +1.0-- a a a a no 0 0 00 0 0 0 0, 0 a a 0 8 p0 000 00 +0.5— • 0 a • sao a a 0 a 0 0 •, 0 0 0 0 o • „ 0 $ o : 0 0 0 • 0 0 • • 00 0 a 0 „ 0 • @ 0 8 6, ® 0 • t 0 0 1 • • • o @ e®° • oo •u po ne al : 8 t cx--• 0.0 w , 0 a e ..0 • • n o 0 • • ® o o 0 oil, ••i o oo °o2 ••• W ®0 8 •® 0 80 • • 0 so • r .0 ! : • , •0 0• • • 0 0• • 0 0 0 mgo •o o e o 0 0 o o o ® o o • 0 0 0 -0.5— 0 0 • 0 • o • 0 o 0:* 0 -10— 0 -2.0— 220 230 240 250 '260 270 280 Analytical day FIG.5.7 100 8 6 / 5 ,~ / ~ .t iI'@ 3 I ~PCE~% ' 10 PERC NT ~ Y 2 J (I) ~~ V ~ 10 • .:) (I) 8 u; /. ~ a: 6 5 "'" '1!',ii z Z. ::: w 4 "":1/' w ~ ~ ''''' ;: 3 'OS'- ...... - to- w /Jv: a:l 2 .,..'- w ~V· U ~1I l.I _ ~ 1 ~ ex: w 8 I' "" 6 / ""0 5 ". 4 / ~iI' / 3 7 2 / 0.1 / 2 3 4 5 6 8 10 2 3 4 s 6 B 100 2 345681000 MEAN OF RESULTS ZINC 10 0 6 /. 1/ 5 ~ 4 / .... 1 PERCENT~V 3 -- 10 PERCENT ~ 2 vV 1/ ~b "... I"", ~ 1 -J 8 :) / ; (I) 6 w ; c:. 5 7 .... z 4 / ~ '" 3 '"~ /~/ t- 2 II)'" 1I11 / ~.l'" V ex: 8 '" .; '"... 6 / ... 5 ./0' J!:: / / 0 4 / /. 3 / / .... 2 V 0.01 a.1 2 3 4 5 6 B 1 2 3 4 5 6 8 10 2 3 4 56 8 100 MEAN OF RESULTS CADMIUM PRECISION CONTROL CliART FOR DUPLICATE RESULTSIAA) In a set of duplicate measurements on many samples where for each sample the precision of measurenent is 10 per cent at the 95 per cent confidence 1imit (I.e, crill ::: 0.05) the Indicated proportion of points will fall above the diagonals. The scale of the means must be 10 times greater than the scale of the differences. FIG.5.8 1 04 precision technique that presents a rather erratic among-days variation. The analytical control for the atomic absorption and colorimetric analysis was kept with a statistical series of four samples (Stanton, 1966) analyzed in duplicate within every batch of 250 samples. The precisions at the different concentrations found were estimated graphically according to the method described by Thompson and Howarth (op.cit.), in which a desired level of precision is chosen and the values of the differences and averages between duplicates are plotted and compared with selected theoret- ical precentiles at the desired precision. In the present research the precision chosen was 20% and the percentiles 95th and 99th, as may be seen in Figure 5.8 which displays the graphical control of precision for samples of the detailed survey. In addition, during the analysis of the samples obtained during the detailed surveys precision was similar though further controlled by the addition of 10 duplicate sample? in every batch of 100 samples. 5.2.3.6 Distribution of the stream-sediment samples in the studied area As indicated previously, more than 10,000 samples were collected in Northern England during the compilation of the Geochemical Atlas of England and Wales, 4075 of which were obtained in streams draining the area studied in the present research. The average number of sites sampled in the 106 cells into which the area was subdivided was 36, giving an average sampling density of 1 sample per 2.80 square kilometres, though this value ranged in individual cells from 7 to 58 samples (1 sample per 14.2 km2 to 1 sample per 1.6 km2). Forty-two cells have a sampling density smaller than the average, but most of them (36) have a density higher than 1 sample per 5 km2 , the six remaining cells being areas that include varying proportions of sea in them. Table 5.15 gives the distribution of the cells according to the number of samples collected in them, and Figure 5.9, the histogram of the distribution, FREQUENCY DISTRIBUTION OF THE NUMT1ER OF SAMPLES COLLT:CTED PER CELL 0.94 0.833E+01 * 0.00 0.110E+02 * 0.00 0.137E+02 * XX 4.72 0.163E+02 * X 2.83 0.190E+02. 0.94 0.217E+02 * XXX 5.66 0.243E+02 * X • 1.89 0.273E+02 * XXXXXXX * 13.21 0.297E+02 xxx 6.60 0.323E+02 * XXXXX 9.43 0.350E+02 * XXXXX * 10.38 0.377E#02 * XXXXXXX * 13.21 0.403E+02 * X 2.83 0.430E+02 * xxxxxx - 11.32 0.457E+02 * xxxx 7.55 0.483E+02 * XX 3.77 0.510E+02 * XX 4.72 * * * * 0 20 40 50 eo 100 PERCENT NU"RE; OF SAMPC7S = 105 MEAN = 35.198 VARIANCE = 103.379 STANDARD DTVIATION = 11.155 SKEW -f1.300 KURTOSIS = -0.371 CHI SQUARE = 32.79 DEG'EES OF FQEEDOM = 15 FIG.5.9 • 1 0 5 which shows a clear bimodality with modes of 28 and 38 samples and a slight negative skewness. Regarding the distribution of the samples according to the geology of the collection site, it may be seen in Table 5.16 that there is a high degree of agreement between the actual number of samples collected in any geological unit and the theoretical optimum calculated according to the area covered by each unit. Exception to this are the Silurian and post- Carboniferous terrains, the former having almost 20% more and the latter 25% less than the optidum. The possible explanation for the latter point lies in the fact that the Silurian terrain has a relatively low, smooth rolling topography, an area that has a large amount of rainfall requiring numerous minor collect- ors to be drained, since there are seldom main rivers due to the relatively young topography. On the contrary, the New Red Sandstone terrain is mostly coastal or interior lowlands heavily covered by glacial debris, where most of the drainage takes place along main streams that were avoided during the sampling procedures due to the high probability of contamination. Besides, in the latter area there are many important populated centres (Penrith, Carlisle, Workington, Whitehaven, Barrow-in-Furness, etc.), rendering the collection of uncontaminated samples very difficult. Regarding the distribution of the samples, it is worth noting that the number of them collected in each cell does not have a significant statistical correlation with the values attained by the average of the elements selected. In Table 5.17 the coefficients of correlation and respective t-values are indicated for all the selected elements with respect to the number of samples collected in each cell. As may be seen in that table, the coefficients and t-values are not significant at the 0.01 significance level, a confidence level considered adequate to accept when dealing with coefficients of correlation. TABLE 5.15 DISTRIBUTION OF CELLS ACCORDING TO THE NUMBER OF SAMPLES COLLECTED IN THEM NO. OF SAMPLES NO. OF CELLS MORE THAN 51 5 50 - 46 13 45 - 41 15 40 - 36 25 35 - 31 16 30 - 26 15 25 - 21 9 20 - 16 7 15 OR LESS 1 TABLE 5.16 DISTRIBUTION OF SAMPLES ACCORDING TO SITE GEOLOGY Unit Samples Collected Theoretical Optimum Liassic 18 15 Keuper 103 132 Bunter 234 295 Permian 113 157 Coal Measures 136 1 169 1 f 577 598 Millstone Grit 441 429 Carboniferous Limestone 1769 1755 Silurian 450 387 Ashgill & Coniston 25 i 9 1 1 371 f 384 Borrowdale Volcanics 346 375 Skiddaw Slates 265 224 Ingletonian 4 2 Intrusive Rocks 95 86 TABLE 5.17 COEFFICIENTS OF CORRELATION BETWEEN AVERAGES OF SELECTED ELEMENTS AND NUMBER OF SAMPLES REPRESENTED BY THEM (N = 106)* Element Coefficient of correlation T-value As 0.05 0.48 Ba -0.15 -1.51 Cd -0.00 -0.02 Co 0.11 1.14 Cu 0.22 2.31 Fe 0.14 1.40 Ga 0.14 1.42 Li 0.15 1.57 Mn 0.22 2.32 Mo -0.11 -1.10 Ni 0.20 2.08 Pb -0.03 -0.27 V 0.15 1.54 Zn 0.03 0.30 * T-value significant at the 99% confidence level: 2.648 1 0 6 5.3 PRELIMINARY HANDLING OF THE GEOCHEMICAL DATA The 4075 stream-sediment samples collected in the area rendered 57,050 analytical determinations for the 14 elements selected, a quantity of information that obviously needed to be dealt with by computerized methodes of data handling. Prior to the calculation of the average value for each element in the 106 cells considered, it was decided that, since a great deal of smelting and mining has taken place in the area, it was desirable to inspect all the results in order to detect obviously contaminated sites that might have passed unnoticed while the sampling program was being implemented. The necessity for this painstaking task was reaffirmed by two facts. Firstly, a preliminary and rapid visit by the author to the area showed that most of the mining works are collapsed or filled-up and that practically all the mine dumps have been overgrown. Thus, in most cases, it is very difficult to notice a possible source of contamination in the vicinities of sampling sites, if these are not marked on the 1"/lm Ordnance Survey maps. Secondly, a preliminary analysis of the frequency distribution of the selected trace-elements, done by dividing their range into 18 equal class intervals, showed that most of those elements had a strong bimodality and positive skewness, features that indicated the existence in the set of a relatively high proportion of high values, part of which might have possibly been the result of contamination. To overcome that situation, the values of the different elements at each site were checked as well as the sample number and coordinates. If the content of any one element in a sample was higher than its detection limit that sample was set aside for further examination. Once the whole set was examined those samples suspected were referred to their respective 1"/1m geological maps and were plotted on transparent overlays in their proper, position. If any of those samples was gathered at less than one G 7 kilometre downstream of a mined vein, it was regarded as contaminated and was not considered in the statistical analysis. In this way 209 samples were rejected, representing 5.1% of the total. In addition, 60 samples of the set were collected in areas that lie in the coast of north-west England, outside the 106 cells considered, and thus these samples were not considered in the analysis. Therefore, the final set of geochemical samples with which the forecasting models were built up consisted of 3806 stream-sediment samples, each of them having determinations for 14 elements, totalling 53,284 bits of information that needed to be analyzed and interpreted. Since the selected geochemical elements were determined in two types of units (ppm and percentage) and since those elements measured in the same units present widely contrasting ranges (e.g. lead has a range of 0-1500 ppm and V a range of 0-265 ppm), the necessity of standardizing the data before calculating the average values for each cell was considered. Prior to the standardization of the data the frequency distribution of each element and of its logarithmic transform were determined for the whole set of samples and for subsets formed by all the samples collected within the same geological unit. Applying Chi-square and Kolmogorov-Smirnov-tests at the 0.05 level, it was seen that some elements conformed with a normal distribution, others agreed with a log-normal distribution and others did not even conform with either, though they were more akin to one of them than to the other. Considering the non-uniform distribution of the different elements and that the possible role of site geology should be investigated when designing the forecasting models, four types of standard scores were cal- culated for each element in a sample, according to the following expression: 10 (X - Score = 50 / s 1 0 8 Those scores, which will be referred to as scores types A, B, C and D, differ among each other in the following aspects of their calculation: (1) Scores types A and B were obtained from statistics representing the whole population. (2) Scores types C and D were expressed in terms of statistics represent- ing subsets of the population that were selected on the basis of their site geology. (3) Scores types B and D consider X as the arithmetic mean for each element and s as their respective standard deviation. (4) Scores types A and C were calculated depending on the distribution of each element. If an element conformed or was more akin to the normal distribution, its statistics were calculated as for (3), but if an element conformed or was more akin to the log-normal distribution, the value of X was that of its geometric mean and s its logarithmic standard deviation. The use of the indicated expression for the calculation of the scores, instead of the most usual one, was preferred in order to ease the performance of transformations that operate only within the realm of the positive numbers and to avoid round-off errors that are likely to occur when dealing with very small numbers as might have been the case for some values if the usual expression would have been used: After each score was calculated for all the samples, these were separated into their respective cells and their scores averaged in each case. Appendix III gives the values of scores A, C and D for each cell, values that represent contrasting types of calculation. The statistical significance of the differences existing between those scores for each element is given in Table 5.18. 5.4 DATA HANDLING The 64,078 analytical determinations (including those of the reconnaissance survey) that were dealt with in the present research needed, TABLE 5.18 T-VALUES OF DIFFERENCES BETWEEN MEANS OF GEOCHEMICAL SCORES (N = 106) Element Score A - C A - D C - D Fe 0.319 0.431 0.147 Ga 0.035 0.029 0.133 Cu 0.020 0.440 0.600 Pb 0.232 0.042 0.423 V 0.406 0.084 0.258 Ba 0.143 0.190 0.057 Co 0.223 0.442 0.679 Ni 0.048 0.292 0.467 Mn 2.447* 0.316 3.594* Li 0.022 0.033 0.059 * Significant at the 0.01 level 1 G 9 as is obvious, computerized data handling procedures, not only because of their large number, but also due to the fact that several techniques of multivariate data analysis employed cannot be performed if computer facilities are not available (e.g. stepwise multiple regression, multiple discriminant analysis, factor analysis, etc., including up to 36 variables). The handling of the data was done using the facilities and comput- ing time kindly provided by the Imperial College Computer Centre (ICCC). The processing of the data was performed on the CDC 6400 computer existing in that Centre, and in a minor proportion using the CDC 6600 computer existing at the University of London Computer Centre (ULCC) which is linked to the ICCC through a CDC 1700 peripheral computing system. In addition to the minor computer programs designed by the author to perform routine checks on the data to calculate residuals and forecasts and other minor tasks, the main programs used during the present research, either in their original form or modified according to the requirements of this particular work, are indicated in Table 5.19 where the author or source and purposes of the programs are also indicated. TABLE 5.19 MAIN COMPUTER PROGRAMS USED IN THE PRESENT RESEARCH Program Source Purpose BMDO2R Univ. California Stepwise multiple regression analysis STEPGR IBM Stepwise multiple regression analysis PLTLP2 Howarth, 1971 Production of grey level maps, classes as selected by user PLTLP3 Howarth, 1972 Production of grey level maps, classes are percentiles of frequency distribution of variables GESTAT Garrett, 1968 General univariate statistics GNHST2 Howarth, 1968 Production of histograms and computation of Kolmogonov- Smirnov statistic SCORE Garrett, 1968 R-mode factor analysis BMDO5R Univ. California Polynomial regression BMDO3M Univ. California Multiple discriminant analysis S 1 1 0 CHAPTER 6 REGIONAL GEOCHEMISTRY 6.1 INTRODUCTION In this chapter, the regional distribution of the trace-elements selected in this research is discussed in terms of their general spatial scattering as related to type and age of bedrock geology and in connection with the mineralized structures known in the area. Besides, the distribut- ion of some major elements is briefly reviewed in order to analyze the possible existence of patterns related to hydrothermal alteration produced by the mineralizing brines while migrating towards their final site of depletion. The analysis of the different aspects is performed in two ways. Firstly, the statistical features of the distribution of the elements is reviewed and later graphical methods of pattern recognition are employed. The former analysis was done with the help of the computer programs GESTAT designed by Garrett (1967) and GNHST2 designed by Howarth (1969). The first of these programs estimates general univariate statistics (mean, variance, standard deviation, product-moment correlation coefficients, eigenvalues, etc.) and includes options for logarithmic transformations, Chi-square tests for normality, plotting of histograms and scattergrams, etc. The second program plots a histogram of up to 99 classes and calcul- ates the value of the non-parametric Kolmogorov-Smirnov statistic for curve fitting against normal or log-normal curves, a statistic that has proven as good as Chi-square, when assumptions that need to be made to apply the latter test, cannot be met (Mitchell, 1971). The graphical analysis of the patterns displayed by the different elements was done by means of the computer program PLTLP designed by Howarth (1971), a grey-scale method suitable to deal with large numbers 1 1 1 of irregularly spaced data. The output of this program is a grey levels map at any desired scale, where the data falling within a class interval are represented by a determined grey overprint symbol plotted at the location of the sampling site as given by the coordinates of the system used as reference. Since the symbols have a finite size, overlapping occurs when dealing with maps at large scales, a case in which the mean (arithmetic or geometric as desired) of the overlapping values is calculated and plotted in the respective concentration interval. The resultant map is smoothed to a degree dependent on the amount of overlapping. Considering that modern geostatistical theory regards geological data as regionalized variables that normally have "internal continuity", it is desirable to analyze the effect that values of adjoining groups of samples have on the values at any specific location, in order to delineate meaningful overall regional variations or patterns in the distribution of geochemical elements. Bearing this fact in mind, a moving average or rolling-mean technique was employed for the smoothing of the raw-data. This method reduces background noise produced by analytical or sample variance and stresses the among-sites relationship, enhancing the regional trends that may exist. The validity of the employment of this method of smoothing in pattern recognition is discussed by Howarth and Lowenstein (1971). e The window (cell aperture) used in the present research averaged all samples lying within 9 contiguous cells, each of them having an area of 0.625 square miles at the chosen scale (1 inch:10 miles or 1:625,000). Thus each symbol in the map, represents the average of the samples lying within an area of 5.825 square miles. In using grey-levels maps one of the main problems that need to be solved is the way in which the data are going to be grouped, that is the establishment of the class limits for plotting. Two ways of grouping i 1 2 the data were used in the present research: one type of map was produced using deciles of the frequency distribution as class intervals, for which purpose a routine was attached to the main PLTLP program to calculate the deciles on the total range and recalculate new deciles on the range min- imum value-99th original percentile. The latter deciles were plotted in map form with a frequency distribution of grey-]evels that tends to normal- ity, and these maps were used in the analysis done in the present chapter. The advantage of the indicated type of mapping is that it expresses very clearly all the trends that may exist in the sub-anomalous region, a feature very important when dealing with elements that have strongly skewed distributions and which is difficult to achieve by the use of arbitrary selected intervals. It must be considered that in regional studies this fact is of primordial importance since it allows one to analyze and detect normal regional trends (as opposed to anomalous trends). The other way in which the maps were produced was by selecting class intervals in terms of standard deviation units, a method that was used with forecasting purposes, as indicated in Chapter 8. By this means, the anomalous areas are clearly pointed out and a very strong suppression of background noise is obtained, an ideal feature for the application of the technique to mineral exploration problems. 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IT *******worrel r I £ 8==-++++....+=-=8E3E838 EEEE +.-"0 E It. I k110261110011104 I =7-4++ +...+8511883==BEEEEEBBE001E It I I EE ++0+ ++ 4.. BBE0E=••=EBEEE1- BOEBBB IT IMIN*****1111 r I E ++. 01--=EBEE - --=BOE== Ii I /41+++++++++++ +++++ ++4.44++++++4+444+++44-4+++++++++++++++++f++++++++++++++++4.I. I 0 10 2 30miles FIG.6.10 - HISTOGRAM OF AS VALUES IN PPM HISTOGRAM INTERVALS ARE LOGARITHMIC X a 1.45 .100E+00 * * 0.00 .182E+00 * * 0.00 .3311.00 * * .08 .6031.00 * XXxXXX * 11.04 .1 1 11E+01 * 8 0.00 .2001.01 * * 0.00 .3631.01 * XxxxxxxxXXX 8 22.73 .6611.01 * XxxxxxxxXxxxxx * 27.04 .321.02 * Xxxxxxxxxx * 19.89 .2191.02 * XXXXX * 9.72 •398E+02 * XX * 4.57 .7241.02 * a 1..51 .1321+03 * X * 1.0e .2401.03 * * .66 .4371.03 * * .08 .794E+03 * • .11 .145E+04 * .13 0 ?0 40 60 80 100 PERCENT FIG 6 lb •V1 ***MINIX NORTHERN FNGLANO*nARIUM B.R. OATIOWRCENTILE MAPS*** LOW-PASS FIL1LR USING EFFECTIVE RAOIUS OF 1 CELLS /++++++++++++++ff++++++++++++*++++++++++++++++++++++++++4.4++++++44-4, 444.rn++++1+ I -,,,+t ...„.._"...B= ce , rs. ..,1--4.-.. /I LESS THAN -.002 BLANK I +++--313 - 13IEE0 BE=.-=-==n= I BB 4.,.-=130 8888.---6=6=E --==BEE88II II FROM -.001 TO 109.184 I 1 ' onnallBOBB3 88=3UPTATIE0EEEE===B-=-=+ t.,.. ==898 II I 1 8 =BEE0O88==0E00030C0001E60EEEEB= r-++, ,++- // I ' 0- 0110044CE00E= =E8=88=-=0 -*,,,+--++,+++ Il I I - d -E084C000E --+= + +++,+ i+ /I I • --+ +, --+++--+ CEO 0E- FROM 104.185 10 139.507 I I ' --- -+ -B* OF.=-+,---**1+4 +1... ts;T:111: li I " LI BEem E.-O. ---++ . ,+++-=6--, II I B1396.13o30e £3138 ++- -60B-B II 1 I --..q.....r.saj....3c.B0 BEEdB1313E000 £988 -+ B=1=0 if =000BEBO II 1 I --..,..9.-=.oar=d3o..-+---=BEEEBBOT000 3--- EBBB= i*t., + BE=EC8 It I ' ----BOOE1BEEBBIE10==+f -=BEE BflE0E383=-4-++=BBBE==+-.,,,-=EB+300 Il FROM 139.508 TO 167.817 I I • ===108660EEMECEO,": 4=-++-= FOOE OFECEEB33=,,++.*=BBEECE==,,,,+-- , -=0 I/ ++++.444.4.4++ I 0BIE0086040560E00M8E= -++=E08 EC8EBEE4 =4., +- EtIEE03-,,,+-5 +-=B II +4+4++++++41+ I 000e6550600e0M It 613B-fff=E0 EEE04EEF8 , -=B e0e00E.,.+-.--+=13E II +++44-4+4+44+4 I' 06680s00EC40000 003-4++=BEI RE00E000 264:ra".9 --=-t R88 II h4+++++1++4++ I ' ei10040EE98UCEUE E0C6 *4-.1; Ecoocoem ++++++4++++ ++ I 080806==d006883E OCEBC 13== OE 133860$ MilemMOSII II ncEE013...-++ FROM 167.818 TO 193.511 I 060E===136813=8BE BEI=BEE0011 00 880100$E13-- CE3== II I LIEB= ---=OBEEEEEEE qEEEB.31EE=- -- .EE III OtmeeeileeeeEo= EBB-= II I I BR ====65,3BBECeEE9300,4EEEU.39EF. ++ ==6 0888 090000060M, 11 I I ' ELI 803330EECE OEEB8==.36EEEEBEEOE +-*+++00000111 Militteemoo00EEEEB II I I • =8E00E808308 OEE CEFACE00E8- -+,,,-3E00060 10I04000e13eEEEEB I' / I ==E8OEE39====3CEE1B=== OOECOO 8F0-++I-,,,,++=.'3£1390 i CEE003==881= /1 FROM 193.512 TO 216.422 I ,-=000EE3=-===883033=38 0'0480 GOEBB==+,....++=BEE0 £00- --- B I/ I I ' ===EE0E0==-=B8•3==36B=B1 $08 ezEBEE5 4-880000e B--+ /1 I / . =-==11.-..-- 80d8===B3 13 000 £813 888 T=Baeteee EB £- II I I 988=-=3130 B6E8330 UBE EEE 8E0 43e153 .,, ..,+==E000E8+3388EE ==B=-, I I I BB=-=BEE =93 .IEE00E1= =3E BOJO ... . 83CEO 13-+:0==9 E3==- I I I I 03==CEE.--=8 B8Bdef.EEE6BH13E 0E30-,**-++ === -+-=-BE 0 EEC= II FROM 216.423 TO 241.944 I I =--DEB=--- 0 EEBEFGE0000EFEE3 e06Eg=f+ ------=- EMI EC II 050983;1030039 I I -- =i1==--- -HBEEEF00400ee0ELEBBEE0BEB= B0=---++ 9E0B.* 0000 CO II 04.M3688830U99 I I ,--== --- =B-BBOOE006MOOMOCECOEEEE015EE EiB.*++ 00E.+315 MOSE, • II 01583893133.3833 I I + 88=-3613=8£ 0655660000EEEEEEEE4EFE 04EEB-- OELNWEE /I 863118891363838 I =E1=- E06000 0000f)00000 ,= 3D3O331311R333d I I ;CEEECECEF:CEEE EE0E *4 0 0 xi1 I /IEEE 008608840005040000EBE EEEEEEEEECEEE ....*= E813-= 00000 II FROM 241.945 TO 275.845 I I c80 809000884ERo8HEETEEEB BOEEEEEB====-+ ,rf,,+-= ,---. 80800 I/ EEEEEEECEEEE I I 086 0680880064E00000ECECE==BOEEEEB====-+....,+1 -===,.+++1 @EBBE II GEEEEEEEEEEEE I I 0000000000000E.P.E0040EC13 -=BECEEE0-++ -+ +,+--+++++-+,- -,, /I CELEEEC8F.E8E.F. 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I/ FROM 330.819 TO 473.428 I I B.- --89££133-+++,r++--B1E1-+++,+++ = I/ 0e08088088000 I I 3CBI3==BLIBBE0E3=- -+ -++.. ,+ BBEI 0 II 8e58688503lits I I 803E.= EECE3===B1=*+*- ,, +++E08110080 II 8500800003885 I I BBEE=+*---,, ,+-145Meeelle9 If 6S(6D55<7158666 I EE OEBB == BB = 0805686008600 I I i 0 - - I,. 0 1 I+++++++++++++++++++++++++++++++++++++++++++++++++++++rtr+r++++++++++++++++++I I GREATER THAN 473.429 I 111111112INVIIIN1I I atecamoussa 4 I IN ------NVIN I / 0 10 20 30mdes INNIMSX#ASSIN I 1111110111211EIMENNNI FIG.6.2a I 2 ------HISTOGRAM or BA --VALUES- IN' PPM- HISTOGRAt4 INTERVALS ARE LOGARITHMIC -- X _ _ - 1+66 - 0.461E+02 * X • 1.06 0.562E+02 * X 0.605E+02 + X 0.836E+02 * XX 4.20- 0.102E+C3 XXX • 5.93 0.124E443 * XXXXX 9.61- _ 0.152E+03 . XXXXXX 12•37 - - XXXXXXXX " 16.95 0.22504-t3 4 XXXXXXXX • 15.94 0.275E+,3 XXXXX * 9.01 11.335E+V2 XXX • 5•82 0.409E+03 * XX • 3.63 0.499E+C3 * X 4 2.25 11.60 11E4-C3 * X * 1.43 0.7142E*C3 * • 1.54 0.935E+13 * - * 0.81 ii.1i0E*E4 * XX • 3.93 4 2. 40 50 00 100 PERCENT FIG.6 2 b ***MINCX NORTHERN b6LAND*CADM/UM A.A. DATA*PERCENTILE MAPS*** LON-PASS FILTER USING RFFCCIIVE RADIUS Or J. CELLS I++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++V I • •• +- 4.4.-4.--4.. . -4.4. ++,.,- it LESS THAN -1.002 BLANK i I +++ +++*"-".11* fTs","'TT ,T[r FROM -1.001 TO .019 I 1 - 1 ...... +rntl:"" 4- r . -:::: - I ...... Eil. I I ++ .Hf:i::::: 41::::-'21+;::: I! I 1 + 13". ,, +.i. +++.. if1. I I -- + +.... .- .8-....,0.---- FROM .020 TO .033 I ' ---+4... ++ ,, 4 ,,,,,++.--+-8...0 +4-=BBB- li I 8+...-=8E8r. if I ' Ofit14 44 4-B * ,..5 "41" . - I • ++ --4- ++-=BC= .I . II I I ++ 4-B8- 0813108 -==8= 1 ++ ,,.,-88®11£2.110=+,.,+==8=--, -+_ -+ ..,+ ii FROM 034 TO .045 I +-"8+ +-8- +--,++B*EEC88D-t+,+-8E8=..,-...... If +++++++++++++ 1I , ..0.----++-808+ --- -+8+-++= OCC 08 ••-•••BDB•...-•-BE +,,. It I ... ,,,+,:::;a08 BE 08-,,..++- =+- ++ E 801 D-• --4...+81,..++,+, V +:+:::+4+++++ I I ' 0B- ...... + +-.... =13 80008=,+.8- +::+. 0;1 ii 44444444-1444.4 1 I ' 1++...--= ,,==D-... COBC ...., ^=••+.+=BE 800000=+ ++44+4++++++ I I ++-4....-=88- mu.= +++ -+ .,-800 1188000== FROM .046 TO .056 I , +-B=+ .4...a.+++-.. ++.+ 4 +-gg 0000MOBBBC8=4; 1.= ff I i s..,=13=+ ,, ------II. .. 4,, 118 C00500ECE88=-= =.--,+ If I .. ...1-861e=6=4-+---+++.--58=---+ .. +.+ 4.--. 801='-+=E1,... V I1 I/ ++ ..+818..=1138 ,--•.++.00BB==+---•+ ++ ' -=8 +.--'-=B- - „. p ,..s. I I +1...+=88+0 +.-++.,-0 ==-,,++=++,. +,...... +-=- +4 r I +,.,,,+--+...,..4-4,,.+131 =-,,,+ -...4-....-+ +...++ . ••- ++ II FROM .057 TO .068 I I ...... + ...... +--+.,..-as ++„. 80=83=4 + CCEB , +++- If I I .....4.....----++++Eom ,++ eeeEog= ,,, +810 EBB=-t,, It 1 I 44 .I1 I ...+,.608 +=130==8 OBB ++ BOO CE=+ ...++ +....+*--EEC•1---80 88= I0 I - .4+0-BE .+- ..=+-,,. +=E1 E.,. ...+. . +B=8- BBBE---C £8801 Xi I I - ...0.-BEEB+++ 0.----=+++,+-8 83 +-++44++ '''-'"" 1381-.1=E 8 0001 T[ FROM ov14 1 I - " ...,-=8=-.- ... =...-...E1E88=-++.888 0011==++++++8 IRE BBC EOM 08 r 138301S10141300 I / ' ...++=== +++=8=8F0081=-=EBBBBEE801=4- ..+1---800 =8===C 15081 es r OBS3BOUBUIR411 t 6BBOOBBO 00333 r I . 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BBE=-•=0 BBB ..,++ ++++-B BEESC180001 80 BM ID 38030683:=81 1 I += -11 + 0 B. ..+++ 4444+ 81010400 . 8 - r, OM:K-100000080 I I B-4-.. 8-4.,, ...... 1-... -==C31011 0 I • 4,.. ' - 1-8- EM08- If FROM 2.045 I I ' ,.. ***14...... 1+-E3===0E888E n Ii...... ttiO4,4440, 1 r. eem”mtetc5158 1 . .0-4-, +BBE==B088 8008 100. 0 00000,metemeol 1 , ..0-, . =8BECBC8000C0,00010049041 P et.s.intr9v.tnt 1 I - ,...,• ..,+ -- .4+ 881,018001800180008000000 If t,”6653bOttefa 1 I . • .... 801C91088 B 08008810 I( I rif+44,++++++++++++++++++++++++++++++++Z;++++++++++++++++++++++++f+++++++,..frIc GREATER THAN 2.046 I [ PlitAttitiOr011 1 I EfONCOM11111011 I I rrfrtrrrrtttM I ..... U14112044 I 0 10 30mdes 20 i I FIG.15.3a L. I HISTOGRAM OF CD VALUES It, PPM 4 4 * 0.00 -0.356E+01 * * 0.00 -0.302E+01 * * 0.00 -0.2401+01 * * 0.00 -0.194E+01 * X * 2.12 -0.140E+01 * X * 2.12 -0.8151+00 * XXXXXXXXXXXXXX * 27.41 .-04314E+00 * XXXXXXXXXAXXXX *27.41 0.2270+00 * XXXXXX *12.54 0.760E+00 * XXXXXX *12.54 0.1710+01 * XX * 4.74 0.185E+01 * XX * 4.74 0.239E+01 * X * 1.11 0.2930+01 * X * 1.11 0.3471+01 * * 0.95 04 4010401 4 * 0.95 0441- 81+01 * X * 1.13 0,510:4011 * X • 1.13 I 0 20 40 60 ec roo FIG 6.3b ***MINX NORTHERN ENGLAN0wc0oAL7 0,R. OATA*>ERCENTILE MAPS*** L044-PAS FILTER USING EFFECTIVE RADIUS OF 1 GILLS 1++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++11 aa-+,, I/ LESS THAN -19.102 0LArvc 1 I ',JO* -- 4--....4, , H.- 0 I I '- ++ 1,,,, tttttt +++++++ + ++ -9--4-,-...... II FROM -19.1D1 To 5.601 i I t"feitt. ,,,,,,, +++++--9==++,+ , = ,, =9 ==-4-4--=- Ti I 3 0+ +++4• . . 1,,, -1 +I- 4 --3== 1--.-3E0== =,-. BER I-- II I I B=---+ ,,++ 4-4 +.88= -BBC=- - =9EBE09-=BEEE I 11,1 +1$ -==85899Ecc8==B=BEE, 009-=8E00e===8 "+"+"-4-0441. 4 4 ,,,,,, II I I +*...... , -000E805E0 14BE8EIEse009- =88589:- Ii I I--+++„ ,,, + 0@£81 -BEEF050 018-55E0E0--- FROM 5.612 TO 6.470 I +++,+++++++ 4.4 ++ - (4E9 FICEE0E0Eed8 E0EEE88- II I +++„„++++,0-4.4.0. ++,,,, -- 5 E=-BB 55E50 E CEE0000E8- II I I --++,„0.4.4.,,,4-4.4.0. +,,,, - EE --BF 11E06a 014E041050-- V I I I ==f- ++ 41,++,,,,+++++++,,+++,..,-BE0 wicesa 00060 ==9EeeeEe5t II I I 0=--++,,,s++,,,"---+++1++ ,,,,, +=00 EuE000 EEc00E04cE9 B E53850 II I I 0£(3-+ t+ „,+++++++-=--++--_+ *,,+--BEECE4000E89400005555EE088800 I/ FROM 8.471 TO 11,415 I I .9=-,,+++ 1888--+, -8-+ -+ BEE99c00008=1C00005E=BOE ==c0 II +,I-++++++++++ 1 I • --=--,+--==39===3EC3=-++-=9= -=Ee==-8 Ed9 00 =14:00E=-=8B8E -=8,3 II +++++++1.,+++ I I ' ..--41-,..EEEE00 3E 0E6-41.4-.9 -,-..--..E a 000 EjecoE= -00.-f=oe II 1-1-f1t+++4-11,ff 1 600==.4 4-Etetneel 0089--4---=E ,---+==5 0000ea0000 /I 441,4-44,4-4.11,4h I EE8=- BBB 44-1-4144.4A-1.1.4-4. I i • 433588==e0emegass Sete ,,,, = ++++,+=n 00E00EcE EE eee II I - -=.3888E00ese1eSS SIMS 3110 -+ ++-.EE E5E5005E 98 0089 I I FROM 11.4/6 TO 14.932 I1 I =888E006514meg CtsecE98+, ++,++-=913 EREEE00O£0000E 00E3= I =438E0eS5eesSess1ll ernsiaCEEE-+ ++ 44+ =dB 10000 i 8=-BEEsisilesessesseeelate00058 4.4. +++ --=B 0000E1E880E8- it I 498 89E011411124 els0e9eee540019000E 1 I : ++++, +4.4-=85 5£5E00005000EEE811 0£00E0==00.-- III I I - EOC==Eelissel 1mseeEE9 00E00000E9= ,,,, ,,,, --8- 0e8850000E8===-- II 1 I 0EB-=8011pienfised0E5E EEEBEE 0E6=,,.„ ,,+,+4---- s 90000008---- II FPOM 14.933 TO 18.662 1 I • 1110E.--.E40E05011M60E1000 E090J 0000- ++,,++++ O0e0EE-4.,+- 1 I 5E8=--=E0093505eacEzeme BEB e0e0CG= , ,+++ +Kee e00E=+,++ II I EE5C4138c BE0000cEe 60 ,++,„„,++B001 EE 00EE1.3-4.4.4 /i I I eeE 015001003 1 I BBEEEECIEE BCECEEE 804 aEE Mee 11005 ,* ...t,,+-00EE=EEE0Ot 01.0==- I 1 I B30=09EE 0E8 895'3e£98 =30 00.'0 .. . 4-*-=5 11==E0r0E 00E3E II.I " '''' r I =-++-900600E ,.+E4989E5E9-==8 00EE-+++ --- +4-- ==E0E5F. e 0000 II FROM 18.663 TO 22.453 I I +,,4=86080 9 ===1100E1.E839==8E 00010=-++ -=- - +++ BEE 000 Be II BEIM31011J3331 I ..,-=OFEE 000Ec00e00000900cEEdeaesee9 99==-+++ 000000 eaCE 05 II 1 I .,013E0010see0015040esea000000E8e0e30EE ===---= se00E00 00898 II 56+11030U43133O I , -(450000000 00Bee09e0000eEE4001E59 EEEEB-- 000EO00£EE5 II 131133963NTUBti I I +-.8010e808 000003000000e0E5E5040898 5555 == 55000E19 3 II I Mi.1103LOKR113.5' 1 I -==. 000000001e0e909e0000E ECEECERB3EEE0 ==-=EE eEEBB +-05e f t FROM 22.454 TO 26.829 I I -=E 0e00900006800e0000018 =90EEO8.==3E183 £00-=3EE BBB= --BEE II EEREEEEEEEEFE 1 I 89008550EEE000000ele900cE-4-18d5E9===983-*===--=88E898= ++ II EtC8EEITEUFF8 I 1 03001160PEEE000EE000000E ++-8BBEE8- =Eori- 4.4-=888808=+++ +,, II EEEEEEEEEFi'Ei I 1 000 *00 BEEEEEE80000058- -300E9B=HEO@E- +4- .0989E.+,++ +, II EGEFF8GLIACO' I I 00000 BEEEC55N3333EE=- =5£53===E1111E013=-f++ = ==6I -+,++ - I/ 5EEEEEECEEFEC I I EEEE EEEE3...E00E==-=+-+-----=E0eEE9==-++ === ,,,.+4.--=0 11 FROM 26.821 TO 12.925 I I 588== 00055=-500er= =-+,4---4-*-=E93-===-*--8==== 4,013==== II I I -- £008E1 08E40 =+,,+++4.4.-.B=.4.4.- -4- c. II ggvAtm I I 0000E5 00E +,,,,,f++---4,"+- ,+-B ++ 06 000= T. 00014,41348 ,3 I £588 + , e II oatio00,1**01 I I + II 05 + +11.11 ,, 68 I. 850048084040 1 I E=.4.4. ++++.--=.-+,,,. ,,,44-=++ 8 I 1 I -...,... + 11-1 II FROM 32.906 TO 46.835 I I === 88888=-=E00c3=-++- + , II 558005E1058600 I I 8 6108838-=E00(5588=-=-+,. ,, +++. B II 1080100868058 I I E03CE4 ebg60E1.£f.B=++-1=+„+-888=898- It cecest5ele!..nano I • es tav,t,toelmln I I .. 0505 EE 080 EME-4,59-0--DEEBB..+4- 05088005851500 r I e ea 0E3 S0-4-E8-+ C EI£BS=-, 11 1 GRCATER THIN 45.935 I / !IMAM ,,,,, I I IIIIIIVIVI441411 I I ,,,,, 41141114i I I ■I4AVARKKIKAX I 10 20 30miles SKIRIMISICIA4, FIG.6.4a I T ' HISTOGRAM OF CO VALUES IN PPM HISTOGRAM INTERVALS ARE LOGARITHMIC X 0.589E-1/ _* - 7777 - -- 77- * T0.24 7-2-777 0.116E+10 1 0.21 0.229E+60 * 0.11 _ 0.452E+00 * '0.3 2- 091E+00 * 0.88 - 0.176E+4:1 * X 2.01 0.346E+01 * XXXXX - * 9.67 0.683E+01 * XXxxxxXxXXX * 21.18 8.135E+02 * XXXXXXXXXXXXXXXXX * 33.47 0.256E+02 * XXXXXXXXXXX * 22.30 0.524E+12 * xxx * 5.89 0.103E+13 X * 1.77 0.204E+03 * • 0.43 0.402E+13 • * 0.13 0.793E+13 * * 0.08 0.156E+04 * * 0.00 0.309E+C4 * * 0.00 4 4 4 4 4 0 20 40 60 80 /00 Fa64b PERCENT ***AINEX NORTHERN CNGL4ND*G1P1'1 R 8.P. OATA*DERCENTIL6 MAPS*** LOH-PASS FILTER USING EFFECTIVE RADIUS OF 1 CELLS I++++++4++++++44.4. 41, 44.144.4i4F+++44+++++++f4+4.44.1-4.4.4-fft4++++++4+4.44++++++444+1.I. l 1 B=-+,, ,,,,...... --+,,, , -,, ,,,,...E if LESS THAN -5.002 BLANK 3 I ..** 4.4-4-,,,,,,f444f++,,,O. ,+++ + 1-;rf: Irf FROM -5.001 TO 4.913 1 I ,,, ++,.,++-+++ ,,,,,, 44. I I U 011.-t--4,. ,„+++,+i---4, 4-„,4--4.4444- -.- +-BCC II I I 61£8e£ 0..3e.-+„++.„4-4. ___ _ _++04---++++0-.-+++=10 r1 I I £13=r1==+-+++38D--,,.+0-, +1-4++ BE Ii I I ---++++++-E00=- ,,,,, +t=1E---- - ++,,,++++ _=B 4 ] I £3 4`=--•+f+-... ..+,,,,.0..) ....4. 8=-+4,++-4f i +-_-- +--=== IT FEom 4.904 TO 6.555 1 I £8- 4- +4.4---f,--4..„,a---. ..1-.--+++==-4.4.--++„ -4.44.-=== It , ., . I I £88 - +.----++ +++-- . ,, = , ___.... 4 4.- ,,, ---- II. , 1 I EEH=++ +++++-++++„„+,-+----, ...... 5 --+,+ B---- II 1 I BB=r+-+++ ++ ++,,, ++,+ +++ 1 , , 83- =0138BEB= V I I 0E.--+,++ 4-4-4-+-0= 4-4- 4-44ra 4 m.4 f =BUBB= + 13=- Ii I 008=-0== ,, ===0,===BBB==-==BB +++---+,+-=B_ =B= _--=0E_ __--+++- I I BE- ___ ,..,. fl PROM 6.856 TO 8.854 1 I - 0830=EEEEBEEEE£04ECB--+-BEE8 ==8==--+,,.:7.- EETEIER M4+4+44464+ 1 I ' OCEB6=E0E04040000004E-++=D0E -=E +++--==B .,0, II .411.4.44.t1-11,4 1 I ' 00£E0c9mom5M01 ea 006+,0DEE -=BE=--+- t Mog;;::::,,+-==-.+- I +++++++++.... I I loo£ocEcote5mace 58E= „-BEEF 013=+-=3 1 1.1.41,4A-1-1-4144f I I M100000000emoifin tewl -rmni -0,1=.4==B ---BEEE= =8 -+ _ I 14,44.144.41-41.+4 I " Coeepewooaomtnes gme'm =- +-=BEE 1 - 88E .=EEE8=- ++ 04+ r,I FROM 8.955 TO 11.913 iI I ' 4tect(5atomegAll sm#4604iall8= -0.388E13 +-=0/31313E13813=++ +++f- I I I - Ei000ti9”6osillimeall le45980 8e£9 -- -== EBB -=BBEOBBREE8-+ -+--- 1 1 I IS 0808252.59 BIWMAIM000ept000000 -- -== 9=== 009E0==0- 1 1 I - Re 8E051111151155 4e55t88£0800e00480 E==+,.-===BEe IL 1 I - itsE=Semassile 111501146E 00800000E0E 1 -...."0.__,_=,c EER=M:a1B-- Ii 1 I saa=80191atw)DeginalimsoJo0 88£88 000EEL3=++++,,.+-B8B 0 =FIBEOEE0B/3=5 IT F? -HISTOGRAM- DF DV ---VACOEs-IN PPM HisT0GRA14-1NTERVALS ARE -LOGARITHMIC -+- X - - 1.71 - 0.177E+01 * XX 0.227E+11 * * 0.00 0.292E+91 * x --• 2.19 - - 0.37 6E+11 * X ± _2.71 0.483E+01 * xxxx -8'0E4 ir.621E4I1 XX • 4.55 0.799E+91 * xxxxxXx * 23.72 0.183E+02 * Xxxx xX 4" 11.12 0.132E+92 * xX Yx x , 9.80 0.170E+82 4' XXXXxx --_ - . • 12.89 0.211:+82 * XX XX XX 11.42 0.281E+92 * xxxx • 7.91 0.361E+12 * xx • 4.33 0.4641+12 * X * 2.90 0.596E+62 * X • 1.49 0.76q:4:2 * • 0.84 0.946Efr2 * x * 1.30 • * • 4 • • * 0 20 40 60 80 100 rurcoT FIG.65b • ***NINEX NORTHERN ENGLAND*GALLIUq D.R. DATA*FERCENTILE MAPS*** LOW-PASS MICR USING EFFEOTIVL RAOIOS Or i CELLS /++4.44.1- ++44.4...4.44 ++++++++rfirnfrt+f++4tr+++++++++++++++++++++i++444.4++t+++f++11 ...,: - I I .14 +4,,, ftf41-444, )44 V*40... LESS THAN ^32.802 BLANK I I -+++++++++++,,,,++,,++++,,++ + -- I FROM -32.101 TO 2.542 I IT B ++++--+,,, ,,++++,++-++ ,,,,, 0'4'0'0', +4+ .,,..■ # I ++----+t r OEECOO +4+4 - - 44-.0,1.4,441, ,.,+..+..,+.. I I EB.B..+-+t++++++ +-+++------+,,++-- -+ „0.4„.04. n I I --++++++++++-++,+,,,,+.38--.--=.3 ++++++---+ ++ II I 1 =2 ++-++„,+++ ++,+,„,+=j == ,, = ++---#.-+,.++ .,+++, II r =....4. I FROM 2.543 Tu I 4+++4++,40.+4++++,+,,,f+.1 - + ^-ft+-"tt tt.t.+1, 3.027 1 I --++++,++-+++---+++„ ,,,,,, ++-=C -+-== -• - f+ r I ' £3.4,04-4.4,..4.c+-==++++ -4 + 4 4 I ,,,,,.,, 4-.EIE --=3 ----4 n====ii--+., # I I EB.+++++++-+++ 4++ ++-0E4 =0000= ECEE0 000ECEFB--- 11 I I - 040r+f++++ frr ++++++++++++13= -.330= 13ECEE000CE6 E0B--- I I I opc..--+++---+++-- +++--+,+-.R1==COOCEEECECE8==00C=--= I I I 803=4- - -1E0-- -0E0- ++-==-+,+-=„33BBEBEEN3BBBF,B.-.=8 +++= I FROM 3.9213 TO 4.431 I I * ==0--+-==J3B1==80.E4 , 444-4441-“4+41. I -565 +-008=-4 -0i 13 5 033(18=-++---= +- 11 +++ti-f4L+++++ T I ' = ,,,,,, = EC0000 CE 00F1 -0E -+-=3=--- 0 EEE EEEBB.,- ,,+=8=- 0.-- +4-40.144+++44f I (1=0==--950M5M500 5556====0E6 + 13 CECOCEOEB= fri+tr+++++++ 1 505010065051MM MOMM ==-=0 +---++=03 073=3E0D laa- ::= .44.4-.4.4-+1.4.1.rf ,,,,,,,,, I ' = 035550000102101 emir 1303 .- 4.4.-=88 --BUEB=- • BE5E6mogionlams ummE50.9== -+,,-===80 ==03E8=00ECEM -"-- FROH 4.932 To 6.775 i 9ECE41000001011104 000165a€:5000 -- -== I 1 4 + _.... =113 808BEEBBOCC0== =-=-- # I I DO EE00051050000111A4011040Me554 - ...B 0000E- --- + I I ' 00 3E6noswill50 Imeamma401015M5S00 =--++,--==830 8==BOSOE II I I ' 055,150(0101110 *00011015M 001001500r.= -4,1,,+-+,--.- C0==C0000E0= - - I I I ' 045=56000201100110000550 learn e550--+ + -4-F4- 15 501406E0=-=-= 1 I I ' 0005=350110w550000214500 011040 05550=4-1,..++1 0-4- t - 6668=-4_+_= I FROM b.276 TO 7.773 I I E0E0oC400000001105110555 CIO 65050E3 ,,,r-++„t,+-896 5.--++,1• I 1 405455E0 951115505 55 400 5555555E .+--+,,,,4 f-=5r.4 =3 0=-+,,,+- II ,,, I I 8EE00800E MINIMS e0M 1155 Ott 1051 .41- 1-=33E=BBEEEB +,,ri- II ... ___...... ____ 1 I - £5555655 ENO 05155205E -00 5040 ... . +41--- -=6C000= , 4.-- I I 08==8EOSSNIB -.05/155855==05 6445=444.--+ 4- 4- + 61366 E8= 8 r=== 1 I ---=E00/3511 5 FROM 7.'772 TO I I E CPS 005 S4E0DEE4 04M1E8----==+ 1-4-4- E80 8== == k oBno983993Sal 9.742 I I 10- =GINION 111194004,M4560Mdm044a005§E8 39=-+++ 4- 555005 E£8- =- li T I ,++-E0SSOVIIRIBM8MOMOSS0004040006040E 3=----= OSOOCOO CC.-- - It 114=121 8 I I , =565000050 0555000040000444501055 EMBEIB== *6EEEEE888- 33 gEIR4A3413R,H133 I I -39E0000055 e55505445455054550544EEE CEEB 33 EC5EC88 = 3 1 aBG03a3063033 I I =GEE IIMMMMMM04000M0000608'G cE05EEEEEEEE0 BG8=.8 EBB.- I 1 I - 9.743 TO 12.348 I E00 eltimppa5m0,36880000E 3E5E5E3883=3=3 8030===8 8==- ---++ II FR" EtrrppecErc5r. I I ' SM65085500015S041050400008=OCE33830 ‘:ErTEEE/527,P7. I I ' [email protected] ==BEEB3MG====------:2P-27: :1, -1" I £CEEEtt:EFALEt. I I 550 II! EU00MMEEEEEEEE== BEFE3=BOBE89==== -- f--=138..8.+,„ -+, 31 ETEEEEEECEECE I I oases EMOMBEGaBBECEE== EEEE===08E80 _ _ _ ,++.B.-+ 1 7.CECEEEEE2E2e 1 I 5131313 000E3==013E80==- 3=388===B8B8EE==---- === ++,++===- I I I ' 0000E MOdEEMBGECE0== I FROM 12.049 To 14.577 I EBB-- --- + - 33==8 --- 000duomdt,o006 I I EE OB#MEE EMMOO 0558...---.-.+++-++ -3....---- EB==== i gooleo,4e,),. I 000E5E0 lite 033.-+ 4- ,,f+- +,- 8 + EC ER= II ... 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XXXXX * 10.45 0.752E+I1 - - _ XX XX . • 8.09 - 0.90114.01. xxx * 6.93 0.105E+C2 XXX - - 5.93 0.120E+52 XXX * 6.01 0.135E+02 * XXX - • 5.66 0.150E+02 * XX * 4.68 0.165E+I2 * XX * 3.74 0.1805+52 * X * 2.54 0.194E+52 * X * 2.17 0.209«+t? XX * 4.49 4 * * 4 • 20 40 60 81 1.10 PERCENT FIG.666 ***MINLX NORTHERN ENGLANO / TRON O.R. OATA*VERCENTILE BAPS*** LOW-PASS FILTER USING EFFECTIVE RADIUS OF 1 CELLS p++++++++++++++++++++++++++++++++++++++++++++++++++++++4++++++++++++++++++++11 1 444,,. ++----+---+,„ ..+- +++0- ,11 L1-SS THAI) -.902 BLANK 1 I 4-44,+444.1-. I I „„..,,,,,,,,,, t+444,41-4.+44..4++ii. IT FRum -.001 TO 14558 I I , ,,,,,,,, ,.1,..+++++ 4- -f-4+ +++4- ++,i++,++ /I 1 I ++-1.-.4-14,,,+ + 7 .....- ,,+++ 4 I I +*.■,+ ,,+.+ ,, 7++ . +0---+„+- u / I + f ---+ 11 I I + .... 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DATA.PERCENTILE MAPS.** LOW-PASS FILIER USING EFFECTIVE RADIUS OF 1 CELLS /+++++++++++++++++++.+i++++++++++++++++++++++++++++++++++++++t+++++++++++++++I I 4+,40.41 + + • -...... += I I 4-44..4----44. - 4-4 I I ---4-1-4-.4+ 4.4.4.4-*- I1 = -4••• --.4-4-4.44 - I - I'I 1 I -..-+-= .+++ +++ ++++++=-==19===+-++-01.1099---== I LESS THAN -.002 BLANK 1 --+---....++4....4.+++.4+4.4+-+ ____ ----0 --- -=.000=-..=. 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I 8086800000600 1 I -.13. = = " --...... --...- 0 8 ,1-•" I I 86=-+ + .+++++++ ..+-...++... = I GREATER THAN 193.212 I I 0-f. ...+++.++.„+-==-+++++++- I VOIRSOROIMIRO I I -+. ++++++....++++--+++++.+-+ 8 I mutimmismalms I I +=f-++-....++++---..... +-=9 8968 6 I 1011112401181114 I I -=--+...... ------m=380818000- I 5821188888888 1 I 336 _ .. .. aeleeeeeee I sommemimml I I 8 +- .+- =-+-=0-== - aaetammit i I 1+++++++...... +...... +++++++++++++++++4....++++++++++++++..+++1 T 10 20 30miles FIG.68a HISTOGRAM_DI PEI VAIUFS 1.1_ Pp 11_ HIST °GRAM- IHT_ER_VALS-ARE-LOGARIT TMIC- - -X- - - 2 - I:1.320E1:Di _ _ 4. 97 0.436E+01 * _0,593E+91 • 0, 8 07E+ 01 * XX - - -• 211 04110E4-02 xX XX 7.15 - 9,149E+ 02 * _ XXxX x X -- 0.203E+02 * XX xx xX * 12.40 - 0.277E+02 • XXXX XX 0.376E+02 * Xxxx Xx *-12.21 0.512E+02 * XXXX - 7. 88 _0.697E+02 * XXX * 6. 77 _ 0.948E+02 XXX * 5. 06 __ 0.129E+03 * XX 3.25 _ 0.176E+03 * X * 2.44 0.239E+03 * * 2.49 0. !25E+ 3 X * 1.94 0.442E+03 * XX 4 3.57 * a 4 * 0 20 40 60 f0 100 PE prt NT FIG.6.8b ** *MINIX NORTHERN INGLANB*LITHION O.R. 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FR" 8868588085880 I I +.--+, +-+++0000E8-=E00EBBBEEE001400E IT 6665858585800 1 I EE ,,,, -- B== 110008==OBEE8=8E0S000E8= II 0880E05003806 I C --, 80508515005000 I I I, 011+-=OBEE = E0000E=- IL I I++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++II GREATER THAN 1.7;72 I tsimoilmirigs* ****12640**** i I ------WIWI 0 10 20 30nkles I -7.100.11118=11.111 I mmailosesomm • FIC.6.11a HISTOGRAM OF MO VALUES IN PPM ' misTOORAm INTERVALS ARE LOGARITHMIC Xxx • 5.62 .1006.00 0 * 0.00 .1586.00 * Xxx * 5.23 .251E400 * XXx * 6.96 .3986+00 * xXxxxXxxxx * 20.73 .6316.00 * xxxxxxxxxxxxxxxxx a 33.29 .1006+01 0 XXxxxxX * 13.95 .1586.01 0 Xxxxx * 10.48 .2516+01 0 X * 2.15 .3986.01 0 * .87 .6316+01 0 * .45 .1006.02 * .16 .158E+02 * * 0.00 .2516.02 * * .oe .3986.02 * * .03 ,h316.02 0 * 0.00 .1006.03 a O 0.00 .1586.03 * .0.00 a a a a 4 0 20 40 60 60 100 F106.111) PENCENT • ***WWX NORTHE,04 iNGLANO*WCKrL 0.P. 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EEBEE00tMMtM51506 C000EEEE9=- -+ +-- 338 88EEE686EEEE8. 88388 k I -- asettimoot 80t000=336E0000E9 ==-++,----8E0 888E900E8 - - V I -=08015E4t00 0d40E8-+ 88CEEE3---- +++ :,-,t,-4:7 : Emlocom„.... ii I BBEBIEt0t900t11040EEd== 93E3d= :4 .2 - (5 I +==898E001:3330000EC6=== 8=3-- =3E06=+.- „,+1- 4- 4„++- CEOB=-++,0- It ER0H 21.240 TO 25.836 I B=88=880EE--=E0E3==3=== 3E8 EE009E3 „++-++,.„+-006 . I ==-=BEEC --4EE===8 +4 EEO BECOOEE3 .+--+ ----- +-E960 EE Al2B:1:1; il I E38E6E0-+ 41-0. tto =Ed etc): .++ stel,0- =E0EEB000000 CB= -+ il I E333== -+ BB= ---=8CE8 --= £CEO ... . +-==8 ==6000EE ER. 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I ++--OEEBE0065RetSIMMatt03=d060t0000J9Eql- - -OEM= - ---++ - ErEEEEEEEifrt I ' +--=EEOEM.MMSSOtMENREMM0 ==E850)55@FE=:0E1385 8888855--+ „ Zr EE.F.EfEEEECieF I --8 000 otommotttetetego Ettemooteetoo3n=--+-=sEumes-+-- -4, V ECCCECEEECZE f I =8000 toommotatotellEa ottmateettetocEo=-++ - oio +, ___ V EECEEEEECE;ECf I =3EE 01.0t0T3E000EE66-8=0E0EE0001$0003=--++ R6B „.---5 4 FROM 38.649 TO 46.641 I ----3E tatmoo=or,em000 6===EEE33E00g8-8==-+--6986E =+-t6=--- II 892113899013 I . -8 8888§8 E==CE 8--=88833EEE13 =4 83=688=-- EBRBEB It I E055048 -88 - +„++- 4 --743 EE 00E3 Zr of,44800V)1-1 I =EOM £ B +- .+ - _ +,,,,. +-_=8=_ + £ E8 Ir 004350d*Oug I BEE03 _ ++++,,, ++-_=8= E II §0000000a0”0 I EdEE +- -+,..+-=8- BBBBA= 1 181 FROM 46.642 Tu 58.265 I 000 -+..5=-+++-=13=1-19 t. • It @levsteeeP,s115 I a BEEE8,18--=338- -- +, 1111+-+. = I/ Ott8S8t8888,8 I 808EE0 0E36====8.6=1--=E=-0.+-0E0=--- u stmneemmetf,at I EE Ban EE 0E= ==E8=+-30E8----8E9E8-++, II emtemnmtoset I £ == £=, os--Be-cO= 6 68EE6-,. II betttaS6tM5t0 I+++++++++++++++++++++.++++++++++++++++++++++++++++++++++++++++++++++++++++++Ii GREATER THAN 59.767 t I t ....I 0 10 30mies20 I kososseatily I NENWEMU= FIG.6.12a f filIMUNNIM I AISTOGRAH OF _AI__ .-VALUES It *----0. 27 - 0.04- _ -.1.426E+01 * _ _ - * XX * 4.79 _ 0.750E+01 * XXXXXX 42, 59 - 0.135E+02 * * / 6. 32 - 0.194E+07 4- _ XXXXXXX * 13.18 0.253E+02 * -.-,--XXXXX * 10.69 0.313E+02 * XxXX 8.50 0.372E+02 * - --Xxxx -7.09 _0.431E+02 * _ * E. 44 0.490E+02 * XX - - -- 4. 41 _0.5495+02 * XX 4.82 0.609E102 * 4- X 2.E0 _0.668E+02 * X * 2. 00 0.727E+02 *- X - 1.41 2.786E+02 * XX * 3. 00 4 • 0 20 40 60 ED 100 PE:qt.:ENT FIG.6.12b ***MINEX NORTHERN ENCLANU.VANADIUH D.R. OATA*PERCENTILE MAPS*** LOW-PASS FILTER USING EFFECTIVE RADIUS OF 1 CELLS . 44++441.4--4,,4 LTSS NAB - .002 BLANK 4-- --4.40,,,44,,,,440+4444-444444.444 +4 +-44444.,,,444,,444,444+4+ FROM -.001 TO 8.052 I M +-1-4 + 1 0., +11+++,+ --1,9,t).0-++++, ',I .,,-- h ------I OEBBEE 4-4--44.4. ++ 4*...4,4.41-,,,44.-41.1. -- 11 I 6.-=--,++++++++ 444. ..114.4,4-.41-0-4^...- +4+ + 4 ..- 11 1 4+,1-,4+44.4. - 4- 4-4,- -4,4+ - 41. V . 4- ,4 -+ 4.- .....4.4-, ,i.-...-.4.-.■....4 4.1-44, 11 1 4... g,44,,,4 FROM 9.053 TO 16.780 I -.4.4.0-0.44.41.4,,,,4.,-....4„,0-44.3 ...1.,,.,,41.4.4-0.-..4.1., „4.4.■++, I I --"+"4-+-+"--"4.1-,,..,..**,-.0 -++-+ +-rr, + r--r--=--+ II EEO+++ +.----++++,,,++,+,,--13. +-.13 +r--- +++ - -+- II I EE= 4- -B. ++++..+++.,,+ =B BBB= 050=B 13= 11 1 000.4 .- . -4,0 _ = 000=- 50030005= =8= -- V I 00E5----+- _ 03- --B= +„+++,-.00.--.35505580=.--*--5-1-= 11 FROM 16.781 TO 22.575 I BOE0==3= - ENEEM. =HEE. ++.__-+, ____ =60 **++- ,,+- h 414.1411444-444 I BOB===35BU0EECWOO5JE===3E00 +-E4ED=- =53 =5 +I..- 4,0 - II 44441-4444-44-44. I BB- -BEE0000 00 00E9=- ==EO -4-.3BIBB a 0330 (1.9..-+..1.-..-,,++ /1 4.44444+4.44414 EEEBB=.3E0050/111 OFT5E0....Bes 4.-..=BEE Ell3=5EEBB.- r=0=4" 1 44- II 4.44.44.44.44.4144. RECCERF:0080808411 MA ====8 +--++ -BBE EBB=EEOB =El -++ v 41444- 44444444 1 BBEEE05M0t51008.0 00180 CE9 =- ++=BEE ==E000E= .. --++ 11 FROM 22.576 TO 29.345 . EEEE00000000801 1100150FEEEBE ++,-,_.=a0 =00880F.0.00==------li I ' BE 8E0090088000000 aeme0e000RE .- -== Bac BE00140EEEB8-- =-=-- I - 410 BBE0001800800001000880008000 -- ..= ===e 000E8=-0- itAl I - 00 B8E0082000 000110000008000000 E33 -- f--==EEE EB=UE00E====-+-+ 11 I ' amEosE0088 ee 0matimmoo 0e/40008880a L=.4, -4 -1-8==. 0E3=5EEEEOB=--+- /1 I ' 00,7.9ecoot80008886300800 000000 1100000.3++„,..-4+++ 6 BEEEEBB=--++ I'I FROM 29.346 TO 38.286 I ' 000EBEE00E00000000044 00000 OPOOQE= -+,„++„,„+ BBE8=--++. 4- II I - E0OPEEE00EEE000800019E(:E 080 1400052 ++++-+ +BEE 13.-+++,., Ir 00000efu 000000000 03 SU 111111110.4E r+- r ++=BEE =0 B.++,+,,, II I BEE0085C3 8000000 0E6) *gm OMR 'WI +-- ,„++,+-===a0B00000 +++++, /I I EEr.£EdEI3 008 000000190 =Eo oaEB ++, . ----- __=ELE== -444. j1 -4+ I B3==BEEE0005 5E000200000800 003E8 =BLEB== = ---- It FROM 38.287 TO 48.767 I -4=0E0000 O 0000880000au.008 0000E00=-00- +44 BEE =-- == I/ BM1 3 303053518 I ..-000800 0011110M000011140000M000050080EE EEB= -+++ REELER BB= - == /I 0BT3d30003331 I ,--=E0881111114111188115511050,00000080S,80@ ED- - £U1C1,3E0 BB.-- + II 003003I030900 I + =0088101188 800008808800/908s088000 0E3=0== E=8=9BBOBB - II 0033838U09030 I -9BE00111088 0O5508mo0000oto000090000 000= == =.080.= B 5 IT B003838008003 030,3 imarseet000m00,40008oe e001=0eaa0ace -- _=BESB Ii FROM 48.768 TO 61.871 ROO 616215e04000000008080 00004PEEBEEB------BBE03 If EEiCEEREEEEEE I 0001111m1000400190doe880000cEozz.:E0133a- -+ - --- -80 £00== If FACC£eEeU1EC (160411110000000000088880 OEI:000::05==3=, -= ------33-- II EcEF.EEEEC£LEE add III 04000000000000CE E000EILI3EE933- - II CEECCCeilf.EUA UMW.- 00000EiEr200000EE E005E3E;RE33811B=-- - +++_-- - 4 IT gEL0EECCEECC4 I 0000 000003E004EECEBEEEE0==556.=BE= -+-== --- ,,,=--+-- 4 FROM 61.872 TO 77.703 1 00000 00000E1E0000EE 000EEE5==3B.- +*=-+++====--= -++18--+- II 0000000001000 00 08000d £0000 000EER +++.-++ _ 1 0100010000000 I 0000000 ONO 090-4- +++=== 4.--=-..4.44.44- == 13=-+ IL 0000000400*0 I 0000 E 0 II lea-++ ++ -=a f __ , • = =- V 0030000000040 I 00EBB -+ r - B a II 0000008000000 I COLE ----... -- .- ---+ -88===9B=.- II FROM 77.7,, 4 TO 95.891 I OEE B===3= --=== --- =01310=308=r3 I/ 0880808008550 I 0 =0580E9------BEEEB=90 EBB= 4+1 = II 0688588882085 I =8=813 8803==3BEEE9BEOEBBB------I/ 9880600080100 I ea ======EL= BBEE5==0006=5==-=13==-+++ II 8888688688000 I 0 =- E=- E3-=00500 B +., II 00888888808 T8 /++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++4 GREATER THAN 95.492 I ------%NUM KlifiRstolfelsVit I FaCtraitettliti 0 10 20 30miles 114188881111441 _30111010111101101=1 Anna HISTOGRAM- OF -VALUES- IN PPM =0.-245E+12 * • 1013 -0.157E+12 * -0.689E411 * - - X * 2.57 8.192E+Ci * - - xxxxx---, • T-9:5 8 0.1137E402 * XXXXXXX - - - 13.59 0.155E4[2 * XxXxXxx 11" 14.08 ----- '0:283E412 XXXXX -1* 0.371E+12 4 XX XX * 0.23 --- 0.45,1E402 XXXX * 7.17 0.547E4E2 * xxx * 6.96 0.636E402 * xxx * 5463 0.724E+02 xxx * 5.17 0.812E+02 XX * 4.36 0.q00E4C2 x x * 3.82 0.188E+92 * 2.30 0.108E413 4 X * 1,92 0.111,0+03 xx • 3.98 4 . 4 20 40 60 80 100 PERCENT FIG 6.13b ***MINEX NORTHERN ENGLANO*7INC A.A. DATA*PERCENTILF NAPS*** LOW-PASS FILTER USING EFFECTIVE RAnius OF 1 CELLS /+++4.t++f+4.+444.-+4.f...-f+fm++++++++...... tr++4.ftti.tr++++++++++++4+444-++++++4.4.4.I* / I +++== B1==-=BBBB=B= + EON ----= /I LESS THAN -1.002 ()LANK I I ' ---4, 4-...... 4.-=-_=B=B3-- --B=BBB== BE=8 1 ..... 4....=.33.Bwm=___,B(1...... n co_ _ tm III FROM 1..001. TO 36.527 I I ++++..+ I I • .+....+++... + .... =B=OBEF=---^=3E EEOEB=BBB II 7 +::1::-.....44 . -f2... 44. ++-=13EFIEBBEEB=--=BBE--- - EOCEB=BEE II. I 1 : -0E06- -BEEB3.=808 B= BEEFEBBEE II 1 I ' --+++++++-=0E8=-4-444--++=EOCB--=8 BEBB=BEB--- -BBBBBBBE I ED =---4, 11 I ' -....+4-- B-+....-+-+ E=--- =8BO=600- OBBBBB £E II 36.524 TO 54.357 I I " enr.....--45-4-f+4.f+-4.1...,-.44-1. BB -----133B=BEE+-=B BB8BBEEE Ii FROM 44A-1544.4.1.111.44- I ===--4441.--t+44..*-+++..+++-++-3E 8-=88 BBB=B - ECEEFEEFEE1 II ttrir++...... 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II I EGO@E001500081811008180000CEEGEOGE9EEEEEEEEEBEEEE==n6EBBSBEB 111440431 II 0000008080000 I 1000082000000 1 EE00009000000eMeeS18800 EEEEE0E0EEBEEEEEEEE0E88BBBB68EEOBE B== II 0003021 ease I I 000 800 OEEE000000000008 EEEECEEBBC@OEECEEOEE8==-=8BB=BB 88= II t004000400000 I"- 08600 0000000000008E11 EEE 0EE 0=88151300000EEE E 6.= 138503=8803= If I EEE0 E5E0C8=0E0EBB=B=FBFB83B8=8EB69EE060E 000 EEBOaBCE£ II OBBBC 000000==8E0C-= BB001883- =B=BBEECE00A0/041 Seeee0ECE "" WAg44;g644304.953 I I =B EE0000 OBOE B=-=B8=== ---- ==BBEEE00.0000EllesS 000000 I' ...,..,, , • 7 I - E000000 EEO =080===-4++--==80 8E01000048e Vs 0E0 II 8t8.8.,.868;i886 I 9858tnrytioe55 1 I ' EEEE E e BB BB-- 4+ --=B BE000000 0 il CE II 086'8059885080 I OEB=B ==----+++--==B ==898000 0 I/ 1 I ' EB== ++4---=BEEB90000000 IT GREATER THAN 3n4.994 I I - 8. = ===-4.88+...+=600880800998 11 IT vglimvvillingiv I I • = ----444-+...+=B80008849 0480 Sell= £ II 180 ----- *WI I ' ---+++ +...+=8BEE0stelleeeeeteVee000E I/ ------10,12 I i ' 80 ..++ -- -+4 ilikeiliwalseolin r I BB01,000#500000,0C0000,000tE!I II KNOMO ---- O --- r I+++++++++44++++++4++++++++++++++++++++1;++++++++;44.844+4=+44,=1:+11.14 r 10 30miles FIG.6.14a HISTOGRAM OF ZN VALUES It PPM * 0.00 -0.506E+03 * * 0.00 -0.421E+03 * * 0.00 -0.336E+03 * * 0.00 -0.251E+03 * I--; 0.00 -0.167E+03 * * 8.00 -0.818E+02 xx 4 4.27 0.301E+01 * XXXxXXXXXXXXXXXXXXX * 37.44 0.8751+02 * XXXXXXXXXXXXXXX * 29.81 0.173E+03 * RXXXXXX * 13.32 0.257E+03 * xxx 4 5.59 0.342E+03 * xx * 3.24 0.427E+03 X * 1.79 0.512E+03 * .0.95 0.5971+03 4 .0.10 0.602E+03 * 4 0.43 0.766,:+03 * .0.29 0.651E+03 * X * 1.65 0 2n 1411 01 FT tno FIG 614b I I 3 Summing up those distributions, it may be concluded that most trace-elements are present in rather high concentrations in the Lake ' District and within this area in terrains underlain by pelitic rocks. The Pennines region normally presents average concentrations of the different elements, striking differences being manifested in the con- centrations between the rigid faulted block of the Northern Pennines and the similar though essentially marine rocks lying in the Northumberland trough, and in the Carboniferous rim that surrounds the Lake District, areas that normally bear low levels of most elements. In addition, within the faulted block itself, it may be noticed that its southern portion (Askrigg Block) bears lower concentrations in most elements than the northern part (Alston Block), reflecting contrasting geochemical environments possibly related to 'different tectonic settings already developed in the early Carboniferous. It is also worth noting that the post-Carboniferous terrains bear low contents in most elements, a feature that is especially evidenced in the samples collected in the in the northern part of the Solway Basin (Carlisle Plain). Regarding the distribution of the elements itself, it may be stated that Fe, Ga, and Ni conform a normal (Gaussian) curve; Li and V are quasi-normal, having only a slight departure from that curve; Cu, Pb and Ba are clearly log-normally distributed; and Mn, Co, As, Zn, Cd and Mo display complex distributions (normally bimodal) that cannot be ascribed to a normal or log-normal one. The main statistics of the distribution of the different elements are summarized in Table 6.1.- 6.3 REGIONAL GEOCREMICAL PATTERNS AS RELATED TO BEDROCK GEOLOGY As indicated in Chapter 3, the geology of the area is dominated by a Paleozoic sedimentary-volcanic pile, which overlies most of the Lake District and Pennine regions. Minor outcrops of clastic Mesozoic rocks are also present forming the Vale of Eden, Solway Basin and coastal area TABLE 6.1 BASIC STATISTICS OF SELECTED TRACE ELEMENTS, NORTHERN ENGLAND (N = 3806) Element X S Chi-square X(geom) S(log) Chi-square Distribution As 21.1 99.8 7936.54* 8.3 0.550 6436.83* Complex Ba 394.6 1013.2 369.08* 225.4 0.345 19.64* Log-normal Cd 0.7 2.0 360.88** 1.0 0.276 17997.28** Complex Co 26.2 43.1 135.49* 13.4 1.180 128.76* Complex Cu 21.8 66.9. 287.89* 13.2 0.436 15.56* Log-normal Fe 3.5% 1.7 13.25* Normal Ga 9.0ppm 5.9 20.33* Normal Li 63.0 38.6 26.76* 27.2 3.395 724.94* Quasi-normal Mn 2633.3 3285.0 313.32* 1068.3 0.624 55.67* Complex Mo 0.8 99.8 1746.54* 0.7 0.361 2873.83* Complex Pb 103.23 288.7 279.74 37.6 0.535 8.55* Log-normal Ni 31.2 23.6 24.59* Normal V 45.9 35.2 26.02* 31.0 0.579 29.44* Quasi-normal Zn 160.6 827.8 168.43* 61.5 0.840 23963.11* Complex Value with 15 degrees of freedom ** Value with 6 degrees of freedom 1 1 4 south of Whitehaven. In addition, intrusive rocks ranging in composition from granite to gabbro and in age from Caledonian to Alpine are present in some places forming bosses, phacoliths, sills, and dykes. From a purely lithological point of view, five main rock-types may be distinguished in the area (Figure 6.15): (1) Argillaceous rocks, a series of mudstones, shales, slates, greywackes and clays that constitute large tracts in the Lake District and Solway Basin; (2) Arenaceous rocks, friable or hard sandstones found mainly in the Vale of Eden, coastal area south of Whitehaven,Solway Basin, and in large areas of the Pennines; (3) Calcareous rocks, massive limestones forming important outcrops in the Pennines and Furness District and the post-Silurian rim surrounding the Lake District; (4) Volcanic rocks, a series of andesites (mainly) that forms - the central part of the Lake District and isolated patches to the north of that area and in the Cross Fell Inlier; and (5) Intrusive Rocks, granites, quartz-dolerites, felsites, gabbros, etc., found in bodies of various shapes and sizes in the central Lake District and Pennines. Transitions and combinations between the first three groups are common. The main geochemical characteristics of the rock-associations found in the area, follow- 6.3.1 Clays Clayey argillaceous rocks form the Carlisle Plain and Walney Island in Furness where they represent Mesozoic levels that bear some evaporites interbedded. The average trace-elements content of these rocks is well below the regional mean and below the average content of similar argillaceous rocks throughout the world (Turekian and Wedepohl, 1961), with the exception of Cu and Mo, elements that are found in rather high levels. The relatively high Cu concentrations found over these rocks in the Solway Basin (up to 250 ppm), appear to be related to industrial contamination arising mainly from Carlisle, the high values being concentrated Rock-associations inthearea o 10 20 30 "rig; ."i"{5! &* "t it ? BEit.#4'F.;9gzg r=-=-=l Muds lanes.5holes.Hard ~ Clays § So,yjsbnt"S and Massive lslonc. Mud"one..Sholes and DID Siales and Greywackes ~ Hard 5andl'ones [S] Friable Sandstones f±m Volcanic Rocks (2L2 Massive Lirnestoocs ~ Ignl'OUS Rocks FIG.6015 I in the north-eastern end of the Solway Firth, around Port Carlisle, an area that also bears high levels in As, Ga, V and Zn. The high levels of Mo detected in these rocks are related to their origin since they were deposited in reducing environments presumably containing important amounts of H S, conditions favourable for the precipitation of Mo. It must be 2 considered in this respect that these argillaceous rocks are equivalent to the Keuper Marl of North-East England, a unit whose similitude with the Mo-bearing Permian copper shale of Central Europe has been stressed by numerous authors (Eastwood, 1946; Dunham, 1967). 6.3.2 Slate and Greywacke This rock-association forms extensive tracts of terrain in the southern and northern Lake District, where it constitutes the Lower Paleo- zoic sequence that flank that area. Minor outcrops are found in the in- Tiers existing in the Pennines, which include some horizons of possible Pre-Cambrian or Cambrian age. At -this point, a clear distinction must be made between the horizons belonging to the Skiddaw Slates and the remaining pelitic levels because even though they are similar from a petrographic point of view they are geochemically differeht. The Skiddaw Slates were deposited in shallow marine conditions, resembling geochemically a mixture of hydroizate and oxidate sediments, with high contents in Fe, Mn and Al (4.9%, 5.8% and 7% on average, respectively). As could be expected, due to the adsorptive capacity of the Fe-Mn oxides, these rocks are enriched in trace-elements bearing high levels of As (up to 350 ppm), Co (up to 150 ppm), Ni (50 ppm on average), Pb (up to 950 ppm), V (87 ppm on average) and Zn (up to 1000 ppm), and especially high concentrations of Cu (54 ppm on average) and Li (118 ppm on average). The relation of these concentrations to those of oxidate sediments are even enhanced by the average low contents in Mo and Cd present in these rocks. It is worth mentioning that the high levels in Al present are 0 associated with high concentrations of Ga (19 ppm on average), a feature that gives hydrolizate characteristics to those horizons. As well, it is worth noting that these areas bear low Ba contents, an element that could be expected in moderate to high levels due to the presence of import- and concentrations of manganese; no satisfactory explanation has been found for this phenomenon. The remaining pelitic rocks of the area were deposited in deeper marine environments than the former, originally constituting hydrolizate sediments. Numerous trace elements are present in relatively high con- centrations in the sediments of these terrains: Cu (27-33 ppm on average), Co (up to 150 ppm), Cd (up to 5 ppm), Ga (up to 20 ppm), Mo(up to 4 ppm), V (67-83 ppm), Zn (up to 750 ppm) and As (up to 220 ppm). As can be expected, those areas bear low contents in Fe, Mn, Pb and Ba, and very high concentrations in Ni (54 ppm on average). Analysis of 4 rock samples collected in the vicinities of Sedbergh confirmed these conclusions, rendering Cu contents up to 50 ppm, V contents of 110-179 ppm, Co concen- trations of 35-44 ppm, Ni values up to 110 ppm, and low Fe,Pb, and Mn, values (2.1-3.6%, 1024-1543 ppm, 12-22 ppm, respectively). 6.3.3 Friable Sandstones These rocks constitute the extensive Permo-Triassic terrains of the Vale of Eden and Solway Basin, as well as the coastal strip south of Whitehaven and isolated outcrops in the Furness District. As can be expected, these resistates present lower contents in trace-elements than the regional average, with the exception of Mo, an element present in high concentrations in the south-eastern end of the Vale of Eden, and Ba which is present in concentrations higher than 3500 ppm to the west of the Cross Fell Inlier. The high concentrations of Ba found in the Vale of Eden, reflect high levels in this element present in the Cross Fell and surrounding 0 1 "7 terrains, areas that are drained by short, rapid streams that arise from the Pennine Escarpment, and which have probably contributed detrital barite to the stream sediments found in the lower terrains of the Bunter Sandstone. This appreciation has been confirmed by Davies (1971), who performed detailed geochemical studies in the area of Hilton, while studying the geochemistry of stream sediments over Permo-Triassic rocks in England. The high concentrations in Mo present in the area of Brough are more difficult to explain. Possibly, these concentrations arose from the lixiviation of Mo-bearing rocks existing in the Mallerstang and Stainmore commons, the element being precipitated once the waters reached the low- lands, which in that part of Edenside are formed by water-logged peaty alluvium. 6.3.4 Massive Limestones These rocks are found in the Carboniferous rim surrounding the Lake District and associated with other types of rock in the Pennines. The geochemistry of the stream sediments collected over these rocks is complex because the massive limestones lie mostly in low areas, drained by streams arising in highlands composed of sedimentary and volcanic rocks that bear high concentrations of trace-elements. The influence of the latter rocks in those sediments may be clearly seen in samples collected around Caldbeck and Mosedale in the northern Lake District,which bear high contents in Cd, Co, Ga, Mn, Ni, and Zn, concentrations that undoubtedly originated in the higher terrains composed of Skiddaw Slates, Borrowdale Volcanics, and gabbro-felsites of the Carrock Fell igneous complex. Thus, the geochemistry of the limestone need to be analyzed in small areas, as free as possible of the enhancing influence of the neigh- bouring rock-units. Such areas are found in the southern Lake District around Kendal and to the east of the Shap Fells. In those areas the sedi-, ments are typically low to average in most trace-elements, bearing relatively 0 40. 8 high contents in Zn and Cu (up to 120 ppm and 200 ppm, respectively). The high zinc content can be expected in such rocks since this element appears to be a normal constituent of limestone (Goldschmidt, 1954). On the other hand, the presence of high copper levels, though not common, has been reported in these rocks in many instances, mainly as a result of their content in organisms and especially in foraminiferal tests that normally constitute an important part of the limestone (Wedepohl, 1971). The previous results were confirmed by analysis of 4 black massive limestones collected in the Furness District which rendered low trace- element contents as compared to the average contents in similar rock through- out the world; exception to these were the concentrations in Cu, Zn, and Cd, which were found to be higher than normal (4.5-5.5 ppm, 35-40 ppm, 10-, 14 ppm, respectively). 6.3.5 Mudstones, shales, hard sandstones, and massive limestones This rock-association constitutes the horizons of the Carbonif- erous Limestone Series, a unit that forms most of the Pennines region. The geochemistry of the sediments derived from them is characterized by average contents in As, Co, Cd, Fe, Min, Ni, and V, coupled with low' Cu, Ga, and Mo levels, relatively high Ba and Li concentrations and very high levels of Pb and Zn (157 ppm Pb on average in the sediments arising from the Upper Limestone Group and 256 ppm Zn on average in sediments derived from the Middle Limestone Group). Analysis of 5 samples of sandstones, shales and calcareous sandstones of this group confirmed the previous results, rendering Pb values up to 79 ppm, Zn values up to 130 ppm, V contents up to 59 ppm, and Co values up to 27 ppm. In the opinion of the author, most of the elements that are present in high concentrations in these rocks derive such levels from mineralizing processes and thus these contents do not reflect the primary geochemistry of the rocks, mainly representing superimposed patterns whose a 1 9 local values bear relation with the lateral mineral zoning present in that area. Four elements display a clear trend within the stratigraphic units that may be distinguished within the series: Co, Mo, Mn and V. From the base to the top of the succession, Co and Mn systematically increase their average value while Mo and V decrease systematically. This fact, coupled with minor increases detectable in the Fe and Li contents of the sediments, and with increases in Cu, reflect the original hydrolizate nature of the lower portions'of the sequence which gradually was deposited in more oxidizing conditions, favourable for the precipitation of Fe-Mn oxides that would have adsorbed always increasing amounts of Co and Li, thus rendering the annotated trends. 6.3.6 Mudstones, shales and hard sandstones This rock-association is found in the eastern part of the area and in the Cumberland Coalfield forming the Upper Carboniferous deltaic sequence that constitutes the Millstone Grit Series and the Coal Measures. The geochemistry of the stream sediments derived from these rocks is characterized by a generally low content in trace-elements as related, to the regional man, a feature that is especially evident for As, Cd, and Zn, elements which in the Coal Measures have mean values of 10 ppm, 0.1 ppm, and 88 ppm, respectively. The original oxidate nature of these series is manifested by their Fe, Ba and Li contents which are average to high and by a very good correlation between high Co levels and the outcrops of the Millstone Grit. The comparative geochemistry of both series that compose the=Upper Carbon- iferous sequence indicates that their environment of deposition became every time shallower and more oxidizing, a feature demonstrated by an increase in As, Ba, Fe, Mn and V from the Millstone Grit levels to the Coal Measures and by a decrease in the same stratigraphic order in the contents of several elements that tend to concentrate in deeper sediments (Ga, Co, Ni, Zn, Cd, Mo). It is worthing mentioning regarding these rocks that the sediments collected over Millstone Grit terrains bear on average more than twice the content in Pb that is present in sediments collected over the Coal Measures (92 ppm and 41 ppm on average, respectively). This fact indicates that the chances of finding mineral deposits in the latter terrain are very small either because these rocks were not favourable for the emplacement of mineralization or because the remnants of that series lying in the area were too far away from the main centres of mineralization, thus rendering very difficult for non-depleted metalliferous brines to reach them after passing through the highly reactive rocks of the Carboniferous Limestone Series. 6.3.7 Volcanic Rocks These rocks constitute the central part of the Lake District as well as minor patches in the northern part of that area and in the Cross Fell Inlier. Their composition corresponds mainly to andesites, though flows ranging from basalts to rhyolites are'known. Variable amounts of pyroclastic rocks are included together with the former lavas. The geochemistry of the sediments derived from these volcanics is characterized by low levels in Ba, what is to be expected from the low potassic composition of the parent rocks, average to low values of Fe, Cu, Pb, Ga, Co, Mo, Ni, and V, and high contents in Li (64 ppm on average), Zn (248 ppm on average), Mn (4950 ppm on average) Cd (1.6 ppm on average), and As (up to 230 ppm). The high levels of the latter elements possibly indicate the presence of some of them in ferromagnesian minerals (Li, Mn, Zn, Cd) or in ferric iron oxides (Zn,Cd). The high levels in As are more difficult to explain indicating its possible presence in ferric or ferrous sulphides,or its deposition from fluids or emanations that arose as a late 1. 2 1 stage of the volcanism. 6.3.8 Intrusive Rocks Under this heading, the intrusive rocks of various compositions and ages found in the area are grouped. Most of the samples that can be considered to arise from these rocks were derived from the bosses existing in the Lake District, the influence of phacoliths, sills and dykes is very, difficult to separate from that of their country rocks, due to their restricted outcrops. Therefore, the following features refer to acidic intrusive rocks of average granitic composition which constitute major bodies in several areas. The geochemistry of the sediments derived from the intrusive bodies present in the area is in good correspondence with the general acidic nature of those rocks. The elements that during magmatic fraction- • • e ation tend to concentrate in gabbroic derivates are fairly low in the sediments which bear Ni, Cu, Co and Fe contents well below the regional mean, and in most cases well below the average content in igneous rocks (Mason, 1966). On the other hand, the elements that tend to be concen- trated in late fractionates or pegmatitic bodies are normally present in high concentrations in those sediments; of especial interest are very high levels in Li (up to 105 ppm), Mo (up to 3 ppm), As (115 ppm), Ga (up to 20 ppm) and Mn (up to 1%) present in samples arising from the Eskdale Granite, values that are strikingly greater than the average for that type of rock. Finally, it is worth mentioning that part of the northern Lake District is strongly influenced by the Carrock Fell igneous complex which determines the presence of high levels in most trace-elements in the sediments collected in the area to the north of that range. 1 2 6.4 REGIONAL GEOCHEMICAL PATTERNS IN RELATION TO MINERALIZED AREAS In the following paragraphs the distribution of the trace-elements selected in this research is discussed in terms of the patterns that they display over known mineralized areas. Individual anomalies are not discussed in detail, that discussion being delayed until Chapter 8 where the different elements are reviewed from a mineral exploration point of view, with special emphasis on the presence of groups of anomalous samples that may indicate new possibly mineralized areas. The main features of the distribution of the different elements with regard to base metal mineralization, are the following: Arsenic The regional patterns displayed by this element are not related to the known mineralized areas,all of which present low arsenic contents (less than 19 ppm), with the exception of the Caldbeck Fells District where concentrations exceeding 300 ppm on average are found,probably arising from some of the many acidic intrusive bodies lying in that area. Barium In general terms, the patterns of barium in the area do not con- form to the distribution of the known mineralization although most of the deposits in the Northern Pennine orefield lie within zones whose stream sediments contain more than 350 ppm. Limestones from Blackdene mine, Coalcleugh and Garrigil bear Ba contents of 280-665 ppm, confirming this point. The definition of the Lake District orefield is in this case very poor, as could be expected from the relative scarcity of barite as gangue of those deposits; the only mineralized areas bearing concentrations higher than the average are Stonecroft-Barrow, Brandlehow-Yewthwaite, and Greenside-Helvellyn, most of whose deposits bear barite as a gangue component. A point worth mentioning with respect to the distribution of 0 123 barium is that if values exceeding 470 ppm are considered,the southern outer margin of the fluorite zone in the Alston Block is perfectly delimited. This situation is not evidenced in the remaining part of that area nor in the fluorite zones of the Askrigg Block. Cadmium The spatial distribution of cadmium with respect to mineralization is characterized by two contrasting features. Firstly, the Northern Pennine orefield is well defined by the patterns of this element, if concentrations greater than 1 ppm are considered. On the other hand, there is no relation between high concentrations of cadmium and the lead-zinc districts of the Lake District, with the exception of localized high concentrations in the area of Thornthwaite. Within the Pennines, several features may be observed from the cadmium patterns. The northern part of that region (Alston Block) does not contain concentrations exceeding 2 ppm, but a remarable accordance exists between the patterns of the range 1-2 ppm and the main zinc-productive areas (Nenthead, Grenhurth, Smitter Gill, Stonecroft-Greyside, Langley Barony). It is worth noting that in that area, the most important Cd concentrations are found to the west of the Burtreeford Disturbance, and that those concen- trations soon disappear outside the fluorite zone, a fact that agrees with the known lateral zoning in that block. The mineralization in the Askrigg Block is evidenced by higher cadmium levels than the former ore deposits with a delimiting point of 1.5 ppm. It is worth mentioning that in that area levels higher than 2 ppm evidence all the zinc-producing districts and that there is also a fairly good agreement between the fluorite-bearing zones and high cadmium concen- trations (greater than 3 ppm). • Cobalt j2 4 The regional patterns displayed by this element bear no relation- ship with the mineralized zones, being controlled by lithological factors. However, a faint pattern is noticeable in the main lead-zinc productive area of the Alston Block, where a strip bearing values from 25 to 45 ppm coincides with the known ore deposits. Copper The distribution of copper in the area with regard to minerali- zation is characterized by two main features. Firstly, except for a small high that occurs to the east of Appleby, no important concentrations in this element are present in the Pennines,indicating that the copper ores that exist in that area are very marginal as compared to the lead-zinc mineralization. Secondly, the main copper districts of the Lake District orefield are enclosed within two of the three main areas bearing on average more than 30 ppm. The latter districts are well defined by the copper patterns, their streams bearing concentrations exceeding 40 ppm. A very well defined anomaly comprises the Coniston District and the Tilberthwaite-Greenburn deposits. A much wider feature is found in the Derwent-Bassenthwaite area comprising districts as Thornthwaite, Goldscope and Force Cragg, and a minor feature defines the copper-prdductive areas of the Caldbeck Fells (Redgill, Driggith, Roughtengill), as well as the Threlkeld area. It is worth mentioning with respect to the distribution of copper that several zones with contents exceeding 40 ppm are found in north-western England in areas where no mineralization is known. Some of these are related to industrial contamination arising from Port Carlisle, Workington, Maryport, Lancaster, Grange, etc., but others, such as those in the Bootle, Shap, and Loweswater fells, undoubtedly arise from geological features worth investigating. 1. 2 5 Gallium The regional distribution of gallium is not clearly related to the known mineralized districts in the area, showing a clear lithological control. However, it is worth noting that concentrations higher than 18 ppm are not clearly controlled in the Lake District by lithology but they constitute a broad zone approximately coinciding with the area where base metal deposits (economically exploitable or not) lie, thus possibly suggest- ing a certain genetic relationship. Iron The distribution of iron in the area is not related to minerali- zation, presenting a fairly strict lithological control of its high values. However, a faint pattern of enrichment in this element is present in the main lead-zinc productive area of the Alston Block where a strip bearing sub- anomalous values (from X to X+2s) may be noticed extending from Nenthead to Langdon Beck. Apparently, this pattern may be related to hydrothermal alteration connected to the mineralizing processes that affected that area. Lead This is the element that displays the best spatial relationship with the known mineralized regions of the area. Considering values over 100 ppm, all the mineralized districts are evidenced with the exception of the Coniston and Upper Swaledale areas, both of which mainly have copper veins. Features worth mentioning regarding the distribution of lead are: firstly, almost all the areas that have values higher than 200 ppm coincide with mineralized districts. Exception to this are high concentrations found south of Corbridge, east of Haltwhistle, around Bootle, and in the Outer Pennine Fault area; the first two may indicate ore bodies buried under the glacial cover of the Haydon Bridge District, and the latter may represent mineralization lying in the Dufton Fell, while the levels found around Bootle merit further investigation because no mineral deposits are 1 26 known in that area. Secondly, it is interesting to note that the most important lead concentrations lie in the Alston Block and within that area in the periphery of the fluorite zone, with the exception of a north north-east trending pattern that extends from Nenthead to Greenhurth, coinciding with the main zinc-producing area of that zone. In this area, the limestones bear lead contents well above the average for this type of rock (26-806 ppm). Lithium Several features characterize the distribution of lithium as realted to the known mineralized areas. Firstly, the Lake District ore- field is not evidenced by patterns displayed by this element, though high concentrations (greater than 100 ppm) in the Skiddaw Slates coincide with the mineralization in those rocks, and levels in the sub-anomalous region lie over the main mineralized structures in the Borrowdale Volcanics. Secondly, the mineralization in the Askrigg Block of the Pennines is not evidenced by patterns of lithium, except the Swaledale region where levels higher than 85 ppm are found over mineralization. The mineral- ization in the Alston Block of the Pennines is well represented by high values (greater than 85 ppm), which coincide with the main mineralized area. In addition, it may be noticed that values greater than 100 ppm show a strong concentration within the fluorite zone of that area and that several restrict- ed high concentrations are found around the Stainmore Gap, in zones where no mineralization is known. Analysis of limestones lying in the Allendale area confirmed the previous pattern of distribution rendering average values of 35 ppm Li for samples lying within the fluorite zone and values of 0.2 ppm in samples arising from areas outside that zone. Manganese The regional distribution of manganese bears no relation to known • 2 7 mineralized areas and appears to be exclusively controlled by lithological factors. The only exception is found in the area west of the Derwent Water where levels higher than 1% are found, probably connected to psilomelane disseminations present in the upper levels of the veins at Brandlehow and Force Cragg. Molybdenum The areal patterns of molybdenum in stream sediments bear no systematic relationship to the known mineralized areas. However, if values greater than 1 ppm are considered, a relationship can be established between some copper-producing districts (Coniston, Stone Crag, Tynebottom, Bycliffe, Sir John's, Helvellyn) and concentrations of molybdenum mainly higher than 1.8 ppm. The remaining high concentrations found are due to lithological factors or are produced by contamination arising from populated areas such as Kendal and Furness. Nickel The distribution of nickel in the area bears no relation to mineral- isation, except for some concentrations greater than 60 ppm found in the copper districts of Goldscope, Force Cragg, and Caldbeck Fells. Since that relationship is not systematic and there are important copper districts such as Coniston that bear low nickel values, it may be concluded that this element is independent of the mineralisation, its concentration depending on the lithological characteristics of the terrain. Vanadium The spatial distribution of vanadium in the area is not related to mineralization, since even though high levels (greater than 95 ppm) are present in several districts of the Lake District orefield (Coniston, Roughtongill, Goldscope, etc.)., the relationship is not systematic, the distribution of the element being mainly controlled by lithological factors. I 2 8 Zinc No relationship can be established between the regional patterns displayed by this element and the Lake District orefield. On the other hand, the mining districts of the Northern Pennine orefield are fairly well evidenced by this element, if values bigger than 200 ppm are considered. Three points are worth mentioning with respect to the last relation- ship. Firstly, the good definition of the main zinc-producing areas of the Alston Block (Nenthead, Greenhurth, Smitter Gill, etc.) which are not only defined by high Zn contents in stream-sediments but also by similar contents in limestone (60 ppm in samples from Garrigill, 175 ppm in samples from Coalcleugh); secondly, the high concentration of zinc values to the west of the Burtreeford Disturbance due to the lateral zoning present in the Alston Block; and thirdly, the very high concentrations (greater than 480 ppm) that are found in relation to mineralized areas in the Haydon Bridge district and Askrigg Block. The latter fact is very important from the mineral exploration point of view because numerous zones in that area bear high zinc levels where no mineralization is known, thus suggesting the possible presence of zinc-bearing ore bodies that until now have not been recognized. Finally, in order to obtain a complete picture of the distribution of chemical elements in relation to the mineralized structures known in the area, it is worthwhile to review briefly the distribution of four major elements that may indicate the presence of patterns related to hydrothermal alteration produced by the mineralizing processes. The distribution of potassium is better analyzed in the Pennines where its average content does not exceed 0.6%, strongly contrasting with the Lake District where contents up to 1.3% are common (Figure 6.16). The K content of the stream sediments collected in the Pennines vary in general from 0.3 to 0.6%. 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I 0600000900000 84== 7.0139.3;.:.[37 =-„ -=3=--.92, .., ++-- I 00012000000000 &BB 008067. u1[ -++,,+-==0==--... I 138= 0600008133 --t++++-===-++- +., . -+ FROM 41.733 TO 44.055 I = , BOtO - +-- -,.++-+=10--- +++ I 0808900800888 :4- =.---+++ +,,+-B=OligE3888=- 0088600880080 Ii II+ . 6. £3==-=--+--+-4.091..-.L00003-++ I 068110861180891)8099080960090 + n,,,a=94„...-= 11:18_01.+253.=+1. I 0800800660000 imiummon. 30 GREATER THAN 44.056 1115ammommenn40.60. +++++ 2111121111/1111 11111111111011101244 12041111121111111211IN FIG.6.17 1114 13131613111 1111Ma16I1S1/1 7 1 2 9 Block, contents ranging from 0.6 to 1.3% are found, suggesting that an enrichment in potassium took place in relation to the mineralizing processes; this point is also marked in analysis of limestones of that area which have K concentrations well above 0.5% (o.8% on average). Similar, though not so marked patterns, may be observed in mineralized areas of the Askrigg Block, as Swaledale, Grassington, and Greenhow. It is worth noting in this respect that all the potassium highs lie within the fluorite zones disting- uishable in that region. Silicon is another major element that may be related to minerali- zation. Its spatial distribution in the Pennines (Figure 6.17) shows average values of about 37%, concentrations that clearly diminish to less than 34% over mineralized areas; coinciding the most important lows with the fluorite-bearing zones of the Alston and Askrigg Blocks; however, localized highs may be found in the central parts of those fluorite zones. No patterns of enrichment or depletion can be observed in stream-sediments collected in the Lake District orefield where the distribution of silicon appears to be exclusively related to lithological factors. The patterns of the remaining major elements analyzed (Al, Mg, 'ii, etc.) bear no clear relationship to the mineralized structures present in the area. Summing up the distribution of chemical elements in stream-sediments as related to mineralization, it may be concluded that the Lake District orefield is evidenced by high Cu, Mo, and Pb concentrations, and possibly by enrichments in Mn where disseminations of psilomelane occur in the veins and minor enrichments in Li, Ca and V. In that area, the high Pb values are found in relation to lead-zinc mining districts, and the high Mo concen- trations coincide with copper mining districts. The mineralization in the Askrigg Block of the Pennines is characterized by high levels in Cd, Pb, Li, Zn and Mo. The Cd, Zn and Li 1 3 0 values tend to concentrate in the fluorite zones of this area, the Pb values in the periphery of those zones, and the Mo values in the copper- bearing districts. The Alston Block mineralization of the Northern Pennine orefield is evidenced by high contents in Ba, Cd, Pb, Li and Zn, as well as restricted high levels in Co and Mo. The fluorite zone of that area is evidenced by high concentrations in Cd, Li, and Zn, the latter especially important to the west of the Burtreeford Disturbance. High levels in Pb and Ba characterize the periphery of the fluorite zone, and high concentrations of Mo the copper districts. The ore deposits of the Haydon Bridge area are very restricted in extent and so they do not give broad regional patterns that allow their identification. However, their presence is evidenced in the regional maps by minor highs in Cd, Pb, Ba and Zn. Finally, it is worth mentioning that three patterns probably related to hydrothermal alteration produced by the mineralizing brines were detected in the main mineralized areas of the Pennines. An enrichment in K and in minor proportion in Fe is evidenced over the fluorite-bearing zones as well as a depletion in Si, though the latter is present in high concen- trations in the central parts of those zones. These patterns are in close agreement with conclusions attained on the basis of pure geological evid- ence about the nature of the brines that originated the deposits of the Northern Pennine orefield (Sawkins, 1966; Dunham, 1967). 6.5 INTERPRETATION OF THE REGIONAL GEOCHEMICAL DATA BY MEANS OF R-MODE FACTOR ANALYSIS 6.5.1 General Considerations and Outline of the Theory Factor analysis was introduced in the study of geological data by Imbrie and Purdy in 1962, and since then its use has rapidly expanded, at present being probably the most used of the multivariate statistical • 1 3 1 techniques available. In the field of geochemistry it has been success- fully used in the interpretation of the relationship between geochemistry and regional geology, mineralization, secondary environment, etc., by authors such as Garrett and Nichol (1969), Nichol and co-workers (1969), Khaleelee (1969), Armour Brown (1971), Young (1971) and Urquidi (1973). The main purpose of the technique is to explore the inter- correlations existing between variables (R-mode) or samples (2-mode) of a data set through the analysis of the variance-covariance matrix of the set. The resultant solution is expressed as a set of theoretical variables (factors) that in the simplest possible terms may be considered as follows: If a set of vectors ia available in a multidimensional space, another set - referred to as common vectors or factors - can be imagined in a position such that the correlations or loadings (cosine of the subtended angle) between them and the original set is maximised. Each factor is orthogonal (uncorrelated) to all the remaining factors of the solution and its relation with respect to the original set can be compared to a half-open umbrella whose radiating frame indicates the direction of the original vectors, the factor itself being the axis where the handle is held. Full accounts of the technique may be found in Harman (1967), Child (1970), Lawley and Maxwell (1971), and in general in any textbook dealing with multivariate techniques of data analysis (Cooley and Lohnes, 1971; Press, 1972; Davis, 1973; etc.). Two basic models may be considered in factor analysis:_ Component and factor solutions, whose main difference lies in the variance that they take into account. Component analysis regards that all the variance of the set is explained by the interrelations existing among the variables and factor analysis considers that, besides the common variance, there is a certain amount of unique variance (inherent to each variable)that needs to be taken into account. • 1 3 2 The mathematics of the technique are complex, but suffice to indicate here that starting with a variance-covariance or a correlation matrix of the set, eigenvectors and latent roots (eigenvalues) are calcul- ated and from them the principal components (factors) are estimated. This solution extracts factors in such a way as to account for as much common variance as possible in the first factor, successive factors, in turn, accounting for the maximum possible of the remaining variance, until theoret7 ically no common variance remains. The amount of variance of the set extracted by each factor equals the square of the loadings of that factor on each variable, which is equivalent to the value of its latent root. Since the foregoing method normally renders solutions that have several general factors (factors with several variables with high loadings or variables highly loaded in several factors), in order to obtain meaning- ful group factors (factors with few variables with high loadings which are equivalent to "discharge" the variance of each variable in only a few factors), manipulations that give derived solutions may be used thus suppressing the background effect of the lesser (though significantly) loaded variables. The most important manipulations in this respect are orthogonal and oblique rotations. 6.5.2 Component Analysis of the Data In the present research, an R-mode component solution was chosen for the data, analysis performed with the help of a computer program designed by Garrett (1967). This type of analysis avoids one of the main problems posed by factor analysis: the estimation of the communalities, that is the estimation of the variance of an observation that is shared in common with other observations. In this research, the correlation matrix used as a starting point (Table 6.2) had unities in its main diagonal, thus implying that the whole variance of the set was considered to be common. Direct and derived solutions containing 2 to 14 factors were • • TABLE 6.2 Attov/NEX NORTHERN ENOLANO*FACTOR SCORES ALL SAMPLES6 FACTORS MODE4444 MATRIX TO 8E FACTORED VAR1AU1E NO NAME 1 2 3 4 5 6 7 8 9 1U 11 12 13 14 1 Fe 1.000 2 GA ..331 1.000 3 Cu .ti2 .234 1.000 1.000 4 128 .161 .066 .200 5 V .050 .668 .264 .072 1.000 e 6 8A .116 .014 .128 .407 .025 1.000 7 Co .580 .251 .107 .221 .076 .059 1.000 .8 NI .129 .051 .025 .026 .019 .008 .110 1.000 9 MN .667 .288 .082 .203 .089 .090 .519 .055 1.000 1 Li .555 .28A .067 .097 -.002 .072 .290 .023 .344 1.000 11 wo .174 .112 .380 .132 .082 .03S .120 .030 .128 .067 1.000 12 AS i172 .122 .316 .250 .071 .169 .116 .009 .154 .118 .159 1.000 13 2N .28, .069 .129 .478 .034 .32: .166 .041 .240 .087 .056 .226 1.000 1.000 14 CO .193 .066 .131 .312 .031 .171 .240 .043 .267 .045 .092 .241 .791 1 23 calculated, the latter by means of the Varimax and Promax rotations (for rotated orthogonal and oblique solutions, respectively). The unrotated and obliquely rotated solutions obtained were found to be much more difficult to interpret than the orthogonally rotated solutions. Therefore, the following analysis is based on results attained with the latter type of solution. Two problems arise when solutions are examined: (1) It is necessary to establish a criterion for the number of factors to be extracted. Several approaches have been suggested in this respect, the most commonly used being that of Kaiser (1958) who gave several arguments in favour of selecting only those factors whose latent roots are greater than one. Cattell (1966) has suggested that this criterion is most reliable when 20 to 50 variables are included in the analysis because when less variables are used, there is a tendency to extract a conservative number of factors by this means and when more variables are used there is a tendency to extract more factors than necessary. In this research, a method proposed by Cattell (1966, 1967) was used to estimate the optimum number of factors to extract. This method considers that unique variance is included in all factors, thus rendering it necessary to select their optimum number before the importance of that variance becomes too big, at the expense of the common variance. For this purpose, a graph ("screegraph") is constructed by plotting the value of each latent root against the factor number,the cut-off point being selected where the curve develops in a linear function, beyond which most of the variance can be considered to be unique (scree or litter variance according to Cattell, op.cit.). (2) It is necessary to establish a criterion for the significance of the factor loadings. Several criteria have been postulated in this respect, the most frequently used being those that consider the loadings as correla- tion coefficients or the one that considers only those loadings whose value 0 exceeds ± 0.3, criterion that lacks statistical significance, merely being a rule of thumb that separates the loadings that explain more than 10% of the variance of a factor. In the present case, the loadings were considered as coefficients of correlation, but their significance was modified according to the Burt- Banks formula (Burt, 1952): St. Error of St. Error of V n loading correlation nil-r where n is the number of variables in the analysis and r is the position of the factor during extraction. That expression indicates that as one proceeds from one factor to the next, the acceptable value for a loading should be increased in order P to diminish the effect of the unique variance that intrudes in the solution. It is worth noting that the formula makes allowance for the number of samples and for the number of factors that have been extracted before the one under consideration. Considering the screegraph constructed for the data of the present research (Figure 6.18), a solution including six factors was chosen as the optimum one, a solution that explains 72.4% of the total variance of the set. Table 6.3 indicates the rotated and unrotated solutions corresponding to the chosen model, together with the factor scores matrix and eigenvalues of the data. The underlined loadings and significant at the 0.01% level of confidence, according to the formula previously indicated. As may be seen in the solutions, the sum of squares down the columns equals the values of the respective eigenvalues, and the sum of squares across rows equals the communality, that is the amount of the variance of a variable that has been explained by the factors chosen. According.to that table, the following associations may be consider- ed to be represented in the stream-sediments samples collected in the area 0 • - I -1:-: '— ' ' ' : , • I ' 1 I . 1 : i I ! 1: , ; : : ' ' • 1 i , ' ; 1 : , I■ • : ' I ; : ' 1 : : t: • : ; • ' ! a ! 1 1 , ! • :11 ... I • i ; , , , 1 ,„ ! —4: ; 1' "I- - 1: • • ' ' ' 1 - 1 1 • 1 ""I i'; i 1"I 1 11 ' I • I ' • I , : - I ! - I I , ' 1 1 • I -I" : 1 I - I ; ' I ' I ' I ! • - I 1 ' , : ; ::1 I 1 I ; :1 : :„ , : I' • • :I : j 1', 1 • ; • I • • I : • ; ' ! ! 1 , ' , • ! , 1 ' 1" • ' 1 :: " , a': * :: I :":f 1- n: 1: I r _ i, _-, , !, Screegra, - !!! I- 1 1 • " ; 1 1 ! 1 , , , I r ! ' ' ! 1 I! ! 1 i , „...._, 4 ' 7 1 1 1 .4 EIGENVALUES ' ' - Common yrmance -•• 1 I 1 Unique variance ; 1 • ! r i , -4 4-1- 4---- •I ' - ! ! '- 1-1-- ! , !,- I -'.-- - W I 1- . 1 I ! ' Li ! _ .• -, ' I, , 1 1, „ , . , 1 1 , • .1-L-t-1- - i -1-- +•- 1 . ! I , ' 1 1- . 1 i : 1 , - 1. _ , • , ,- . . • I \ t , ,_!,.• % ! .. t 1 -1,- i ; 1 ft-NI i • • ! 1 ! Nt. - 1 1 ,•*. I -k • H ! ! ! : • ! 1 ! ! I :1 • N, ' I , , ; r- - -4- 111 1 1, I , 1 1, I • I ! 1 '.. " Kmnr titt.=aff. Wig! I ! 1 !I L ! I • t ! 1 • - • I , I 1 • I I • . I up II. it , 12 , ; 13 1 14 1 1 I ! 1 . ■ , , ! ; j I COMPONENT FAVOR ! , I 1 1 , I !, ■1 1 ! : i 1 1 ! 4 I ! ! ; ! , ,p , iI .. I I 1 Optimum number of tactor4 tq ektract 1 , ! 1 11 1 ' 11 ' it r , , H !, ' 11'- L 1 . rIG.6.18,.t I • -111 II HI i 1 , 1- . , 1 1 ' : 4 ' 1 L H 1 ! 1 I • I • - I 1 ; 1 ii I - - • 1 I r- 14 ' I 1_I 1 ; LJH TABLE 6.3 commtraus SOLUTION OF GEOCTIEMICAL DATA TA$LE OF POSITIVE EIGEP,VALUES PERCENT OF COMMUNALITY OVER q NO. E/GENVALUE ALL ( 14) FACTORS 6 ROTATED FACTORS 1 3.471 24.8 24.8 34.2 34.2 2 1.899 13.6 38.4 18.7 52.9 3 1.606 11.5 49.8 1501 68.8 4 1.104 0.5 54.3 11.7 80.5 5 1,017 7.3 65.6 10.0 90,5 6 .965 6,9 72.4 9.5 100.0 7 .014 5.8 78.3 8 .720 5.1 83.4 9 .566 4,0 07.4 10 .548 3,9 91.4 tl .462 3.3 94.7 12 .318 2.3 96.9 13 .260 1.9 98.8 14 .170 1,2 100.0 TRACE nF ORIGINAL MATRIX 14.000 COMMUNALITY OVER 14 FACTORS • 14.000 6 FACTORS • 10.142 UNROTATED FACTOR MATRIX SUM SQUARES DOWN COLUMNS 3.471 1.899 1.606 1.184 1.017 .965 VARIABLE COMMUYALITV MIX NO. NAME 6 FACTORS COEFF 1 FE .766 66.947 .696, •.356 ,-.373 .116 0.042 ...;32 2 GA .845 81.679 .496 - 535 .446 -.381 -.057 ...07 3 CU .680 69.805 22,L1 -.005 ,588 11404 .064 040 4 P8 .616 72.142 c540 , .457 .086 .003 -.190 -.276 '5 V .878 74.014 .294 -.366_ .662 -,466 -.008 +.7136 6 BA .782 81.621 X356 .421 .072 ;451 7 CO .546 61.349 .612. -.245 -.309 :0011 71.iff .047 8 RI .968 47.838 .083 -.001 a 796 ..to. 646 9 MN .649 62.541 ..,:g ::;4 577 -.341 -.017 .004 1 LI .604 79.757 0 -.336. .132 -.296 +.086 11 MO .662 74.940 -5r5 ::11630 .6)6 12 A$ .400 61.711 .438 .194 .247 -.091 .;54'71 13 2N .863 70.841 1/01 .613. +.047 •*.2012 :2676 :13Z1 14 0 .883 83.628 aa .530 +.065 -.258 4ot/37E0 FACTOR MATRIX SUM SQUAREs MOWN coLUMNs 2.516 1.897 1.681 1.584 1.013 1.452 VARIABLE COMMUNALITY MIX mO. NAME 6 FACTORS COEFF i FE .766 36.791 ,858 .060 .061 .108 .073 •,.077 7 OA .845 40.967 .379 -.005 J---....854 .086 .002 .502 3 Cu .680 47.838 -.007 .035 .255 .072 .018 -.130 4 PO .616 99.999 .123 349..-__ .026 .17'. .025 -,668_ 5 V .878 2.1.123 -.042 .028 .930 .099 .015 .01Y 6 BA .782 79.064 .036 .061 -.002 .024 .013 -.881, 7 Cc .546 50.566 .688. .204 .075 .079 .135 .426 8 NI .960 9.322 .072 .008 .016 .005 •981 -.025 9 MN .649 46.620 782 .239 .093 .057 .006 .005 1 LI .644 49.132 .733 +.163 .037 .018 -.110 -.164 11 MC .662 40.610 .116 -.003 -.0387961_--- .063 46914 1 2 As .400 55.091 .117. . 185 .020 .520 -.099 -.269 1 3 26 .863 40.073 .111 ,IIIIL .017 .049 .004 -.307 14 Cc .883 26.918 .132 .923 .007 .100 .009 -.059 SOuAuE0 FACTOR SCORE MATRIX FACTOR 1 2 3 4 5 6 FE .364 -.070 -.057 -.000 .024 +.003 OA .061 -.027 .510 -.069 -.024 .019 Cu -.089 -.060 .067 .505 .010 -.014 P8 -.021 .038 -.009 .017 .021 -.445 V -.120 .025 .594 -.050 .008 -4.006 SA -.029 -.183 -.002 4.006 .026 -.714 CO .775 .066 -.027 -.011 .091 .107 NI -.025 -.029 -.006 -.016 .974 +.034 MN .311 .061 -.017 -.037 -.042 .101 LI .343 -.214 -.050 -.046 -.144 -.139 MO .0n6 -.048 ...140 .580 .048 .175 As -.006 .005 -.060 .321 ...109 -.113 26 .0.050 .475 .009 -.071 -.016 -.032 CD -.038 .566 -.007 m.010 4.015 .195 1 3 5 during the reconnaisance survey (elements are indicated in order of importance): Factor 1 : Fe-Mn-Li-Co-Ga Factor 2 : Cd-Zn-Pb Factor 3 : V-Ga Factor 4 : Mo-Cu-As Factor 5 : Ni Factor 6 : Ba-Pb (negative) Note how simpler the rotated solution obtained is than the one that may be considered from the underlined loadings of the unrotated solution. In order to have a clear frame for the interpretation of the associations found, factor scores were calculated for each sample on the basis of the rotated solution; the scores were calculated by the Harman's method of ideal variables which gives values that are only approximate. The scores were plotted by means of the PLTLP program and the patterns obtained were interpreted in terms of bedrock geology and mineralization. 6.5.3 Interpretation of Factors 6.5.3.1 Factor 1 (Fe-Mn-Li-Co-Ga) This association explains 24.8% of the variance of the set. It is dominated by elements that characterize oxidate sediments with the exception of Ga, an element whose presence is explained by the degree of correlation existing in the present case between Al and Fe-Mn. Thus, the couple Fe-Mn "drags" Ga into the factor with a significant loading, not because of their affinity with Ga itself but due to their relation with Al in whose contents the concentrations of Ga depend. As can be expected, the areal distribution of this factor (Figure 6.19) bears strict lithological controls. The highest values are found in the slates and greywackes that consitute the Skiddaw Slates, a sequence that was deposited in shallow marine environments having a mixed ***HINEi NORTHERN ENGLAN1ISIX-FACTORS MODEL*PERCENIILE HAPS OF FACTOR ONE." LOH-FAGS FILTER USING EFFECTIVE 4AOIUS or i CELLS 1++fm+*++++++++++++++++++++++++++,+++++++++++++++++++++++++++++ 4+++++4+++++/I ass „,N -4.175 WANK I 1 --rf„ 4 f---.„ , .-- 4...4-4.- 1, i 4.1.,„".$.11,.$4 ++++c+ + -++++++ -.- +. 40- +#-- Ii FROM -4.174 TO -.956 I I ++++++-4---++,,+++--- -+,++++++ II I I ' t 99999 1,P*4. Ttl ,++-+ II I +4-14,4 5 +, ' B.B3. =.8. +++4- I I I I ' WI+, , 640 I I I - 4-14,44....4,,.. -9EEEB0=0=0E0 0E0+ =0130- I/ I ....- 9941.41. 44 +=DEB-.000/0 BEBEIBB0048.++ - - II 1 t+ +--++....., +1 'I -- 0E393 =CEE3344E0==-=0,300.-- II FROM -.957 TO -.767 1 +++++++--"t+ ,,,,, ++.tott..,+=. 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In addition, average to high values are found in sediments derived from the Upper Limestone Group, a unit that bears important amounts of Li and coinciding with the outcrops of the Millstone Grit Series, mainly due to the high cobalt content of the sediments derived from these rocks. Some isolated highs displayed by the factor in several areas may probably be due to secondary environmental conditions which produce the co-precipitation of Fe, Mn, Co, etc., from waters arising from acid and reducing waterlogged soils when they reach the more alkaline and oxidizing environments of the open drainages. These processes have been considered responsible for similar associations found in Wales (Horsnail, 1968), Ulster (Young, 1971), Perrin Mountains (Butt, 1971) and other areas. 6.5.3.2 Factor 2 (Cd-Zn-Pb) This factor explains 13.6% of the variance of the set. It is dominated by the couple Cd-Zn which enters the association with loadings higher than 0.86, lead being marginal in this respect (loading of 0.349). The interpretation of this factor is rather complex because it does not represent a primary association. Tentatively, it could be assumed to represent the zinc mineralization in the area. The analysis of its regional distribution (Figure 6.20) indicates that the high values of the association are fairly erratic, concentrating mainly in the Askrigg Block of the Pennines and in the southern Lake District. Comparing that distribution with bedrock and mineralization features, it may be seen that no clear relationship appears to exist between those geological features and high values of the factor, except for the coincidence of the main highs with mineralization in the Askrigg Block, an area that bears very high concentrations in Cd. A fact that complicates the matter is that the main mineralized area of the Alston Block, where the most important zinc-bearing districts of the area lie, does not corres- 1 i7 pond with highs of the association and, what is more, the few highs present in that area are found outside the fluorite zone, an area that is practically barren in zinc ores. In the opinion of the author, this distribution is a consequence of the limitations that may be encountered when manipulating the data while obtaining rotated solutions. Originally, the factor was bipolar including a positive "mineralization" association (Pb-Zn-Cd) and a negative "shale- greywacke" association (Fe-V-Li-Ga). When that matrix was rotated the latter association was subdued by the former and the factor appeared as a pure "mineralization" one. But, when the factor scores matrix was calcul- ated to estimate the scores, part of the "shale-greywacke" association crept into the final values, mainly through the not so low negative loading of Li and through the negative loading of Ba, an element that, as indicated in the previous section, is negatively correlated with the mineralization. Therefore, the resulting scores are a balanced weight of both associations at each site. In this manner, average to high values appear in parts of the Silurian terrain (which has no mineralization but high Zn and Cd values and low "slate-greywacke" values), and in connection with the mineralization in the Askrigg Block. The latter is a true "minerali- zation" association, which in this case has been enhanced by the very high Cd content of the sediments in that area, coupled with their low "slate- greywacke" values (especially Li). In the case of the mineralization in the Alston Block, both associations were balanced, the "mineralization" values being counterweighted by the contents in Li and Ba. The foregoing discussion shows very clearly that when factor solutions are used all the components of the solution need to be analyzed with care if correct interpretations are to be achieved. This fact indicates that not only the final solution must be analyzed, but also the direct solution and factor scores matrix, aspects of the technqiue that I ." 8 are frequently underestimated and not regarded worth inspecting. In this context it is worth pointing out that, in several cases, the data is transformed in order to obtain a close correlation between the intrinsic interpretation made of the factor and the patterns displayed by the scores; apparently, many of such transformations are not justified deriving their apparent necessity from the complex mathematical manipulations applied to the data while obtaining derived solutions. In such cases, if the transformations are not consistent throughout the analysis, the inter- pretation that is done of the transformed data is clearly arbitrary and it cannot be ascertained whether the patterns obtained reflect real associations existing within the data or correspond to "mathematical" variables whose relation with the geological or geochemical features may have been obtained by chance. 6.5.3.3 Factor 3 (V-Ga) This association explains 11.5% of the variance of the set. It is formed by two elements typical of hydrolizate sediments which enter the solution with very high loadings (greater than 0.85), explaining between both of them 96% of the latent root of the factor. The enssemble may be defined as a "Lake District" association, showing high values over the essentially pelitic rocks of that area (Figure 6.21), with some minor influence of the Eskdale Granite, an ,intrusive body that renders sediments bearing high Ga values. It is worth noting that several minor highs may be distinguished in isolated areas, representing industrial contamination. Of special importance in this respect are the highs found to the south of Grange, around Port Carlisle and in the Whitehaven-Workington area. Similar factors have been found in several areas covered by argillaceous rocks in Zambia (Armour Brown, 1971), Wales (Urquidi, 1973), and South-West England (Dunlop, 1973). ""MINEX NORTHERN ENGLANN.SIX -.FACIBRC NOBEL.PERECTILE lans OF FACTOR THREE**. 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It is dominated by three essentially calcophile elements that enter the association with loadings varying from 0.796 to 0.520. The interpretation of the nature of the phenomena represented by the factor is complex due to the scattered nature of its patterns of high values (Figure 6.22). On one hand, it represents high concentrations in these elements present in the hydrolizate sediments that constitute the Silurian terrain and on the other hand it represents two magmatic features: the mainly acidic Caledonian intrusions of the Lake District and the copper mineralization present in zones of the Lake District and Northern Pennines orefields. The matter is further complicated by the presence of highs related to industrial contamination in the areas of Furness, Grange, Ulverston, Kendal, Lancaster-Morecambe, etc. The "hydrolizate" components of the association are mainly mani- fested in the southern Lake District and in places where the Skiddaw Slates and Millstone Grit series outcrop, both sequences bearing hydrolizate components in them. The part of the factor related to the igneous intrusions is manifested in highs present around the main bosses of the Lake District and in Borrowdale Volcanics terrains pierced by minor acidic dykes. The "mineralization" part of the association is evidenced in copper-producing districts as Coniston, Force Cragg, Roughtengill, and Goldscope. Finally, it is worth mentioning with respect to the spatial distribution of this factor that, due•to very high Mo levels present in the southern end of the Vale of Eden, that area displays high values of the association. As indicated previously, these values appear to be related to Mo-bearing rocks occurring in the neighbouring terrain, partly in the Mallerstang and Stainmore commons, and partly in the Dufton Fell area where a high of the association is present, possibly related to mineralized structures. • 1 4 0 6.5.3.5 Factor 5 (Ni) This is a unique factor constituted by nickel, an element that explains 95% of the latent root of the factor, which in turn explains 7.3 of the variance of the set. The causes for the existence of this unique association lie in the fact that nickel is, among the 14 elements considered, the only totally independent variable, not being correlated with any of the other variables in the set (see Table 6.2). As can be expected, the distribution of the factor in the area (Figure 6.23) has a very tight lithological control, mainly being concen- trated in the southern Lake District over the Silurian shales and in places of the Pennines over Millstone Grit terrains, presumably where there is a predominance of shale over the remaining rock-types that constitute that series. It is worth noting that, if a comparison is made with the distri- bution of Ni (Figure 6.12), it may be seen that the lithology has a much more tight control over the factor than over the element thus giving a much clearer pattern and contrast in this case. 6.5.3.6 Factor 6 (Ba-Pb) This is a negative factor explaining 6.9% of the variance of the set, being dominated by elements mostly introduced in the area by mineral- izing processes. It may be seen in Table 6.3 that Ba enters the association with a loading of -0.881 and that the loading of Pb is -0.668. In addition, it may be noticed that Zn and Li, elements that are also related to mineral- ization, are negatively loaded and explain 11% of the latent root of the factor. Therefore, this factor may be termed as "Northern Pennine Mineralization" (galena-sphalerite-barite veins and flats) explaining the four annotated variables 95% of the latent root of the component. The regional distribution of the association (Figure 6.24 shows a very good agreement with the main mineralized' areas of the Pennines, the 0 444MINEX NORTHERN ENSLANOISIX-FACTORs HonEoPERCENTILE NAPS OF FACTOR FIVE*** LOW-pASS FILTER USING EFFECTIVE RA0IuS OF i CELLS IF4h444144t444444444444444444444414+4444444#44444444F++414441+44444.(444444444 4- I I EEEEEE 605=3 rB33008900==. 0 ERE cEBBEg II Liss THAN ..3.307 BLANK 1 EERBEOCaannOBROBBF0CER=000=10030== BEBEEEEEFF0 1 BBREBBLB33BR0===Bran 010= 4 =0 UEEE=.8fE 1 i FRom -3.306 19 -.i9s i I 0E8E81E8.= /1====813=--- BBOE---- FOE =BEEF: L I I OEMB BBEEEEEE0==n3===0384'n=+++++--=-==Bra0===EaEt==6EE II I E=-==•-, ,-=0BEEE808 BEBFR=4.,+ =0= a Fa= EFQ0EBBEO II I --+++++.BEEaEEB======E0E0=-+,+.. -=f3===REEE0=-=BEEEBBE0 II Ms++ 4-...-=fl=11=0=.8CEEEcfcc Xi 1 -= -=--+-+=-03 E=--=== - === FROM ■.194 TO ...152 I I +-4.--BROFEB----BBB=- E0=++,,,------==-=- BEEEeEE9 II 1 B■4■ -.-.• 4 ---- 4 --... ----- B---- 4.-- - + .44=E000EB-. 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Features worth noting regarding this association are: (1) The fairly well defined 167 patterns found in connection with the borders of the Alston Block, a feature that is especially evident by a pronounced low in the Dufton and Murton fells areas. Apparently, this feature would suggest the presence of undiscovered mineral deposits in the Pennine Escarpment; (2) The low values found in the vicinities of Bootle, where no mineralized structures are known; (3) The definition by low association values of the barite-bearing lead-zinc deposits of the Lake District ore- field (Greenside, Stonecroft, Brandlehow, Ywethwaite); and (4) The low pattern displayed by the factor in western Cumberland, a feature that is not related to the presence of mineralized structures in that area, but to high barium concentrations existing in horizons belonging to the Coal ' Measures of the West Cumberland Coalfield. Summarizing the results of the components solution, it may be stated that the 14 original variables may be explained by 6 rotated factors representing lithological assemblages, mineralized areas, or a mixture of both. The factors representing lithological assemblages are three: Fe-Mn-Li-Co-Ga, which represents the slate-greywacke association that constitutes the Skiddaw Slates; V-Ga, representing the pelitic components of the lithological assemblages of the Lake District; and Ni, unique factor that reflects the hydroJizate sediments that constitute the Silurian terrain. 14,2 The lithological assemblages of the Pennine region are represented by a mixture of those factors, mainly because of their lithological heterogeneity, which contrasts with the fairly homogeneous nature of the sequence in the Lake District. Massive limestones and post-Carboniferous terrains are not evidenced by the model mainly because of their general low content in most elements. The mineralization of the area is represented by two factors: Cd-Zn-Pb, an association clearly related to the ore deposits of the Askrigg Block of the Pennines, but which is obscured by components of the "slate- greywacke" association (Fe-Mn-Li-Co-Ga) that creep into the scores during their estimation; and Ba-Pb, a factor representing the Northern Pennines type of lead-zinc deposits (veins and flats bearing galena, sphalerite and barite as their main components). A mixed factor found (Mo-Cu-As) partly reflects hydrolizate sedi- ments of the Silurian terrain, partly the acidic bosses of the Lake District and partly the copper mineralization scattered in the two orefields lying within the studied area. Finally, it is worth mentioning that several of the factors present high concentrations related to industrial contamination arising mainly from the Whitehaven-Workington, Furness, Kendal and Lancaster areas., • 1 4 3 CHAPTER 7 FORECAST OF BASE METALS MINERALIZATION IN NORTHERN ENGLAND 7.1 INTRODUCTION When the problem of forecasting the mineral potential of an area was discussed in broad general terms in Chapter 1, it was stated that two approaches may be considered: (1) An empirical approach based on implicit probabilities assigned to the existence of mineral wealth supported by the geological knowledge available about the area in question and in many cases on comparison with other areas that display similar geological features or environments; and (2) A theoretical approach based on the design of stat- istical models with the aid of one or more techniques of statistical analysis. In the case of Northern England, the first approach is exemplified by the analysis of potentially favourable areas done for the Northern Pennines, by Dunham (1944, 1948), which is based on the distribution of favourable lithological units, the general trend of mineralization structures, and other geological factors. The second approach is exemplified by the work of Bozdar and Kitchenham (1972), workers who forecast the lead mineral potential of the Askrigg Block of the Northern Pennines, on the basis of the ••■ analysis of the spatial distribution and output of known mines in the geo- logically similar Alston Block of that region. Considering the circumstances and pressures under which mineral exploration programs are carried out at present, in the opinion of the author the annotated approaches when applied on their own are highly restrict- ive and unlikely to be successful, a situation that is especially so for the case of the pure theoretical statistical models. It is here postulated that the best approach to solving the problem of forecasting the mineral potential of an area would be to design a theoretical model based on geological criteria selected according to the available knowledge about the 1 4 problem, to interpret from a geological point of view the validity of the model, and according to the results of the latter analysis to accept or reject the model and its results. Therefore, special attention must be stressed on the fact that even if the mathematical or statistical formula- tion of a model is correct, its results need not be meaningful from a geo- logical point of view and so the likelihood of its success as an aid in the resolution of a mineral exploration problem would ultimately be highly dependent on its correct interpretation. Finally, the usefulness of a scheme needs to be demonstrated by its application on one or more test areas. In the present research, the forecasting of base metal minerali- zation in Northern England was attempted with the use of geological and geochemical indexes which were related by statistical means to different types and combinations of output parameters that were considered to depend on the former. The main statistical technique used for the design of the different models was multiple linear regression analysis, a method that was combined in some cases with other statistical techniques in order to assess the effectiveness of the use of a combination of multivariate statistical methods for forecasting purposes. 7.2 MULTIPLE LINEAR REGRESSION ANALYSIS 7.2.1 Outline of the theory Details of the classical theory underlying multiple regression analysis cannot be presented in this work due to the length and complexity of the subject. For those details the reader is referred to Works by Ezekiel and Fox (1959), Li (1964), Yamane (1967), Chase (1967), Hope (1968) and Koch and Link (1971), where the theory is presented in a traditional, easily understandable way that does not presuppose a high degree of mathe- matical training on the part of the reader. More sophisticated, though clear, accurate and modern approaches may be found in works by Draper and Smith (1966), Goldberger (1968), Sprent (1969), Cooley and Lohnes (1971), I 4'5 Press (1972) and generally in most modern textbooks dealing with multi- variate techniques of data analysis. However, it appears desirable to review here the general regression model, the concepts and assumptions associated with it and the criteria that may be followed to test the significance and validity of a model designed by this means. The concept of regression introduced last century by Francis Galton has undergone several changes and at present it may be stated that any problem involving the expression of the mean value of a variate as a function of other variates or variables is certainly a regression problem. In principle, the establishment of the stochastic relationship between the dependent variate and its predictors means that the necessity of specifying the full set of conditional probabilities of the distributions arises. However, in practice most interest is stressed on a few parameters of those distributions, particularly on the population regression function, which describes how the average value of the dependent variate varies with the different values that may be attained by its predictors. In the present research, special emphasis has been placed on the use of multiple linear regression analysis as a means of forecasting and hence the following discussion is concerned with this alternative of regression; it is worth mentioning that the term linearity does not indicate that the model designed may be ascribed to a straight line, but that the model is linear in its parameters. Also, for the sake of clarity, variates and variables will all be referred to henceforth as variables. The simplest regression problem that may be visualized is the fitting of a straight line as a means of summarizing the relationship exist- ing between two variables. That model would be represented by the equation: Y = A / BX f E (7.1) where X and Y are the variables, A and B parameters that need ts5 i 4 be estimated (intercept and slope of the line), and E an error term expressing the departure of the observations from the fitted straight line. A, B and E are unknown,and in fact E would be very difficult if not imposs- ible to estimate since it changes for each observation of the variables. However, A and B remain fixed and even though they cannot be found exactly without examining all the possible values that X and Y may take, they may be estimated from the available data. Thus, the real relationship may be represented in a statistical manner by the equation "Y‘ = a + bX (7.2) where is the predicted value of Y for a given X, when a and b have been estimated. The estimation of a and b is made by the least squares procedure, which renders estimates that have the following properties: (1) They are estimates that minimize the error sum of squares irrespective of any distribution properties of the errors (i.e. an assumption that the errors are normally distributed is not necessary to perform the estimation although it is required to test the significance of the model and to obtain confidence intervals). (2) The estimates are linear functions of Y that provide unbiased estimates of the parameters which have the minimum variances, irrespective of distribution properties of the errors. (3) If the errors are random independent variables distributed according a2(i.e. then the estimates are the maximum likelihood estimates of the true parameters. The resolution of Eq.(7.1) by means of the least squares method considers that the resulting estimates of a and b should minimize the sum of squares of deviations from the true line, that is: n n S=/ e.1 2-- "/ (Yi - A -14.3(1.)2 =1 i=1 i should have the minimum possible value. M + • 147 By differentiating that equation, a and b may be obtained through relations known as normal equations: y Y. = an + b y X. (7.3) i=1 i=1 n n n XYiXi iaXX.+b X X.2 (7.4) i=1 i=1 1 i=1 1 The solution of Eqs. 7.3 and 7.4 for a and b are: EX. Y. - ((EX.)(CY.))/n C(X. - Y. - Y) 1 1 1 1 1 RH b = 1 (7.5) • e(x. - Ex.' .- (CX.)2/n 1 1 a = - (7.6) Substituting Eq. 7.6 into Eq. 7.2, the estimated regression equation is obtained 2 = Y - b(X - where b is given by Eq. 7.5. A more general situation including more than two variables can be treated by extension in a similar way, being in this case convenient to express the different relationships in matrix notation: Y = XB + E where Y is the vector of the observation, X is the matrix of the independent variables, B is the vector of the parameters, and E is the vector of the errors. In that case, the normal equations can be written: X'Xb = X'Y where b = (X'X) X'Y Solving these equations, the parameters may be estimated and the estimated regression equation may be expressed by the following relationship: = Xb 1 8 The measure of precision that can be attached to the estimated equation is given by the following expression: + icY. = 1(Y.1 - Y.)1 2 - SYY = SR SE where the left hand side is the sum of squares (or SS) of deviations of all the observations from their mean, the term SR is the SS of the deviations of the observations from the predicted or fitted values (i.e. residual or unexplained SS), and the expression SE is the SS of the deviations of the fitted values from the mean of the observations (i.e. SS due or explained by the regression). In matrix notation, that relationship may be expressed as: Y'Y = (Y'Y - bX'Y) b'X'Y The respective degrees of freedom associated with each of those terms (i.e. the number of independent pieces of information required to compile each of them) is (n-1), (n-k-1), and k, respectively, for k variables considered in the model. With the annotated relationships, the following table for the analysis of variance may be constructed: Source Sum of Squares Degrees of Freedom Mean Square Regression SE k SE/k (MSR) Residual SR n-k-1 SR/(n-k-1) (5,2) Total SYY n-1 SYY/n-1 An additional measure of the precision of the regression is given by the multiple correlation coefficient or coefficient of multiple 1 4 9 determination: C(Y. - i)2 1 - SR 2 SE R SYY SYY e ) 2 1 This statistic varies from 0 to 1, tending to 1 the more perfect the prediction. It is usually expressed as a percentage,measuring the proportion of the total variation of the mean value of the independent variable explained by the regression. Care must be stressed in this respect because R2 may be made equal to 1 simply by using n properly select- ed coefficients and an intercept in the model since in this case the equation will cease to be stochastic being deterministic and fitting the data exactly. Furthermore, even though the addition of a new term will always increase R2 , it will not necessarily improve the precision of the estimate. This is due to the fact that the reduction in the residual SS attained with the addition may be less than the original residual SS, and since one degree of freedom is removed, the resulting mean square (i.e. variance of the estimate) may become larger. The statistical test of significance for:R (i.e. its statistical difference from 0) may be performed according to the following statistic which follows an F distribution with (k-1) and (n-k) degrees of freedom: 2 F R (n-k) (1-R2)(k-1) It is interesting to note when dealing with correlations that a very good way of analyzing them is by means of the regression structure coefficients (Cooley and Lohnes, 1971), a statistic whose vector is obtained by dividing the vector of predictors-criterion correlations by the multiple correlation coefficient. This interpretative device places little emphasis on the magnitude of the regression coefficients, a fact that is of special importance when dealing with small samples, when the beta weights show extreme fluctuations notoriously evident when strong collinearities between 1 5 0 the independent variables are present, as in this case. It must be noticed that this way of analyzing a regression model shows that the predictors are more correlated with the regression function defined on them than with the response. In a similar manner to R2, the statistic known as standard error of the estimate may also be used as a measure of the precision of the predictions. This statistic is in fact the standard deviation of the mean estimate with respect to the mean, and is expressed by the following relationship: s = Aesidual Mean Square Once again the 'variation of this statistic must be considered with care since although in general terms the smaller its value the better the estimates, s may be made equal to 0 by including enough parameters in the model (just as R2 may be made equal to 1). The statistical significance of the regression model, that is the probabilistic test that a similar relation between the variables , could have not been reached by chance, may be done by means of an F statistic. Two particular functions of the independent variable are important in this context. The mean square due to regression (MSR) and the residual mean square (s2). Their ratio follows an F distribution with (k) and (n-k-1) degrees of freedom, a fact that may be used to test the hypothesis: 111 :131 =1:12 =—=L=CI by comparing its value with the 100 (1 - c)% point of the tabulated F distribution. Similarly, test for individual regression coefficients (i.e. H1: B AD) may be carried out by the use of an F statistic or a t 1 statistic squared. Other tests applied to a regression model are the partial F-tests. If several terms are present in the equation they may be thought of as entering the model in any desired sequence. If 1 5 1 SS (bila,bi ,b ) i=1,...,k k is calculated, a sum of squares with one degree of freedom will be obtained which will measure the contribution to the regression SS of each coefficient b. given that all the terms which did not involve B. were already in the model. In other words, it will measure the value of adding a Bi term to an equation that originally did not include such a term, that is it measures the contribution of B.as if it were added last to the model. The corres- ponding mean square equals SS (since it has only one degree of freedom) and it can be compared with s2 by an F test. This particular type of test is called the partial F-test for Bi. Other parameters of a regression model that are worth mentioning are the partial correlation coefficients of the independent variables with respect to the response, values that indicate the correlation existing between each independent variable and the response, after allowances have been made for the presence of the other variables in the equation. If the regression model is of the form: y = a b1X - b X 1 2 2 and y, after X has the partial correlation coefficient between X1 2 been accounted for, equals: r X - r r y 1 yX2 X1X2 r yX -X 1 2 ((l-r2 )(1-r2 )) yX X X 2 1 2 where r - yX 2 2 )) 1/2 ((eXJ (ear 1 is the correlation coefficient between all the independent variables and the response. A final test that is usually performed to assess the validity of a regression model is based on the examination of residuals which are the differences between the observed values and those predicted by the model (i.e. Y.-Y.). In performing a regression analysis, several assumptions about the errors are made, namely that they are independent and normally distributed, with zero mean and a constant variance. If the designed model is correct, the residuals should display tendencies that confirm those assumptions or at least should not exhibit a denial of them. Several ways of examining the residuals are available. Overall plot, plot against the fitted values and plot against the independent vari- ables, are some of the graphical approaches that may be followed. These graphical methods are the most commonly used since they will almost certainly reveal any violation of the assumptions serious enough to consider the model incorrect. Besides, the plots will clearly identify the presence of out- ' Tiers (residuals with absolute value far greater than the rest), which indicate data values that are not typical of the set, thus requiring careful examination before being included in the analysis. In addition, several statistics have been suggested which provide a numerical measure of the behaviour of the residuals. These methods are seldom used, except in cases when graphical methods indicate the presence of serious anomalies in the model. The behaviour of residuals and examination of outliers is the subject of detailed analysis in papers by Anscombe (1960, 1961) and Anscombe and Tukey (1963). 7.2.2 Methods of Multiple Linear Regression Analysis_. Several statistical procedures may be followed to select what may be called the best regression equation which expresses the relationship between the independent and dependent variables in the most meaningful,and significant way possible. No unique statistical procedure exists for doing this and personal judgement as well as the type of facilities available play an important role in the selection'of the method to be used. 1 5 3 The different methods available would not necessarily lead to the same solution when applied to the same problem although in many instances they will achieve the same answer. The most used methods are described in the following paragraphs where emphasis is placed on their advantages and disadvantages. (A) All Possible Regressions This method requires the fitting of every possible regression equation including a constant term plus any number of independent variables. k Since each variable can either be or not be in the model, there are 2 equations that need to be analyzed. In general, this method while giving the means of analyzing all the possibilities, also implies that a large number of equations that may be rejected beforehand are examined and hence a proportion of the computer time used is wasteful. Besides, the physical effort of examining the print-outs is enormous when more than a few variables are used. As an example of the latter assertion, it may be indicated that in the present case 16,384 equations would haVe been examined for every output variable considered,while designing only the geochemical model. (B) Backwards Elimination Procedure This method is an improvement of (A) in the sense that it does not attempt to examine all the possible regressions but only the best regressions containing a pre-fixed number of variables in them. It is a satisfactory method to use if as many variables as possible are desired in the model, being much more economical in computer time than (A). However, if the X matrix is ill-conditioned (i. e. almost singular), this procedure may easily give wrong results due to rounding errors, a problem that may be largely avoided by the use of double precision in the calculations, though the computing time in this case is greatly increased. 0 1 5 4 (C) Forward Selection Procedure This technique's aim is similar to (B), but operates in an inverse way, that is inserting variables in turn until a decision is reached on the equation to use. The order of insertion is determined by using the partial correlation coefficient as a measure of the importance of the variables not yet in the equation. It is a very good method to use since it is more economical in computer time than the preceding two and it avoids working with more variables than necessary while improving the equation at every stage. Its main drawback is that no attempt is made to explore the effect that the introduction of a new variable may have on the role played by the varibales already in the model. (D) Stepwise Regression Procedure This technique is an improved version of the latter, involving the re-examination of the model at every stage in relation to the variables included previously in the equation. It is interesting to note that regression methods do not only operate by taking into account the relation- ship between the response and each independent variable, but as important in their operation is the relationship that might exist between the variables included in the equation. Hence, a variable that may have been the best single variable to include in the model at an early stage may, at a later stage, be superfluous because of its relationship with variables incorporated later into the equation. To check on the inter-variables relationship, this model relies on partial F-test which are compared with pre-selected levels of the approp- riate F distribution. By this means, the contribution of each variable to the model is judged as if it were the most recent variable entered, irrespective of its actual point of entry into the equation. Variables that provide non-significant contributions are removed and the process continued until no more variables may be admitted or rejected. I 5 5 This is one of the best methods of multiple regression analysis, though sensible judgement is required in the initial selection of the variables and in the critical examination of the model. In this context, it is important to note that the researcher should not rely too heavily on the automatic selection performed by computers, but must, up to a certain extent, guide the computer in the selection of the variables. (E) Stagewise Regression Procedure This method does not provide a least squares solution for the variables included in the final equation. The idea is to calculate a regression between the response and the independent variable most correlated with it; calculate the residuals of that model and use these as response to be regressed against the remaining independent variable most correlated with them, a process that is continued until any desired stage. The estimates obtained by this means are smaller in absolute value than those obtained by least squares, by a factor proportional to R2, implying that the variable that is added is actually more important than the technique indicates. The . advantages of this method lie in the fact that it enables the researcher to select the variables for reasons other than their correlation with the response and to force into the model variables that would be considered' unsuitable by any other technique. In spite of this apparent advantage, the estimates obtained by this means are almost always worse than those obtained by stepwise regression, having always a higher residual mean square; hence, the use of this technique is not recommended in multiple regression analysis, excepting particular cases when the effect in the response of a peculiar combination of variables is to be analyzed. The annotated methods are by no means the only multiple regression techniques that are used to select the best possible regression equation from a set of variables, but are those most used at present. Variations of all of them have been employed for different purposes with varying degrees 1J 6 of success depending on the type of problem to be solved. 7.2.3• Multiple Linear Regression Techniques used in the Present Research From the different possible methods that can be used to perform multiple linear regression analysis, a variation of the classical stepwise regression procedure was selected in the present research to analyze the relationship existing between the various production variables considered and the geochemical and geological indexes. For this purpose, the main calculations were done with a computer program taken from the Biomedical Package of Computer Programs prepared by the University of California at Los Angeles (1968). That program (BMDO2R) computes a sequence of multiple regression equations in a stepwise manner, adding at each step the variable that makes the greatest possible reduction -in the residual sum of squares. Equivalently, that variable is the one which has the highest partial correlation with the response partialed on the variables already in the model and equivalently is the variable that, if it were added, would have the highest partial F value. Besides, variables can be forced into the regression equation, a feature that is extremely useful in particular cases such as the present one, when high correlation exists between the independent variables. While analyzing the different models obtained, the selection of the best regression equation was done on the basis of the following criteria, which had to be fulfilled by the model if it was to be accepted as correct: - (1)' The F-value of the equation should be significant at the 0.05 level of the corresponding F distribtuion (I.e. a 95% confidence level was taken as a minimum level of significance for the model as a whole). (2) The partial F-test for each variable included in the model should be significant at the 0.10 level of an F distribution with 1 and k degrees of freedom (i.e. a 90% confidence level was considered acceptable for the individual regression coefficients). • 157 (3) A decrease in the standard error of the estimate of at least 5% was considered an acceptable contribution for a variable to make towards the improvement in the precision of the estimates, in order to regard its inclusion in the model worthwhile. (4) Any variable entering the model should contribute at least 2% of explanation for the total variance of the mean response; that is, each variable to be entered should increase the multiple correlation coefficient by an amount greater or equal to 0.141. As it may be seen later on, the variables that comply with condition (3), on almost all occasions complied with condition (4), both being measures of the significance of the estimate almost equivalent in the present case. (5) The residuals of any model should confirm the assumptions made about them or at least should not show features contradicting those assumptions. The analysis of the residuals was made in each case by graphical methods, plotting them against the fitted values and independent variables included in the equation; as well, overall plots and tests of normality by non- parametric means (Kolmogorov-Smirnov test) were performed on them. A very good account of how stepwise regression operates and of the calculations involved may be found in Efroymson (1960). The method used in the present research,as indicated previously, was a variation of the traditional method. Normally, the technique is employed in such a way that whenever a variable is removed from the model due to its low partial F-value, that variable is rejected and is not considered in the analysis from that step onwards. In the present case it was found that, due to the high correlation existing between many of the variables, the traditional method was not the best to apply, but in many cases variables were maintained in the model even though their F-value was lower than the minimum considered suitable and their influence in the equation was examined in relation to new combinations of predictors that were developed in later steps. • It was found that by this means, geologically significant variables which at a certain step had a non-significant F-value became statistically significant in later steps when other variables with which they had partic- ular relationships were included in the model. In other words predictors that at any one step were non-significant or removed were not altogether rejected but were at later steps considered in the-analysis since at that later step the model was formed by a new combination of variables which could "support" in a significant way the inclusion of the variable in question. The main advantages connected with the use of the program BMDO2R over other programs available are the following: (1) By selecting adequate F levels for inclusion and rejection of pre- dictors, the researcher deals at every step with equations fully significant at the chosen level and if a variable is removed from the model it is not rejected altogether but at every succeeding step it is analyzed as if it had been in the equation. As indicated previously, in the present case this was a required feature of the program to be used. (2) Variables may be forced and rejected from the model, disregarding the value of their F statistics or they may be maintained in the equation even if their F-value is below the one selected for rejection. For this purpose the program includes seven degrees of forcing and thus the variables may be entered into the model in any desired sequence. (3) The program has a means of fixing the number of steps desired stopping the computations once the required step is reached. This device allows the researcher to save computing time since once a satisfactory step is reached, the results of the addition of new variables, either by the normal way or by forcing them, is usually evidenced within the next two steps, and hence in most cases there is no need to go through all the calculations (i.e. allow the program to complete the whole solution), a feature especially important when a large number of variables are involved. 1 3 9 (4) The printout is very clear and easy to check, a fact that is extremely useful when a large number of solutions need to be analyzed and compared. Besides, plots of the residuals may be obtained at the same time, a device that saves working time and which allows complete control over the results at every moment. - In order to check the results obtained, some of the equations were tested with the aid of the STPGR routine of the Scientific Routines Package prepared by IBM (1965). This routine performs a stepwise regression adding at each step the variable that reduces most of the residual sum of squares. Its printouts are not as clear as those of the main program used and the additional facilities of the latter are not available, Therefore, a limited use of this program was made during the present research. The core requirements of the BMDO2R program are approximately 25K, a typical running time is 3 seconds for 15 variables and 100 cases, and the number of pages of the printout equals: 54-No. of steps (23+3/4 No. of variables), all figures referring to a CDC 6400 computer. 7.3 FORECASTING MODELS BASED ON MULTIPLE LINEAR REGRESSION 7.3.1 Generalities As indicated in Chapter 5, it was considered in the present research, that the base metal production of Northern England was defined by three kinds of output variables: (a) Total production figures; (b) Average value of the production per deposit; and (c) Number of deposits per cell. These variables were computed for all the productive cells within the area, according to the procedures indicated in that chapter, each of them being subdivided into five production categories representing different types of base metal output: (1) Total production; (2) Lead-zinc production; (3) Lead production; (4) Zinc production; and (5) Copper. production. 1 6 0 Considering the widely contrasting outputs obtained in the region for the different base metals, a feature that is greatly controlled by extra- geological factors (e.g. economic conditions, mining techniques used, etc.) it was regarded that a simple model for the forecast of combined production or reserves would be highly unlikely to be successful. Therefore, it was decided to design models for each individual base metal and later to try to combine these forecasts to obtain a more realistic model for the prediction of combined reserves. To assess the validity of this assumption, models including combined total and lead-zinc production were computed and their results were compared at the end with those obtained by indirect means. Also, in order to include in the forecasting models the maximum possible amount of "local" weight, which would ultimately render more mean- ingful estimates than regionalized models, it was considered that the optimum forecast would be obtained by following a twofold or convergent path and to integrate the results of both paths at the end. For this purpose, average reserves per deposit were estimated for each cell and an estimation of the number of potential productive deposits per cell was carried out independently; at the end, both estimates were combined, rendering M1 models for the potential reserves of each metal, we well as combined lead- zinc and total potential reserves. In order to test the validity of this convergent method of forecasting, straightforward models were calculated and their results were compared with those attained by the convergent means. According to the foregoing procedure and since three types of model were designed in each case (geochemical, geological, and combined geological-geochemical), the need to build up 45 different models arose (considering those used for testing purposes), requiring the examination of more than 1500 equations to arrive at the final results. 7.3.2 Preliminary Investigations Previous to the design of the different definitive forecasting 1 6 I models, numerous preliminary equations were examined with a fourfold purpose: (1)It was necessary to decide which independent variables were to be included in the geochemical models, that is, the different geochemical scores (see Chapter 5) were examined in order to choose the best of them for the pursued purposes. (2) The possibility of using models without a constant term (i.e. with 0 intercept) needed to be evaluated. (3) It was necessary to decide in which way the variables were to be included in the models. (4) The possible influence on the models of geological environments as a whole,and of the number of observations considered for each cell, needed to assessed. The first problem is related to the evaluation of the geochemical indexes (scores) obtained in different ways, as a means of forecasting the different output indexes considered, and to choose those most favourable to depict the relationship, output-geochemistry. The second point refers to the analysis of the need for the presence in the model of a constant term, the lack of which would imply that the regressors being equal to zero, the response would be zero, a method that has been successfully used in several regression problems and hence whose use in the present case merited investigation. The third problem was concerned with the different transformations that may be applied to the dependent and/or independent variables in an attempt to obtain more meaningful results than those obtained with the raw-data. This procedure is normally recommended by different authors who have dealt with regression problems and, what is more, in many cases its use is unavoidable if significant results are to be obtained. By comparing preliminary equations obtained with transformed and untransformed variables, a final decision was reached as to the way in which the variables were to be included in the models. The final point refers to the occasional need to introduce in a model variables that do not take values within a continuous range, but take values in two or more levels, as for example variables that indicate the number of samples which an average represents, or the type of geological environment from where a sample or observation has been drawn. In those cases, scaled or dummy variables represent such factors which may have a deterministic effect on the response and thus need to be investigated. 7.3.2.1 Selection of Geochemical Variables As indicated in Chapter 5, four types of geochemical indexes or scores were computed for each cell in the area, with the purpose of assess- ing the influence that the geology of the sampling site may have in the results. Two of these indexes (A and B) disregarded the local geology and two (C and D) were calculated taking into account this factor. Besides, scores B and D were obtained in the usual way of calculating standard scores, without considering the type of distribution of the different chemical elements involved. On the other hand, scores A and C were estimated considering the frequency distribution' of each element by comparing those distributions with the normal and log-normal ones. The selection of the scores that best display the relationship output-cell geochemistry, was done by regressing each type of score against the different production indexes for the five output categories distinguished (total, lead-zinc, lead, zinc, and copper). The comparison between the equations was done taking into account the standard errors of the estimates obtained and the amount of variance of the response explained by the equation, as given by the squared multiple correlation coefficient. It is important to note at this point that since the latter is highly dependent on the number of variables present in the model, when comparing equations that have different numbers of variables in them, it appears appropriate to use an adjusted R2 that penalizes those models that have a higher number of variables, particularly when the number of observations is small. For this purpose, the following statistic was used, after Goldberger (1968): R2 -= R2 N-K-1 (1-R2) 2 where R is the computed multiple correlation coefficient squared, N is the number of observations and K is the number of regressors present in the equation. When selecting the geochemical scores, it was considered that the best way to operate was to use elements determined by the same analytical method in order to avoid any influence that those techniques,and their implied differences in accuracy and precision, might have in the regressions. Therefore, 10 elements determined by spectrographic methods were chosen for this purpose; thus, the following discussion is based on scores calculated for Ba, Co, Cu, Fe, Ga, Li, Mn, Ni, Pb, and V. Firstly, the scores were regressed against absolute production figures for the five output categories considered. The correlations between the scores and the response, and the resulting equations, were carefully examined to arrive at a preliminary conclusion. The correlations are summarized in Table 7.1, their most important features are: (a) By far, most of the elements are not significantly correlated with the response at the 0.05% level; (b) Several elements present negative coefficients,of correlation with the regressand, a feature particularly evident for V and Ba, elements that have negative coefficients in almost all cases; (c) Scores A and B present significant correlatiOn with the response in the cases where the lead output plays a decisive role; (d) An unusual feature arising from this table is the high correlation of Li with the response, which was not to be expected considering the deposits are meso or thelethermal; this feature indicates the strong influence of the geological environment on the generation of workable ore deposits; (e) An antipathetic relationship 0 fki TABLE 7.1 COEFFICIENTS OF CORRELATION BETWEEN GEOCHEMICAL SCORES AND ABSOLUTE PRODUCTION VALUES TOTAL PRODUCTION PB-ZN PRODUCTION LEAD PRODUCTION ZINC PRODUCTION COPPER PRODUCTION Score A B C D_ A B C D A B C D A B C D A B C D 0 00 O D Fe -0.01 -0.01 0.18 0.19 -0.00 -0.00 0.17 0.18 -0.02 -0.01 0.17 0.17 0.00 0.18 0.18 -0.22 -0.18 -0.28 -0.27 C 00 O I • Ga -0.03 -0.03 0.26 0.27 -0.02 -0.02 0.26 0.26 -0.03 -0.03 0.27 0.28 -0.08 c 0.07 0.07 -0.06 -0.02 0.16 0.17 ,-4 n I • Cu -0.19 -0.15 -0.04 0.00 -0.19 -0.15 -0.04 -0.03 -0.21 -0.16 -0.05 -0.03 -0.18 -0.17 -0.11 0.14 0.13 0.26 0.28 00 0 • Pb *0.34 *0.32 0.30 0.24 *0.33 *0.31 0.29 0.23 *0.34 *0.32 0.30 0.24 0.04 0.03 0.00 -0.26 -0.23 -0.20 -0.18 ,- k .0 I • 1 V -0.12 -0.12 0.18 0.17 -0.10 -0.11 0.17 0.16 -0.12 -0.12 0.17 0.16 -0.16 CO -0.00 -0.02 0.22 0.24 0.23 0.25 0 000 I 1 • Ba -0.23 -0.13 -0.20 -0.15 -0.23 -0.14 -0.22 -0.16 -0.23 -0.13 -0.21 -0.16 -0.57 -0.45 -0.34 0.16 -0.19 0.13 -0.15 N 0C4 • Co -0.02 -0.02 0.30 0.24 -0.02 -0.02 0.29 0.23 -0.04 -0.04 0.28 0.22 0.02 0.35 0.30 -0.10 -0.11 0.08 0.21 Cn • Ni 0.02 0.02 0.15 0.15 0.01 0.00 0.13 0.13 -0.03 -0.03 0.12 0.11 0.22 0.34 0.43 0.17 0.17 0.13 0.11 00 0 • Mn -0.02 0.04 • -0.10 0.23 -0.02 0.04 -0.10 0.22 -0.03 0.03 -0.11 0.22 -0.02 -0.04 0.18 0.08 0.05 0.30 0.11 ,- • 1 Li 0.25 0.24 *0.36 *0.44 0.24 0.23 *0.35 *0.44 0.24 0.23 *0.36 *0.45 0.16 0.21 0.26 -0.32 -0.29 0.14 -0.20 * significant at the 95% confidence level TABLE 7.2 STANDARD ERRORS AND ADJUSTED MULTIPLE CORRELATION COEFFICIENTS OF PRELIMINARY GEOCHEMICAL MODELS CONSIDERING ABSOLUTE PRODUCTION VALUES (R2 as percentage) SCORES TOTAL OUTPUT LEAD OUTPUT ZINC OUTPUT COPPER OUTPUT R2 St.Error R-2 St.Error R2 St. Error 2 St. Error A 36 12757 37 11090 32 2738 89 274 B 16 14157 17 12413 56 2178 92 214 C 40 12288 42 10654 u.s. u.s. u.s. u.s. D 26 13308 27 11619 92 773 u.s. u.s. u.s. = no significant equation found , 1 6 4 between Pb and Cu appears to exist, tending to confirm the fact that lead- zinc producing areas bear little copper ores and vice versa. The significant results concerning the comparison between the different equations obtained are summarized in Table 7.2. In that table it may be seen that the best scores to use up to this stage are those of type A which perform rather well in all cases. Scores of types C and D could only be used when analyzing output figures dominated by lead and zinc, respectively. B scores are of little use, except for the case of copper output. In order to do a thorough investigation of the problem, the next stage performed was the preliminary regression of the different types of score against the average output per deposit for the five categories of production distinguished. Table 7.3 indicates the coefficients of corre- lation calcualted between the different scores and the various responses. The most important features displayed by that table are: (a) Once again, almost all elements are not significantly correlated with the response expressed in terms of average production per deposit; (b) Ba, Cu and Ni show negative coefficients when considering lead or zinc output, and, as in the previous case, Cu and Pb show an antipathetic relationship; (c) In those responses dominated by lead or zinc production, a negative Cu-Ba-Ni association appears to be present, as well as a positive Pb-Li association; when the response refers to copper output, a negative Fe-Pb-Li association appears to exist, as well as a possible relation of V with this response; (d) In general, the coefficients of correlation are much lower in this case than those obtained using absolute production figures. The equations obtained by regressing the different types of score against the average production per deposit for the five output categories distinguished are summarized in Table 7.4. These regressions appear to confirm the conclusion obtained with absolute production figures, in the TABLE 7.3 COEFFICIENTS OF CORRELATION BETWEEN , GEOCHEMICAL SCORES AND AVERAGE PRODUCTION VALUES TOTAL AVERAGE PB-ZN AVERAGE LEAD AVERAGE ZINC AVERAGE COPPER AVERAGE PRODUCTION PRODUCTION PRODUCTION PRODUCTION PRODUCTION Score A B C D A B C D A B C D A B C D A B C D Fe 0.10 0.10 0.07 0.07 0.11 0.11 0.06 0.06 0.05 0.05 0.05, 0.05 0.01 0.00 0.15 *-0.87 -0.21 -0.21 -0.27 -0.26 Ga 0.14 0.14 0.14 0.15 0.16 0.16 0.15 0.15 0.08 0.08 0.14 0.14 -0.00 -0.00 0.26 *-0.90 -0.05 -0.05 0.16 0.17 Cu -0.03 0.05 -0.04 0.07 -0.01 0.07 -0.03 0.05 -0.10 -0.01 -0.08 0.02 -0.20 -0.16 -0.17 -0.26 0.14 0.09 0.25 0.27 Pb *0.32 0.26 0.28 0.26 *0.31 0.26 0.27 0.25 *0.32 0.29 0.29 0.28 -0.07 0.08 -0.11 *-0.90 -0.27 -0.26 -0.21 -0.23 V 0.06 0.06 -0.00 -0.00 0.09 0.09 0.01 0.00 0.00 0.00 -0.03 -0.03 -0.14 -0.14 0.18 *-0.90 0.22 0.22 0.23 0.24 Ba -0.12 -0.13 -0.14 -0.09 -0.12 -0.13 -0.16 -0.11 -0.12 -0.11 -0.15 -0.09 -0.55 -0.47 -0.42 -0.43 0.16 -0.17 0.16 -0.14 Co 0.03 0.03 0.03 0.08 0.03 0.03 0.00 0.08 0.04 -0.04 -0.01 0.06 -0.03 -0.04 0.16 *-0.39 -0.09 -0.09 0.14 0.36 Ni -0.09 -0.09 -0.12 -0.13 -0.10 -0.10 -0.13 -0.14 -0.20 -0.21 -0.17 -0.18 -0.05 -0.05 0.02 *-0.38 0.18 0.18 0.14 0.14 Mn 0.05 0.09 -0.06 0.03 0.06 0.90 -0.06 0.02 0.01 0.05 -0.10 0.02 -0.08 -0.05 -0.13 *-0.40 0.08 0.01 0.28 0.08 Li 0.12 0.11 0.16 0.23 0.11 0.10 0.16 0.23 0.07 0.06 0.14 0.22 0.37 0.37 0.43 0.50 -0.33 -0.32 0.11 -0.24 * significant at the 95% confidence level TABLE 7.4 STANDARD ERRORS AND ADJUSTED MULTIPLE CORRELATION COEFFICIENTS OF PRELIMINARY GEOCHEMICAL MODELS CONSIDERING AVERAGE 'OUTPUT PER DEPOSIT (R2 as percentage) SCORES TOTAL OUTPUT LEAD OUTPUT ZINC OUTPUT COPPER OUTPUT R2 St.Error R-2 St.Error R 2 St.Error 2 St.Error A 18 1063 25 948 97 45 84 126 B U.S. U.S. 24 973 70 407 85 122 C 17 1060 22 907 59 481 U.S. U.S. D U.S. U.S. • 7 1060 82 335 62 194 u.s. = no significant equation found sense that they point out score type A as the best to use in all cases. Score type C could only be used when dealing with productions strongly influenced by lead output, and scores types B and D proved to be of little use. As a final step, to get a complete picture of the value of the different types of score as potential geochemical forecasting indexes, they were regressed against production figures expressed as number of deposits per cell. The correlations existing between the different scores and the various production categories distinguished, are summarized in Table 7.5,, where the following features may be observed: (a) Most elements are not 4 significantly correlated with the number of deposits per cell; (b) Cu and Ba show in almost all cases negative coefficients; (c) A large number of negative coefficients is associated with scores types A and B; (d) The out- put figures strongly influenced by lead, present this element significantly correlated with the response, plus a Pb-Co-Li association that may be envisaged in score types C and D; manganese appears to play a certain role in the latter association, in the case of score type D. The results of the regression of the different scores against the number of deposits per cell are summarized in Table 7.6 where it may be seen that scores type A are the best to use in all cases, being the only ones that give significant equations with the five categories of output distinguished. When dealing with production figures strongly influenced by lead, the four types of scores could be used, though D scores perform badly and the results attained with score types B and C are poorer than those attained with A scores. Summing up the preliminary investigations performed with the different types of geochemical indexes calculated, the following points merit consideration: (A) The best geochemical indexes to use for forecasting purposes are • TABLE 7.5 COEFFICIENTS OF CORRELATION BETWEEN GEOCHEMICAL SCORES AND NUMBER OF MINES PER CELL TOTAL NUMBER OF MINES NUMBER OF PB-ZN MINES NUMBER OF LEAD MINES NUMBER OF ZINC MINES NUMBER OF COPPER MINES Score A B C D A B C D A B C D A B C D A B C D Fe -0.05 -0.05 0.22 0.22 -0.05 -0.05 0.20 0.20 -0.05 -0.05 0.20 0.20 0.03 0.03 0.15 0.18 -0.24 -0.23 -0.05 -0.01 Ga -0.12 -0.12 0.20 0.20 -0.12 -0.12 0.19 0.19 -0.13 -0.12 0.19 0.20 -0.05 -0.05 0.00 0.15 -0.20 -0.20 0.51 0.53 Cu -0.22 -0.18 -0.05 -0.01 -0.24 -0.19 -0.06 -0.05 -0.24 -0.20 -0.06 -0.05 -0.10 0.02 -0.11 0.03 -0.21 0.30 -0.04 0.38 Pb *0.47 *0.43 *0.44 *0.34 *0.46 *0.41 *0.43 *0.32 *0.47 *0.41 *0.44 *0.33 0.05 0.00 0.05 0.14 0.05 0.34 0.05 0.40 V -0.19 -0.19 0.12 0.11 -0.19 -0.19 0.10 0.10 -0.19 -0.19 0.10 0.10 -0.07 -0.07 -0.00 0.13 0.01 0.02 0.22 0.28 Ba -0.08 0.05 -0.04 -0.01 -0.09 0.03 -0.07 -0.02 -0.09 0.04 -0.06 -0.08 -0.44 -0.24 -0.34 -0.18 0.06 0.28 -0.04 0.06 Co -0.07 -0.07 *0.35 0.30 -0.09 -0.08 *0.34 0.18 -0.09 -0.09 *0.34 0.28 0.07 0.07 0.33 0.20 -0.27 -0.27 0.16 0.31 Ni 0.07 0.07 0.25 0.26 0.05 0.05 0.23 0.24 0.04 0.04 0.23 0.24 0.29 0.30 0.39 0.22 -0.19 -0.19 0.10 0.07 Mn 0.02 0.04 -0.02 *0.32 0.02 0.03 -0.03 0.30 0.02 0.03 -0.02 *0.31 0.07 0.05 0.05 0.19 0.24 0.16 0.39 0.44 Li 0.15 0.14 0.26 *0.34 0.14 0.13 0.26 *0.33 0.14 0.13 0.26 *0.34 0.14 0.14 0.17 0.19 -0.17 -0.18 0.39 0.18 * significant at the 95% confidence level TABLE 7.6 STANDARD ERRORS AND ADJUSTED MULTIPLE CORRELATION COEFFICIENTS OF PRELIMINARY GEOCHEMICAL CONSIDERING NUMBER OF DEPOSITS PER CELL SCORES TOTAL OUTPUT LEAD OUTPUT ZINC OUTPUT COPPER OUTPUT R2 St.Error R2 St.Error R2 St.Error R2 St.Error A 30 7.9 18 7.9 46 2.5 59 0.5 B 16 8.7 17 8.3 u.s. u.s. u.s. U.S. C 17 8.6 18 8.2 u.s. u.s. u.s. u.s. D 9 9.0 11 8.6 u.s. u.s. u.s. u.s. u.s. = no significant equation found i 6 6 scores type A, which perform rather well when dealing with absolute produc- tion figures, and much better than the rest when regressed against average production per deposit and number of deposits per cell. Scores types B and D are in almost all instances of little use since in many cases they do not render statistically significant models, or, when significant equations are obtained, the resulting estimates are very poor. Scores type C could only be used successfully when dealing with production indexes strongly influenced by the value of the lead output. The explanation for the behaviour of the different types of index is related to the kind of data that they represent. Since each score is the average value of all the samples collected in an area of 100 square kilometres, which in the present case represents an average of about 35 samples, the influence of the sampling-site geology is strongly diminished, particularly when several geological units are present within a single cell, each unit exerting its influence over a limited and varying number of samples. This fact would account for the generally better, or at least similar, results obtained with the scores that disregard the local geology, as compared with the results attained with scores that take that factor into account. It is possible that in areas of smaller size or more uniform geology than the one studied in the present research, the latter scores might be of much more use than the regionalized ones, and hence the possi- bility of using them must be seriously considered in such cases. Similar considerations apply to problems that deal with small cells of fairly uniform geology. The best results obtained with scores that take into account the frequency distribution of the individual elements, may be explained by the fact that transformations that render gaussian the frequency distribution of the independent variables, should give better results than those of on transformed data because multiple regression operates at its best when it deals with muitinormal variables. A point worth mentioning when regarding the characteristics of the data used, is that the averaging does not supress significant anomalous values when the scores for each cell are calculated. These anomalous values will always exert some influence in the final score, depending the degree of influence an the number of anomalous values or samples in the cell, as compared to the number of non-anomalous samples. Single samples are likely to exercise little influence on cell-average, and hence the possibility of loosing•an anomaly picked up by a single sample is relatively high, though this disadvantage is counterbalanced, to a certain extent, by a similar elimination of isolated spurious results resulting from contam- ination, wrong analysis, or other. Areal anomalies manifested in groups of samples of a single cell, will in this case be enhanced when compared with normal non-anomalous scores, thus fulfilling the requirements of a method for the interpretation of regional geochemical results. (B) Most of the geochemical scores or indexes calculated are uncorrelated with the responses at the 0.05% level. Lead is correlated with the output variables in those cases where lead output plays an important role in the production figure considered and Li, Co and Mn are also significantly corre- lated with the response in some cases. No systematic correlation was found between any score and zinc or copper production indexes. These facts are important to consider since they point out the necessity of anal- yzing regional geochemical data by means of multivariate statistical techniques, rather than by univariate methods which would very likely not give the desired answer, at least not in the field of mineral exploration. In addition, the calculated coefficients of correlation show a strong antipathetic relationship between Pb and Cu, and an always negative correlation between Ba and production, the latter is especially evident in the cases of output figures dominated by lead and/or zinc productions. Y 3 El The antipathy between Pb and Cu reflects the known fact that the lead-zinc producing districts of Northern England bear little copper ores, if any at all, and vice versa. The negative correlation between barium and production could be explained by assuming that the most important barium-bearing rocks and structures in the region, acquired the element from hydrothermal sol- utions already depleted of metals, and hence few important deposits are to be found in the zones where barite is a conspicuous constituent of the veins: In other words, assuming that most or a large part of the barium present in the region is of hydrothermal origin, the more- barite that is present in a vein or flat, the less ore that is likely to exist in it, thus giving a negative coefficient of correlation between both parameters. (C) A final aspect worth mentioning in this respect is the correlation between output indexes dominated by lead and the lithium values. This element is not normally used to detect lead-zinc mineralization, mainly because it is usually associated with high-temperature deposits. However, the possible use of Li as an indicator of lead-zinc mineralization in sedi- mentary rocks belonging to a marine environment, apparently merits further investigation,a subject beyond the scope of the present research. 7.3.2.2 Investigations on the use of models without intercept The use of regression models that do not include a constant term, that is that have 0 intercept, has proven successful in the resolution of many regression problems. These models imply a strong assumption which in most cases is unjustified: If the values of the regressors are all equal to zero, the response also equals zero. Therefore, the use of such a model would be justified when it is considered that the regressors are the only factors controlling the behaviour of the response, or when the likelihood of having a response different from zero when all the regressors equal zero, is minimal. The latter could be the case of the geochemical models designed in the present research and hence the possibility of using Y9-- models without intercept needed to be investigated. It is worth pointing out at this stage that the use of such a model does not imply that if the response equals zero, the regressors should also equal zero, and that its use if not justified as a means of eliminating a constant term from the equation, since that term can be removed, without making any assumption about the model, simply by centering the data and using instead of the conventional regression equation one of the form: Y - Y = B (X - ) + B2 (X2 - ) + +Bp(Xp - )+E 1 1 1 2 P where observations on the dependent variable are related by the following restriction: (Y. i) = 0 To investigate this problem, the computer program used (BMDO2R) includes an option that produces regressions with 0 intercept. Unfortunately, the computing time is notably increased in this case because the variances, standard deviations, correlations, and covariances are computed about the origin and not about the mean; therefore, in order to compare the results of these models with those of regressions with a constant term, it is necessary to calculate the estimates and recalculate the values of the unbiased statistics to perform the comparison. Numerous models involving the different types and categories of output distinguished in the present research were designed without a constant term and their results compared with the corresponding models built up including a constant. The results of the comparison may be summarized as follows: (1) By far, most of the models without intercept have higher standard errors of their estimates and lower multiple correlation coefficients than the corresponding models with a constant term. Very few equations approach- ed in performance those discussed in the previous section and only in three cases are the results comparable in efficiency, mainly due to saturation 1 '7 0 of the models or overfitting. (2) A great proportion of these models rendered equations that are not significant at the chosen level of significance (0.05%), a situation especially important in the case of the copper average production per deposit, an output index for which no significant equation could be found. (3) The significant equations found, include in many cases regressors similar to those obtained with models containing a constant term, a situa- tion especially noticeable when output variables strongly influenced by lead output are considered. In these cases, the values of the multiple coefficients of correlation and the standard error of the estimates, were much worse than for those models including a constant in them. Three examples may be given to support these conclusions: (a) Scores type A, lead-zinc average production per deposit: With Constant Term Without Constant Term St. Error 1001.95 1051.28 R2 0.2762 0.1296 19.3% 8.0% (b) Scores type A, number of lead-zinc deposits per cell: St. Error 8.12 8.15 2 R 0.2738 0.2916 2 23.5% 22.9% (c) Scores type C, total average production per deposit: St. Error 1060.35 1094.96 2 R 0.2568 0.0960 2 17.8% 4.5% According to the foregoing discussion, the use of models without a constant term or intercept is not justified in the present research and 17 1 therefore after these investigations were terminated, only models that contain a constant term were considered for the purpose of forecasting base metal mineralization in Northern England. 7.3.2.3 Investigations on the Use of Transformed Variables When dealing with multiple regression problems, the possibility of transforming the variables (dependent and independent) in order to obtain better results than those attained with the raw-data, is usually investigated on the basis that some meaningful extra-terms may arise by manipulating the variables. These extra-terms may enhance the estimate of the response, not only because of their possible correlation with the dependent variable, but also because of their relationship with other terms present in the equation. Besides, it is highly recommended to seek transformations when the results obtained with a model have features that appear to violate the assumptions made when applying the technique; when no significant relation- ship may be found between the regressors and the response, or when that relationship is thought to be complex and it is desired to express it in a simpler manner. Numerous transformations have been used to deal with different problems, their nature and complexity depending on the type of relationship existing between the variables. Most of these transformations are applied to the independent variables and not to the dependent one, because in the latter case the least square assumptions (errors independent, N(O,a2))may be violated. Paper dealing extensively with transformations are, among others, those by Box and Tidwell (1962) and Box and Cox (1964). In the following paragraphs, the transformations investigated in the present research are discussed, with considerations of manipulation performed on the data taken as isolated variables, that is without including cross-products or other transformations that relate two or more 1 72 variables. The latter are discussed in Chapter 8 where multivariate statistical techniques that allow the establishment of quantitative relation- ships between the variables, are analyzed in the context of their use as a preliminary step to multiple regression analysis. (A) Transformations applied to geochemical models Several transformations involving the independent variables and response were investigated while designing the different geochemical models. The most important of these were the following which are compared in every case with the preliminary results already discussed in section (7.3.2.1). (1) Reciprocal transformation: This manipulation allows investigation of the use of the model Y = A + B (1/X )+ B (1/X ) + B (1/X ) + € 1 1 2 2 p p The results obtained by this means showed that the correlations with the response were not enhanced, except in the cases of Ba,Li and Ni which have marginally higher coefficients of correlation. The equations obtained had higher standard errors of their estimates and lower R2 than the untransformed ones, as may be seen in the following two examples: (a) Total average production: Untransformed Transformed St. Error 1063.35 1120.01 R2 0.2568 0.1028 2 18.0% 10.0% (b) Total number of deposits: Untransformed Transformed St. Error 7.99 8.20 R2 0.3679 0.3350 2 29.2% 25.0% 7 3 (2) Square root transformation: By this means the following model is examined Y = A + B - + B X + E 1 1 p p The transformations of this type showed lower correlations with the response than the untransformed models, except for Ba, Li and Mn, elements that present marginal increases in their coefficients. The equations obtained have generally lower R2 and higher standard error of their estimates than the untransformed ones, as may be seen in the following two examples: (a) Total average production: Transformed Untransformed St. Error 1066.44 1063.35 R2 0.2525 0.2568 2 16.0% 18.0% (b) Total number of deposits: Transformed Untransformed St. Error 8.04 7.99 R2 0.3612 0.3679 2 28.1% 29.2% (3) Logarithmic transformation: This manipulation allows the examination of the following model: Y = A + B lnX + B 1nX + +B lnX + E 1 1 2 2 P P Since logarithmic transformation is frequently applied to geo- chemical data, special emphasis was placed on the investigation of its application as a means of improving the geochemical models. For this purpose, all the output indexes for the five categories of production distinguished were regressed against the logarithmically transformed A scores. The results of this analysis are summarized in Tables 7.7 and 7.8. 1 7 4 Comparing the correlation coefficients of Table 7.7 with those for the untransformed models (A scores) of Tables 7.1, 7.3 and 7.5, it may be seen that in this case 1nPb is also significantly correlated with the response when it is strongly influenced by lead output; that 1nBa is negatively correlated with the lead and zinc outputs; and that 1nCu and 1nPb are antipathetic as in the untransformed models. The influence of Li is much less marked when transformed. The coefficients of correlation are in general very similar to those of the untransformed models, showing irregular marginal variations in their values; exceptions to this are the coefficients for 1nMn in the combined lead-zinc output variables, which are consistently higher and the coefficients for 1nCu which are colt istently lower for the copper output variables. Table 7.8 shows that in general terms the use of a logarithmic transformation is not justified in the present case because the results obtained with the transformed models were worse than those attained with untransformed variables, with the exceptions of total zinc production, average copper production per deposit and number of lead deposits per cell. In the opinion of the author, the improvement obtained in those isolated cases does not compensate the deterioration in the results evidenced in the remaining instances , a deterioration that is especially important in the cases of the number of zinc and copper deposits per cell, when no significant equations could be found. Therefore, the use of logarithmically trans- formed variables for the design of geochemical models does not appear desirable in the present case. Since the overall frequency distribution of Cu, Pb, Ba and Mn, among the elements determined spectrographically, approaches log-normality, further though restricted investigations were performed on the possible use of these elements in a logarithmically transformed way, combined with the remaining elements without transformation. The results of the models 111 I TABLE 7.7 COEFFICIENTS OF CORRELATION BETWEEN UNTRANSFORMED GEOCHEMICAL VARIABLES AND PRODUCTION INDEXES AVERAGE PRODUCTION ABSOLUTE PRODUCTION VALUES NUMBER OF MINES PER CELL PER DEPOSIT TOTAL PB-ZN PB ZN CU TOTAL PB-ZN PB ZN CU TOTAL PB-ZN PB ZN CU Ln Fe *0.01 0.01 0.00 0.02 -0.17 0.10 0.11 0.05 0.02 -0.19 -0.02 -0.03 -0.03 0.05 -0.21 Ln Ga '-0.01 -0.00 -0.01 -0.07 0.00 0.13 0.16 0.08 0.00 -0.03 -0.10 -0.10 -0.10 -0.04 -0.17 Ln Cu -0.18 -0.19 -0.20 -0.19 0.18 -0.03 -0.02 -0.10 -0.22 0.15 -0.21 -0.23 -0.23 -0.10 -0.20 Ln Pb *0.34 *0.33 *0.34 0.05 -0.26 *0.32 *0.31 *0.32 -0.06 -0.27 *0.46 *0.45 *0.46 0.06 0.03 Ln V -0.10 -0.09 -0.10 -0.15 0.24 0.06 0.09 0.01 -0.14 0.22 -0.17 -0.17 -0.17 -0.07 0.02 Ln Ba -0.23 -0.24 -0.23 *-0.60 0.14 -0.10 -0.11 -0.11 *-0.56 0.17 -0.09 -0.10 -0.10 -0.47 0.08 Ln Co -0.01 -0.02 -0.03 0.03 -0.11 0.04 0.04 -0.03 -0.03 -0.09 -0.06 -0.07 -0.08 0.08 -0.25 * significant Ln Ni 0.02 0.01 -0.02 0.23 0.18 -0.09 -0.11 -0.20 -0.05 0.19 0.07 0.06 0.05 0.30 -0.16 at the 95% Ln Mn -0.00 -0.01 -0.01 0.00 0.13 0.06 0.07 0.02 -0.06 0.09 0.03 0.03 0.03 0.08 0.25 confidence Ln Li 0.25 0.25 0.25 0.16 -0.30 0.12 0.11 0.07 0.36 -0.33 0.16 0.15 0.15 0.15 -0.14 level TABLE 7.8 COMPARISON BETWEEN GEOCHEMICAL UNTRANSFORMED AND LOGARITHMICALLY TRANSFORMED MODELS ABSOLUTE PRODUCTION AVERAGE VALUE OF OUTPUT/DEPOSIT NUMBER OF DEPOSITS/CELL TOTAL _ ZINC COPPER TOTAL LEAD ZINC COPPER TOTAL LEAD ZINC COPPER 2 2 -2 2 -2 -2 -2 -2 -2 -2 -2 -2 R S.e. R S.e. R2 S.e. R2 S.e. R 2 S.e. R. S.e.. R2 S.e. R 2 S.e. R S.e. R S.e. R S.e. R S.e. u.s. = no Untransformed 36 12771 37 11090 32 2738 89 274 18 1063 25 948 97 45 84 126 30 7.9 18 7.9 46 2.5 59 0.5 significant Transformed 29 12757 30 11118 58 2061 80 265 10 1107 23 954 88 254 98 48 29 8.0 19 8.1 u.s. u.s. u.s. u.s. equation found TABLE 7.9 COMPARISON BETWEEN GEOLOGICAL UNTRANSFORMED AND TRANSFORMED MODELS AVERAGE VALUE OF OUTPUT/DEPOSIT NUMBER OF DEPOSITS/CELL TOTAL LEAD _ COPPER TOTAL LEAD ZINC COPPER 2 - - - - R S.e. R2 S.e. R2 S.e. R2 S.e. R2 S.e. R2 S.e. R2 S.e. R 2S.e. Untransformed 18 1055 35 879 ' 92 203 99 10 23 8.3 24 7.8 100 0.03 47 0.5 Transformed 16 1068 35 879 92 309 99 10 23 8.3 24 7.8 , 36 1.3 47 0.5 i 7 5 obtained were discouraging, in the sense that generally very few regressors could be significantly allowed in the equations, thus rendering high standard error of the estimates and low explanation of the variance of the response. In any case, the best equations obtained were very similar in their regressors to the untransformed ones, but their estimates in this case were much poorer. The following examples, taken from the best equations obtained will illustrate the annotated points: (a) Model for average copper production per deposit: Transformed Untransformed St. Error 172.35 126.50 R2 0.7923 0.9562 2 70.1% 84.2% (b) Model for lead average production per deposit: St. Error 951.38 948.87 2 R 0.3225 0.3419 2 24.3% 25.4% (c) Model for total number of mines per cell: St. Error 8.14 7.92 2 R 0.3565 0.3738 2 28.3% 30.4% (4) Exponential model: This and the two models that are discussed next are non-linear models which by adequate transformation of the variables can be expressed in the standard linear form; thus, they are what is called non-linear intrinsically linear models. It is worth mentioning with respect to these transformations that no direct comparison with untransformed models is possible because the functions do not refer to the same response, in this case being necessary to calculate the estimates and recalculate them into untransformed values to make the comparison. Obviously, this procedure • • 1 7 e is very time-consuming and hence only the models that appeared really significant were compared to their untransformed counterparts. The exponential model expresses the relationship between the variables in the following manner A+B X +B X +....+B X Y = e 1 1 2 2 P p E by taking neperian logarithms at both sides, the equation may be rendered linear: lnY = A+B +B +....+B +1nE 1 X1 2 X2 p Xp The results obtained with this transformation showed that the coefficients of correlation between the independent variables and the trans- formed response are normally higher than those of the untransformed model, though the increase in their value is marginal. An exception to this may be found in Ba and Li, which present systematically lower coefficients of correlation in this case. The performance of the models themselves may be analyzed from the following examples taken from the best equations obtained: (a) Exponential model for total lead-zinc production: Transformed Untransformed R2 0.005 0.4231 2 0.1% 36.1% (b) Exponential model for total lead production: Transformed Untransformed R2 0.007 0.4547 R2 0.1% 37.4% (c) Exponential model for total zinc production: R2 0.044 0.3865 2 0.1% 32.2% 0 1 7 7 (d)- Exponential model for number of lead deposits per cell: Transformed Untransformed R2 0.006. 0.2234 2 0.2% 18.3% As may be seen from those results, the use of an exponential model must be discarded in the present case, since even though the production indexes follow a log-normal distribution and the apparent results of the equations may look good (the respective original R2 of those equations were 0.5242, 0.5447, 0.7619, and 0.5239), when the anti-logarithms of the estimates are obtained and compared with actual-observations, there is no resemblance between both, thus rendering the models useless. (5) Multiplicative model: This model expresses the relationship between the variables as: B B B B Y = AX1 1 X 2 X 3 .... X p E 2 3 where B1, B2, B are unknown parameters and E is a multiplicative error. Taking neperian logarithms at both sides, the equation is trans- formed into a linear one that may be handled by standard methods: lnY = lnA+B lnx +B lnX +....+B lnX +1nE 1 1 2 2 P P The results obtained when testing this model showed that the coefficients of correlation between the transformed response and independent variables, were normally higher than the ones of the untransformed models, though their improvement is marginal. An exception to this is the case of Ba and Cu, elements that present systematically lower coefficients in the present case. The equations obtained by this means were in general worse or, at the most, similar to the ones obtained with the exponential model, and hence this transformation proved to be of little use. Besides, when the multiplicative model was tested, it was found that in many instances 17 8 no significant equations could be designed for the number of zinc deposits and average copper production per deposit. (6) Reciprocal model: This non-linear model was tested in only a few cases due to the poor results obtained when it was tried. The idea is to consider the relationship between the variables and response as represented by the equation 1 Y A+B x -1-13. X +....+B X +E 1 1 2 2 p p which may be made linear and handed by conventional methods by taking reciprocals in both sides: 1/Y = A+B1X1+B2X2+....+B X +E P P The coefficients of correlation between the independent variables and transformed response were markedly lower in the cases tested, than the corresponding ones of the untransformed models. The equations obtained were much poorer than the untransformed ones, after recalculation of the estimates; hence, the use of this type of transformation was abandoned after a few cases were examined. (7) Polynomial transformations: These transformations were used in the present research in models combining the untransformed variables with poly- nomial expressions of some of them, in order to assess the possible influence that the powers of selected variables may have on the variance of the dependent variable. The selection of the powers to be used was done by regressing the different output indexes considered against the independent variables elevated to powers ranging from two to ten. Those of the latter equations that were found to be significant were combined with the remaining variables'and these combinations were tested against the dependent variables. The results obtained by this method of analyzing the relationship geo- chemistry-production, maybe summarized as follows: 1 7 9 (a) The absolute total production was significantly related to Ga up to the 6th power and to Li square, increasing their coefficients of correlation with the response from 0.2631 to 0.5676 and from 0.3574 to 0.4021, respect- ively. When these terms were introduced in the model, the equation obtained had an R2 of 0.3599 (0.301 adjusted) and a standard error of the estimate of 12,576.89. The latter value is fairly similar to the untrans- formed model (see Table 7.2), but the R2 is about 20% lower, indicating that the inclusion of such terms in the model was not justified. (b) The total average production per deposit showed no significant relation- ship with powers of the variables. The total number of deposits was found to be only related to Pb, which significantly regressed against this response up to the 5th power, with an increase in the correlation coefficient from 0.223 to 0.297. In this case, no models including powers of Pb were tested, because the increase in R2 and the decrease in the standard error of the estimate or residual mean square, was found to be very small in the poly- nomial transformations (less than 2% at each step), indicating that nothing could be gained by adding such powers to the general model. (c) The different indexes of production representing lead-zinc, zinc and copper outputs, showed no significant relationship with powers of the - independent variables, suggesting that the inclusion of such terms in the respective models would not be justified. A similar situation applied to the production index representing average lead production per deposit. (d) The number of lead deposits per cell proved to be significantly related to Pb up to the 4th power, though the increase in R2 was so marginal (less than 1% at each step) that it was considered that such terms were not worthy of inclusion in the general model; this appreciation was confirmed by the values of the residual mean square, which diminishes 0.5% from the first to the second step, and from that term onwards starts to increase. Finally, in order to obtain a complete evaluation of the polynomial • it$- 1 transformations, those indexes found to be significantly related to some power of an element (i.e. total production, number of total deposits, number of lead deposits), were logarithmically transformed, and the trans- formed variables were regressed against powers of the different elements ranging from two to ten. In this case, the log-total production was found to be unrelated to powers of the independent variables, the log-number of total deposits was found to be related to Pb up to the 5th power and the log-number of lead deposits was found to be related to Pb up to the 5th power and to V up to the third power. In the case of the log-number of total deposits, the increase in 5 R2 from Pb to Pb was less than 1% per step, and the decrease in the residual mean square at each step was found to be marginal. The variables related to the number of lead deposits performed rather better and hence 2 5 2 3 a model was tested using all the geochemical indexes plus Pb -Pb and V -V . The equation obtained was found to be similar to the one attained with the untransformed variables, without including any of the transformed terms. Therefore, the use of polynomial transformations was discontinued. Summing up the transformations applied to the variables in the design of the geochemical models, it may be concluded that although in.some isolated cases the use of transformed independent variables could improve the model, the improvement would be marginal. This fact, coupled with the poor performance of the transformations in all the cases required, makes use of transformed variables undesirable in the present case. Regarding transformations applied to the dependent variables, it may be stated that in this case theiruse would be totally unjustified, because no improvement whatsoever is introduced in the model by such trans- formations, and, what is more, in numerous cases no significant equations relating the regressors to the transformed response could be found. E 1 8 1 (B) Transformations applied to geological models Several transformations were tested on the variables used for the design of the geological models, with the purpose indicated earlier. The transformed variables were regressed against the different production indexes considered, and the results of these regressions were compared with prelim- inary equations constructed with the untransformed variables. The transformations applied were the logarithmic transformation: of the parameters representing faulting, the expression of the total number and length of faults as a ratio, and the addition in several ways of the indexes representing the Carboniferous Limestone Series. The results obtained with untransformed indexes of production, may be summarized as follows: (1) The coefficients of correlation between the response and the faulting parameters were in all cases markedly higher when those parameters were logarithmically transformed, indicating that the output is related to fault- ing through an exponential function. Since faulting is one of the main factors controlling the emplacement of mineralization in the area, it may be postulated that this exponential relationship could be largely responsible for the log-normal frequency distribution displayed by the different output indexes, as indicated in Chapter 5. (2) The parameters representing number of deposits per cell, were more correlated with the Carboniferous Limestone Series as a whole, than with the individual components into which this series may be subdivided; on the other hand, the average production indexes were found to be less correlated with the total series than with the individual components. The first relation- ship can be explained by considering that, as indicated in Chapter 4, by and large most of the deposits worked in the area lie on one or other group of the Carboniferous Limestone; obviously, if these formations are grouped together, the correlation. with the response will be enhanced. On the other hand, the highest producing deposits of the area were • 1 8 2 emplaced in rocks of the Upper Limestone Group and in the Borrowdale Volcanic Series (case of Greenside). Therefore, by bringing together the groups that form the Carboniferous Limestone, units with a high number of small deposits are included together with the Upper Limestone Group, diminishing the average production of the index as a whole, and hence decreasing the correlation. (3) The correlation coefficient between the different responses and the ratio number:length of faults, was found to be markedly lower than the corresponding coefficients of the individual indexes, indicating that the output is less related to the average length of the faults existing in a cell, than to the actual number and length of those faults. (4) As may be seen in Table 7.9, which summarizes the results attained, the equations with both transformed and untransformed independent variables are in almost all cases the same. Exceptions to this are the models designed for zinc output, which have different standard errors of their estimates and different R2, in all instances the untransformed models being better than the transformed ones. Summing up the results attained by transforming the geological variables, it may be stated that such transformations are not justified in the present case, because no improvement whatsoever is introduced in the models when those transformed variables are included. However, in the opinion of the author, these transformations are worth testing, because some enlightening facts about the behaviour of the response may be obtained from such analysis. Another set of transformations was tested with the geological data, this time involving the logarithmic transformation of the response, which was regressed against untransformed and transformed independent variables. In both cases, the correlation coefficients with the response were slightly different than those of the untransformed models, without showing a systematic • 1 3 3 trend of variation. The models built up with the transformed response were in all cases worse than those designed with the untransformed variables, having systematically much lower R2. According to the foregoing discussion, it was concluded that the usage of transformed variables while designing the different geological models was unjustified in the present case because no improvement whatsoever could be achieved by this means. Therefore, as with the geochemical indexes, untransformed variables were used in the design of the forecasting models based on geological parameters. 7.3.2.4 Investigations on the use of dummy variables In addition to the dummy variable implicitely assigned to the constant term of the models used, two other types of such variables were investigated in the present research, in order to assess their possible influence on the response. The first problem investigated in this connection was approached by the use of a dummy variable which would make allowance for the fact that the observations had been made in three different geological (and probably metallogenetic) environments: The Alston and Askrigg blocks of the Northern Pennines, and the Lake District. To investigate the possible environment- response relationship, two coefficients that needed to be determined at the same time as the usual ones were attached.to dummy variables, to which the following values were assigned: (Z1, Z2) = (0,0) for the Alston Block (0,1) for the Askrigg Block (1,1) for the Lake District The results obtained while analyzing the models that included those dummy variables, may be summarized as follows: (1) The different indexes of output considered in the present research are not correlated with the variables representing geological environments. 1 8 4 (2) The geological models showed significant correlations between the dummies and the following independent variables: Millstone Grit, Middle Limestone, and Upper Limestone, with the dummy representing the Pennines; and Borrowdale Volcanics, Skiddaw Slates, Number of faults and Number of fault intersections, with .the dummy representing the Lake'District. These correlations are to be expected since these are the main geological factors characterizing each of the two contrasting broad geological environments lying within the area. The association of faulting with the Lake District is principally explained by the fact that a large number of faults are known in the West Cumberland Coalfield, where mapping has been resumed relatively recently. This fact, in turn, points out one inconvenience of the geological models for forecasting purposes: the value that the geological variables will attain in each cell will not be homogeneous throughout an extensive area and will depend on the degree of mapping that has been carried out in the different zones of that area, and on the particular purposes that the mapping was supposed to serve. Therefore, when dealing quantitatively with geo- logical data gathered in a large area, usually by different teams and in different epochs, the degree of subjectivity introduced by the geologists needs to be assessed. (3) The geochemical models showed significant correlations between the dummies and the following variables (among those elements determined spectrographically): Co, Cu, Fe, Ga, Li, Mn, Ni and V; only Pb and Ba are uncorrelated with those variables.- Of the elements included in the analysis; Pb, Cu and Ba may be considered the main elements introduced in the area by hydrothermal solutions and the contents of the remaining elements may be largely considered prithary. Therefore, the correlation of Co, Fe, Ga, Li, Mn, Ni and V with the dummies are to be expected, since their contents will be highly 1 8 5 dependent on the lithological assemblages where they lie, which would ultimately reflect the two contrasting environemnts considered. The lack of correlation of Pb and Ba with the dummies could be accounted for by the fact that they are largely alien to both geological environments, since they can be considered largely introduced by processes extraneous to the environemnts themselves (as represented by lithological assemblages). Besides, the lack of correlation could indicate that during a mineralization period affecting a large area, the main elements intro- duced are fairly homogeneously distributed throughout the region, a point already postulated for the Basin and Range province of the U.S.A. by Nolan (1950). On the other hand, the minor elements transported by the mineral- izing fluids, would show a regional heterogeneity, since they would be more rapidly depleted from the fluids than the main constituents of them and therefore would characterize sub-regions or districts. By this means, the correlation of Cu with the variables representing geological environments could be explained. (4) The models obtained were in all cases similar to those attained without taking into account the dummy variables,which are not included in the equations and always enter the model with partial values only significant at the 0.20 probability level. Summing up, it may be said that in the present case the use of variables that make allowance for the contrasting environments lying within the studied area is not justified since no improvement in the equations was obtained by this means. This point would indicate that the particular combination of variables in the equations would on their own be a reflection of the different geological and geochemical environments existing in an area, thus stressing the importance that the relationship between the variables has in explaining multivariate phenomena. However, this point needs to be r 1 8 8 investigated in each case, since enlightening conclusions about the behaviour of the independent variables in the different sub-regions may be obtained in this way. The second problem investigated with the aid of dummy variables was the possible effect on the geochemical models of the number of samples that each score represents. For this purpose, a coefficient was calculated for a variable to which the following values were assigned: 0 if the number of samples in the cell was below the average; 1 if the number of samples in the cell was above the average. The results obtained by the addition of that dummy to the model may be summarized as follows: (1) The geochemical variables considered in the present research are not significantly correlated with the dummy representing the number of samples collected in each cell, with the exception of Mn, an element that is significantly correlated at the 0.05 confidence level. The probable cause for this correlation is the tendency of this element to give high results with the analytical method used, as indicated in Chapter 5. The coefficient, though significant, is not high (0.220), a fact that indicates that the correlation is not strong enough to consider the use of such an element unjustified or biased. (2) The regression models obtained are similar to those attained by the use of untransformed variables, the dummy only being included in the equations with coefficients significant at the 0.20 confidence level. (3) The output indexes considered are not significantly correlated with the dummy, indicating that the use of such variables are not justified in the present case. Summing up the results attained with the introduction in the model of dummy variables, it may be stated that the use of such variables is not desirable in the present case, since they cannot be included in the 0 1 8 7 equations with coefficients that are statistically significant at the desired level. However, the problems that these variables might solve with their inclusion in the models, need to be assessed in each particular case; hence, investigations on the use of such variables must be carried out, whenever it is thought that they could be of help in establishing a more 'accurate and real relationship between the predictors and the response. 7.3.3 Forecast of the Number of Potential Deposits per Cell In the following paragraphs, the best models obtained for the estimation of the potential number of deposits that may be expected to exist in the cells into which the area was subdivided, are discussed. In order to facilitate the comparison between the different models designed, the geochemical, geological and combined models chosen are given in succession for each metal. Emphasis is placed on the physical meaning of each equation, which is discussed in terms of the variables and regression coefficients present and in terms of their structure coefficients, which de-emphasize the magnitude of the regression coefficients, a fact extremely important when dealing with a small number of samples which present strong collinearities. The overall estimates for the 106 cells considered in the present research are summarized in Table 7.10. 7.3.3.1 Forecast of the potential number of lead deposits per cell This output index has a mean of 6.55 among the productive cells of the area, with a standard deviation of 9.05. It is mostly uncorrelated with the independent variables, showing significant correlation with Pb(0.469) and Upper Limestone (0.332); most of the geological variables, as can be expected, have negative coefficients of correlation with this index, a feature that is shared with many of the geochemical parameters. The models chosen for further use in the forecast of base metal minerali- TABLE 710 FORECASTED NUMBER OF DEPOSITS PLR CELL - NORTHERN ENGLAND LEAD RLSERVES ZINC R-SLkVEL:0L, COPPER RESERVES CELL' CH8NO. GEOCH GEOL._ CMBNO. GEOCH CMBNO. GEOCH. GEOL. , MODEL MODEL ,.. MODEL MODEL MODEL MODEL MODPL MODEL -16 -10 -3 3 -43 1 -5 0 0 2 -53 -7 -3 8 -26 1 -7 -6 0 3 -159 -9 ..1 7 •-17 -1 ...4 -3 1 4 -76 0 6 5 -63 3 -0 0 -1 5 -7 -4 8 7 -4 4 -0 -1 -3 6 -1 -0 7 2 2 -0 -0 0 -9 7 2 -3 6 0 26 -2 1 -0 -7 8' -4 1 4 -7 -10 9 -1 -1 -6 9 -2 2 -3 10 -130 2 -9 3 0 10 -10 -4 -3 12 -35 2 -7 -3 U 11 -20 -9 -3 9 -1 -0 -4 -5 0 12 -20 -9 -3 7 -32 -0 -5 -3 0 13 -1 -4 7 10 -44 3 -1 -1 0 14 0 -1 12 -0 -20 12 4 -3 -0 15 9 11 10 3 7 5 3 -2 -3 16 7 5 4 5 7 -2' 2 -1 -11 17 7 13 2 2 -9 -1 0 -0 -13 18 -6 4 -.1. -24 31 19 -1 -1 -9 19 -27 -15 -1 -2 19 6 -6 -3 -0 20 -33 -20 2 0 69 1 -4 *8 -3 21 *.9 -8 3 -4 28 22 -3 -4 -4 22 -21 -8 -1 7 19 -6 -3 -3 -9 23 -18 -9 -1 10 5 1 -5 -6 -0 24 5 2 12 6 10 2 3 -3 -0 25 37 21 15 14 13 14 1 1 0 26 17 17 12 1 0 0 6 2 -1 27 14 15 10 1 -0 2 7 .-1 -3 28 4 8 -1 -11 26 6 -0 -2 -14 29 -4 3 3 -24 12 31 -1 -2 -1 30 0 -0 7 11 30 8 -0 -2 -0 31 ...0 4 5 6 38 ..0 0 0 0 32 1 2 6 3 2 -5 2 2 -18 33 -0 -1 8 10 21 -1 4 -1 -2 34 -7 •..4 -3 12 3 2 0 0 0 35 -0 2 5 10 25 1 -0 -1 -0 36 25 21 12 1 0 -1 3 3 -2 37 14 11 12 2 2 -0 4 0 -3 33 11 13 10 5 -9 2 2 ...0 -2 39 7 11 3 3 41 -3 2 -2 -12 40 -7 7 2 35 -12 36 -0 -0 0 41 0 1 -2 2 2 2 0 0 1 42 1 6 ..i. 2 2 2 0 1 -0 43 -0 .-0 -1 5 •.15 -0 5 1 1 44 -87 5 1 8 1 -0 0 1 1 45 -9 -3 2 11 3 2 -1 •"0 1 46 -5 -0 -1 7 -30 -0 -1 0 1 47 0 6 6 7 -17 3 -1 -0 3 48 9 6 7 5 33 0 -2 7 -13 49 13 16 7 1 0 -1 4 2 -9 50 4 7 2 -23 -0 22 2 0 - ...8 51 5 0 7 7 -29 27 ...A. -0 -1 52 11 3 .,...0 6 -95 22 2 2 12 53 6 -1 3 1 0 -0 1 2 -1 54 3 3 -0 -9 6 -12 0 a 0 55 2 -6 -0 -5 8 -6 3 5 0 56 13 7 7 12 -5 7 2 7 3 57 -10 -5 8 9 11 2 -2 -4 1 58 -6 -5 2 14 -32 4 -1 -2 1 59 7 3 11 7 28 2 0 -4 -3 60 3 3 8 5 9 0 3 -D -6 61 3 -1 5 9 .-5 -1 -0 -0 -6 62 -15 -11 -1 4 -33 -? -2 0 0 63 -3 -0 -3 -2 -67 18 J. 2 15 64 1 0 -0 -8 -25 -12 1 1 -4 65 6 5 0 -4 11 —8 1 4 4 66 -3 1 -1 -1 4 -4 -0 1 4 67 -21 13 -2 -5 17 -6 2 -1 3 68 -32 -5 •0 9 -3 6 -3 -0 4 69 -15 0 3 6 0 1 -1 -1 2 70 4 11 9 -0 -63 0 -0 0 -6 71 8 4 12 1 0 1 -1 *0 -6 72 8 4 11+ 5 73 3 -0 -2 -0 73 -18 -9 -3 11 -28 1 -6 -4 1 74 •4 -5 -3 7 65 37 4 -0 25 75 0 6 -3 -5 31 -c' 1 2 1 76 -0 18 -3 2 68 .3 2 -2 1 77 -3 16 -2 2 -9 3 -2 3 0 78 -18 10 -2 2 ...4 0 -1 0 0 79 -26 2 1 7 1 -2 5 30 5 4 7 5 --42 0 -0 0 2 81 -1 0 4 5 -30 -6 -1 -1 -8 82 6 9 10 2 49 0 -0 .-0 0 83 6 3 10 1 0 1 2 3 -0 84 -1 2 -3 0 -25 -6 2 1 4 85 -2 16 -2 1 -20 3 -2 1 1 86 -3 10 -2 4 26 1 -2 1 1 87 1 8 1 5 -0 0 -3 4 1 59 ...5 4 1 3 -17 -2 -1 0 1 39 -22 2 0 1 22 -1 -2 -0 2 90 12 7 6 10 -28 2 -2 2 3 91 10 3 7 10 -74 1 -2 -0 3 92 3 -0 6 10 -13 3 -2 1 3 93 -2 .-4 5 13 21 2 -3 1 -0 94 7 14 4 2 -34 0 -4 4 5 95 -10 0 - 0 11 -33 1 -3 - 0 - ti 96 -21 -9 -1 15 13 21 -3 -2 -2 97 -2 1 ...1 13 -64 10 -4 4 7 95 5 5 2 14 -5 7 -1 2 6 99 7 3 0 13 -15 1 4 6 100 6 6 10 4 11 2 0 2 -2 101 -4 -1 9 4 6 2 2 -2 -4 102 -12 -0 -1 5 26 -14 1 -5 -23 103 -4 0 -1 5 -10 -12 -2 3 -17 104 0 5 0 11 -13 1 -3 7 U 105 -8 3 -1 11 82 4 -2 -1 4 106 2 11 7 1 1 1 1 1 0 411 1 8 zation in Northern England are summarized in Table 7.11 and Figure 7.1. (a) Geochemical Model The geochemical model selected is represented by the following equation, which accounts for 51.08% of the variance of the response: Y = -30.2467110.94412Pb-0.48985Ba-1.52054Co+1.01909Ni+0.69054Li+ 0.67439Mo-0.65175As The important role played by the Pennines with regard to lead deposits is manifested mainly through the weights of Pb and Li, which are also the main elements influencing the structure of the model and the value of R2. In addition, that influence is further expressed by the negative regression coefficient of Ba, reflecting the general antipathy Pb-Ba that has been noticed in that orefield, and which is evidenced by the decrease in the number and importance of the lead deposits as soon as the main part of the "barite zone" is reached. The relatively unfavourable character of the Lake District in this respect is manifested mainly through the loadings of As and Co, elements that bear negative coefficients and which have a certain influence in the amount of variance explained. Both elements are on the average present in high concentrations in that area. Two coefficients in the model need to be viewed with care. The strong positive weight of Ni could be considered - without much scrutiny - as a contribution. of the Lake District orefield to the equation, since this element.is present in high concentrations in the pelitic rocks exist- ing there. In this respect, it must be considered that Ni is not only present in anomalous concentrations in the Skiddaw Slates, but also in the Silurian rocks; thus, the model could appear to stress an unjustified weight in the last unit, which up to now has proven barren, and therefore the estimates would prove wrong. This assumption may be disregarded, due to the low content of those rocks in the remaining elements that have • TABLE 7511 SELECTED MODELS FOR TEE FORECAST OF THE NUMBER. OF 'LEAD. PER CELL HNLIULL P 2.2147 ` F.SU 0.5108 STO. ERROR OF EST. 7.0332 RS13(A0.1,) 0.3167 ANALYSIS OF VARIANCE OF SU( OF STUARLS WAN MARE f IRMO PEGMETSION 1549.472 221.346 4.475 RESIDUAL 30 1483.972 49.466 VANIAILEG IN EIUATION VARIAOLE CO4FFICILNI STD. ZIRPOR F TO REMOVE STRU6TUNS COEFFICIENTS (CONSTANT -30.24671 ) P9 4 0.94412 0.24338 15.7479 0.616 BA 6 -0.48995 0.20806 5.5007 0.121 CO 7 -1.72,54 0.75198 7.9911 0.126 NI 6 1.J1919 0.59412 2.0423 0.060 LI IC 0.69024 (.30047 5.1102 0.197 NO 12 0.67439 7.36028 3.5(77 0.001 AS 13 -0.65175 . 0.24795 6.1093 0.215 SNAMARY TABLE STEP VARIASLO MULTIPLE INCREASE F VALUE TO NUMBER ENURED REMOVEI RSO IN RSO ENTER OR REMOVE 1 P9 4 C.4688 8.2193 0.2I98 13.1428 2 AS 13 0.5375 0.2892 O. 06 91 3.4'36 3 LT 10 4.5712 2.3263 0. 03 73 4 CO 7 0.6054 C.T605 0.5432 2.0957 5 IA 6 0.6388 0.0081 1.0416 2.249' 6 40 12 3.6803 0.0624 0.0547 3.155 7 NT 8 0.7147 0.5108 3.0400 2.9423 (a)GEOCHEMICAL MODEL MULTIPLE P. 0.5465 - RSO 0.3000 STD. ERROR OF EST. 7.8978 RSO(ADJ.) 0.2333 ANALYSIS OF VARIANCE 0; SUM OF S(1047:5 MOON SOUAPE F RATIO REGRESSION 912.632 3E4.210 4.877 RLSIJUAL 34 2123.765 02.375 VARIABLES IN EQUATION VARIABLE COEFFICIENT STO. ER408 F TO REMCVE STRUCTURE GOEFFICILNTS (CONSTANT -.3.73662 1 N/CLST 6 0.011E8 0.00522 5.0104 0.521 UPFLST 7 0..1513 2.20490 9.5171 0.600 IN1GCT 16 0.29138 0.05097 3.2583 0.355 SUMMARY TABLE STEP VARIAPLE MULTIFLE INCREASE F VALUE TO NOMEER ENTERED REMOVER PSO IN RSO ENTER 05 REMOVE 1 UFPLST 7 3.3317 0.1101 0.1101 4.4520 2 RIOLST 6 0.4830 0.2333 0.1212 5.6264 3 INTSCT 16 0.5485 0.3209 0.0676 3.2853 (b)GEOLOGICAL MODEL MULTIPLE . 0.8734 RSQ 0.7629 STD. ERROR DF EST. 5.4748 RSQ(AOJ.) 0.b762 ANALYSTS OF VARIANCE Or SUN OF SIUARES MEAN SOUCRE F RAT/0 REGRESSION 13 - 2314.044 174.003 5.919 RESIDUAL 24 719.350 29.973 VAPIABLES IN FOLIATION VARIABLE COEFFICIENT STD. ERROR F TO REMOVE STRUCTURE COEFFICIENTS (CONSTANT .559.52045 1 PR 4 0.53628 1.27523 3.7965 0.537 BA 6 .0.45055 0.20933 4.6336 0.099 LI 10 0.58592 0.26559 4.9650 0.163 MO 12 0.76327 7.30333 6.3319 0.001 AS 13 -0.70742 0.31506 4.9423 0.176 1.62575 0.75735 4.6118 0.299 ZN 14 0.133 CO 15 -1.48375 0.79550 3.4753 0091ST 21 0.81617 0.00513 9.9275 0.328 UPPLST 22 0.01123 C.00527 4.9959 0.380 BASER5 23 -0.31678 9.17072 3.1637 0.259 RORPON 26 0.01139 0.00674 3.1303 0.187 0.07191 19.1573 0.223 INTSCT 31 0.31499 0.162 LENGTH 72 -0.02773 0.00929 8.8989 SUMMARY TABLE STEP VARIARLE MULTIPLE INCREASE F VALUr TI NUNREP ENTERER REMOVER 030 IN 059 ENTER OR REMOVE 1 PO 4 0.4688 0.2198 0.2195 10.1425 2 UPPLST 72 0.5621 1.3167 0.0961 4.5154 3 INTSCT 31 0.6576 0.4324 0.1165 6.9769 4 LENGTH 32 8.7089 1.5025 0.0732 4.6544 5 MIOLST 21 0.7422 0.5509 0.0433 3.4417 98SE130 23 0.7644 0.5842 0.0333 2.49,9 6 2.0439 7 LI 10 0.7416 0.6105 0.0266 8 AS 13 0.7959 0.6334 0.0226 1.7005 9 905001E 26 0.8176 0.5685 0.0351 2.0511 10 HO 12 0,8346 0.5955 Nozan 2.4915 11 9A 6 0.9465 7.7166 .0.0201 1.5459 12 TN 14 0.8535 0.7'85 0.0119 1.2117 13 CO 15 1.8734 0.7629 0.0343 3.4763 (c)COMBINED MODEL GEOCHEMICAL MODEL (~ ~ -~~ ~~01~100 '\-J ~ 0@!0:0:0 @:@:@;0f----- : - tI !QQ KEY TOSYMBOLS ·00:0f0 - Dii@:0 i0 than o o 10 ;0 :0 101 @ More 20 ---:---.~ { ° I 00l0®001 @ 11-20 ~o ° 10:0@'@: I 1 o 6-10 ~ ° 0'0'00'0. ; • I· .:.; - I '0:010:0;00,01 O 1~5 \~"~{Ol r\ I -!00:0! Blonk.O \~ ~l0 I 10: 101 GEOLOGICAL MODEL FIG.Z1 1 8 9 positive regression coefficients in the equation (mainly lead and lithium). In the opinion of the author, the positive weight of Ni reflects local ,features, as the high content in this element in cells 25 and 38, which have been two of the most important lead-producing districts in the area; this assumption is supported by the very low influence that this element has on the structure of the model and on the value of R2, in spite of its relatively high regression coefficient. Finally, the positive loading of Mo, an element that is fairly homogeneously distributed throughout the area, must not be interpreted as if this were a generally "favourable" element to suggest the presence of lead mineralization, but it must be regarded - due to its null contribution to R2 - as representing local enhancements in its content occurring in restricted areas that have rendered some lead output (e.g. cell 32). (b) Geological Model The geological model chosen for forecasting purposes accounts for 30.09% of the variance of the response, and is represented by the following equation: = -3.73662+0.01168 Middle Limestone+0.01513 Upper Limestone+0.09238 Number of Fault Intersections The physical meaning of the two stratigraphic parameters included in the equation is very obvious, since they are the two main rock-units containing lead deposits in the Northern Pennine orefield (see Chapter 4). The presence in the equation of the Number df- Fault Intersections is significant, since of the faulting indexes this is the most correlated with the global lead production of the different districts, which is revealed by the fact that from 19 cells producing more than Elm in the area, 9 have a large number of cross-cutting faults, those observations being anomalous. With regard to this parameter as an important index in control- ling the formation of rich ore deposits, it must be considered that local 1 9- o enrichments of the veins have been evidenced at the intersection of faults in both orefields of the area and that highly mineralized irregular masses ("pipes") have been found in the Pennines in connection with those inter- sections. (c) Combined Model The combined geochemical-geological model selected in this connect- ion, explains 76.29% of the variance of the response. The equation representing the model chosen, is the following: Y = -59.52045+3.53628Pb-0.45055Ba+0.58592Li+0.76327Mo-0.70042As+ 1.62275Zn-1.48375Cd-0.01617 Middle Limestone+0.01123 Upper Limestone -0.31678 Basal Conglomerates + 0.01139 Borrowdale Volcanics + 0.31499 Number of Fault Intersections - 0.02773 Length of Faults As may be seen by comparing this model with the two previous ones, most of the variables included in the latter models are also present in this case with similar weights, and hence most of the considerations made when discussing those models are valid with respect to this equation. However, it is worth noting that in the combined model the influence of the geological variables in the value of R2 is strongly diminished, being part of their relevance taken by Zn and by other geological parameters present only in this case. The implications of the additional variables may be interpreted as follows: the strong coefficient of Zn would be a further enhancement of the importance of the Pennine region as a lead-producing area, since this element is generally present in high concentrations in that area. This enhancement is even more evident and localized by the negative regression coefficient attached to the Basal Carboniferous Conglomerates, a unit that does not contain mineralized structures in it. It is worth mentioning in this respect, that the allocated coefficient enhances the negative character of the Carboniferous rimaIrrounding the Lake District, as an area 1 91 where no mineralization is known to exist. The positive weight of the Borrowdale Volcanics, obviously indicates the generally favourable character of this unit within the Lake District. The negative coefficient of the Length of Faults, is a reflection of the fact that this parameter presents high values in areas with a low number of deposits, and even higher in areas that are not known to contain ore bodies. Indirectly, this weight points towards the known feature that the large regional faults are normally barren, a tendency which is confirmed by the fact that the regional faults of the 19 cells producing more than Elm, have an average length of less than one mile. The negative loading of Cd, an element that is present in rather high concentrations in the Pennines, needs to be interpreted carefully. In the opinion of the author, considering the low contribution of this element to the value of R2, this feature is not related to regional trends, but to local, relative defficiencies in this element, present in some important productive areas; it is worth considering in this context, that of the main 19 lead-producing areas, only one (cell 32) has an anomalous content in Cd, and that the largest producing cells have a general content in this element equal to or lower than the regional mean: 7.3.3.2 Estimation of the Potential Number of Zinc Deposits per Cell This index has, among the productive cells of the area, a Mean of 2.53 deposits and a standard deviation of 3.52 deposits. It is not significantly correlated with any of the independent variables, a large number of which bear negative coefficients of correlation with it. The models chosen for forecasting the occurrence of this kind of mineralization in Northern England are summarized in Table 7.12 and Figure 7.2. (a) Geochemical Model The best geochemical model found to express the relationship between this output index and the selected parameters, explains 100% of TABLE 7.12 MODELS SELECTED FOR THE FORECAST OF THE NUMBER OF ZINC DEPOSITS PER CETN, NULTIPL5 P '6 RSO • 1.0030 STD. 60000 OF EST. 4.1.042 ,R601903.3 1.0030 ANALYSIS OF VARIANCL OF SUR OF snueocs MEM =JAR. F RATIO RECFESSION 11 149.231 13.566 754272.131 RESIDUAL 1 4.410 0.164 VARIABLES IN 101181/0N VARIABLE COEFFICIENT STD. ER5ON F TO 1E4(419: STRUCTURE COE FFIC IC NTS (CONSTANT .29:686272 ) GA 2 .-3.31512 9.00149 '39704.32(9 0.053 CU 3 1.8.8.9 1.5'123 422169.35,3 0.099 V 5 2.2210, 0.30133 *.1122.1437 0,072 BA 6 1.74131 1.9'159 54356..6117 0.441 CO 7 /.32637 3.0,177 56212%5125 0.070 MN 9 4.72152 1.942 1 1 5:70'6.7719 0.068 LI 15 t.43080 1.,1133 9595.2176 0.136 HO 12 ..2.51483 4.9,126 514340.8619 0.142 AS 13 ..2.98353 9.0515. 561442.3211 0.065 ZN 14 -9.2.5681 1.10425 '14117.85'9 0.141 CO IN 15.35874 1.05706 '46832.5509 0.043 SUNMA41 7431E STEP VARIAPLE NULTTiLE IMOKFAS' F VALW TO NUMBER ENTER! 0 F./ROVED 7 RS0 IN 171 INTER Jr '::4081 1 BA 6 6.4415 0.144' 0.1949 2.6626 2 GA 2 4.4651 .7.2191 0.4243 4'1.6 3 HM 9 J. 4967 0. 24,7 0.9275 1.3703 4 CU 3 7.5557 0.1125 .4611 4.7145 5 V 5 0,64.8 1.4222 4.1134 6 MO 12 3.6632 ,.4394 '0.7.176 0.1555 7 AS 13 J.6723 (.4624 0.0122 0.11 4 6 ZN 14 5.6814 9.4643 3.3123 0.0.71 9 CO 15 J.7575 E.62 2 3.1559 1.2213 10 CO 7 0.9994 9.9939 0.1747 651.4768 11 LI 14 i', , 1.8,1 8.011/ 9599.7 7, 12 FE 1 1.003;J 1.0°53 1.1' - (a)GEOCHEMICAL MODEL MULTIPLE R 1.0000 PS° • 1.0000 STD. ERROR OF CST. 0.0323 RSQ (A WO 1.0000 ANALYSIS OF VARIANCE OF SUM OF SQUARES MEAN MARE F RATIO REGRESS0010 11 149.230 13.566 13002.656 RESIDUAL 1 0.001 0.001 VARIABLES IN EQUATION VARIABLE COEFFICIENT STD. ERROR F TO REMOVE STRUCTURE COEFFICIENTS (CONSTANT 2.14243 ) COALNS 2 0.05199 0.00104 800.0857 0.089 MILSTN *0.01211 0.00023 2758.5528 0.289 LOWEST 4 0.01246 0.00018 4621.5010 0.157 M/OLST ..0.00146 0.00009 277.1529 0.249 UPPLST 6 0.00736 0.05013 3172.6951 0.085 MORROW 7 -0.01661 0.00022 5824.9748 0.117 INTACT 9 0.06499 0.00091 5119.4953 0.073 FAULTS 10 4.10314 0.00311 3461.165/ 0.031 /NTSPT 11 0./3388 0.00139 9320.5133 0.406 LENGTH 12 -0.02975 0.00020 21724.0449 0.442 CNTFLT 13 .0.82054 0.00140 224.0303 0.093 SUMMARY TABLE STEP VARIABLE MULTIPLE INCREASE F VALUE TO NUMBER ENTERED REMOVED RSO IN RSO ENTER OR REMOVE LENGTH 12 0.4420 0.1953 0. 1953 2. 6702 2 tuaccc 11 0.0920 0.7957 0. 60 0 3 29.3792 3 BORROW 7 0.9504 0.9032 0. 10 75 9 9979 4 FAULTS 14 0.9550 0.9120 0.0083 0.8109 NIOLST 0.9599 0.9214 0.0094 0.0405 6 mum 3 0.9634 0.9282 0. 00 67 0. 5608 7 cosLms 2 0.9744 0.9494 0. 0212 2. 0973 CNTFLT 13 0.9789 0.9583 0.0089 0.6526 9 LOWEST 4 0.9816 0.9640 0.0057 0. 4746 10 UPPLST 6 0.9619 0..642 Oa 00 02 0.0122 11 ANTACI 9 Lem 1.0200 0. 03 58 51 1 9. 4953 (b)GEOLOGICAL MODEL MULTIPLE R 1.0000 .RSO 1.0000 'STD. MOP OF EST. 0.0062 660(003.) 1.0030 ANALYSIS OF VARIANCE OF SUM OF SQUARES MEAN SOUARE F RATIO PEGRESSION 11 149.231 13.566 151624.386 RESIDUAL 1 0.000 0.000 VARIA1LES IN E1UATI09 VARIABLE COEFFICIENT STO, ERROR F TO REMOVE STRUCTURE COEFFICIENTS (CONSTANT 30.79062 ) GA 2 0.04727 0.00112 1419.0700 0.053 PH -0.26475 0.00122 47037.9792 0. 051 BA 0.00579 0.00073 62.3241 0.441 NT .-0.58009 0.00184 99078.4465 10.294 MO 9 0.37812 0.00097 151760.4644 10.068 COALNS 16 -0.06051 0.00054 12605.1075 0.089 LOWEST 18 0.01757 0.03034 35523.3472 0.157 UPPLST 20 ..0.00123 0.10012 4584.1732 OA( 5 MORROW 21 -0.01781 5.00004 176135.1315 0,117 /NTSCT 25 0.24436 0.00029 724941.3519 0.406 LEMON 26 ..0.02442 0.00002 937575.3354 0.442 SUMMARY TAME STEP VARIAPLE MULTIPLE INCREASE F VALUE TO RUMMER ENTERED REMOVED R R50 IN RSO ENTER OR REVIVE 1 LENGTH 26 0.4420 0.1953 04.19 53 2.6702 2 INTGCT 25 0. 0920 0.7957 13 3 0.62 29.3792 907708 21 0.9504 0.9032 0.1075 9,9979 4 NI 6 0. 956 2 0.9143 O. 0111 1.0162 5 MN 9 0. 9520 0.9643 0.05 00 9.7940 6 LOWEST 18 0. 9089 0.9779 01 36 P5 Oa 1.689C 7 4 O. 995 6 009/3 0. 01 34 7.7255 a COALMS 15 0.9990 0.1951 9 0. 0064 14.2387 UPPLST 29 0,5998 0.9196 0.0015 12.4545 10 GA 2 1.0000 1.6000 O. 03 04 43.5034 11 94 6 1. 0900 160100 0.00 00 62.1741 (c)COMBINED MODLU, KEY TOSYr'-1BOlS o Morethan25 @ 11-25 o 6-10 o 1-5 BkmkO FIG.Z2 32 the variance of the response, and is represented by the following equation: Y = -299.86272-3.33517Ga+0.80889Cu+2.22190V+1.74131Ba+1.32637Co+ 4.72082Mn+0.03590Li-2.51480Mo-2.95853As-9.23681Zni-15.35874Cd It may be seen in Table 7.12, that several of the parameters included do not at all affect the value of R , having been left in the equation due to the decrease in the value of the standard error of the estimate that they produce. The positive coefficients of Cd, Li and Ba, represent the general- ly favourable character of the Pennines with respect to zinc mineralization. The negative coefficient of Zn, an element normally present in much higher concentrations in the Pennines than in the rest of the area, and which should thus render positive weights, reflects a counterbalancing effect that decreases the very strong influence of Cd in the estimates. This element is found in very high concentrations in the Lake District, where very high levels of Zn are also found. If the counterbalancing effect was not present, the Lake District would give very high estimates, most of which would not be justified, thus rendering the forecasts unreliable. The negative loading of Mo, an element that is of relative region- al importance according to the structure coefficients, represents the generally unfavourable nature of the Lake District to contain zinc minerali- zation, diminishing even more the estimates for areas underlain by barren Silurian rocks, rocks which bear high contents of this element. According to their negligible contribution to the structure of the model, the six remaining parameters represent local features of the area, however high or low their regression coefficients may be. The positive coefficients of Cu, V, Co and Mn, point to high concentrations in the elements present in the central and northern Lake District, around cells 32, 41, 42 and 53. As well, V indicates high concentrations in the Pennines around cell 49; Co points out high levels around cells 15, 25, It a 3 26, 71, 83 and 106; and Mn rather high values around cells 26 and 37. Finally, the negative coefficients of Ga indicates the generally unfavourable character of the Skiddaw Slates in this respect, and the negative loading of As would reflect the generally low values present throughout the area, with the exception of a small zone around cell 32. (b) Geological Model The geological model chosen for the estimation of this output index, accounts for 100% of the variance of the response and is represented by the following equation: Y = 2.14243+0.05193 Coal Measures-0.01211 Millstone Grit+ 3.01246 Lower Limestone-0.00146.Middle Limestone+0.007 Upper Limestone- 0.01661 Borrowdale Volcanics +0.06499 Acidic intrusive rocks '40.1834 Number of Faults+ 0.13388 Number of Fault Intersections -0.0295 Length of Faults -0.0209 Number of Contact-Fault inter- sections. The interpretation of the annotated equation is the following. As may be seen in Table 7.12, the model is dominated by four parameters which account for most of the variance explained. On one hand, two faulting parameters, and on the other two stratigraphic indexes (Millstone Grit and Middle Limestone). The positive coefficient of the No. of Fault Inter- sections reflects the known fact that these are loci for enrichment of the ore bodies existing in the area, and for the formation of irregular enriched masses of mineralization; it is worth noting that 10 of the 13 zinc- productive cells in the area have values for this parameter that are well over the regional mean of 22.3. The negative loading attached to the Length of Faults reflects the known fact that the long regional faults are seldom mineralized, the ore bodies normally being located in relatively short, rather local fissures; note in this respect that more than half of the productive cells in the 1 3 4 area have faults with an average length well below the regional average length of 0.98 miles, and that the most important producers are included among those cells. The coefficient of Millstone Grit indicates that zinc-producing deposits are mostly located in the central and northern Lake District and in the Pennines west of the Burtreeford Disturbance, areas that have no outcrops of this unit. A similar influence is evidenced by the positive coefficient of the Lower Limestone, a parameter that has a much small influence in the model than Millstone Grit. The negative coefficient of Middle Limestone is rather puzzling since this unit is well represented in half of the productive cells. Apparently, this coefficient would balance the positive weight of Upper Limestone, a unit that bears the most important deposits, but which is also present in numerous areas of the Pennines where zinc mineralization is not known; this feature explains its little influence in the model as a whole. The remaining parameters stress little or localized influences in the model, whichever the value and sign of their coefficients may be. The positive loading of the Acidic Intrusive Rocks reflects their invariable presence in the productive cells of the Lake District; it can not be ascertained whether this influence is related to the main acidic bosses existing in that area, or if it is related to the numerous acidic dykes present. According to the available data, the latter would be a much more logical influence to accept. The positive weight of Coal Measures reflects its presence in cells 6 and 49; this loading is more.than counterbalanced in the eastern- most part of the area by the negative weight of Millstone Grit, which prevents the obtainment of unjustified positive estimates in zones mainly covered by these measures, as is the case of cells 18 and 50. The weight of the Number of Faults, reflects the fact that the zinc-productive cells in the area have, with the exception of cell 6, a 0 1 3 5 value of this index greater than the regional mean of 33.6; however, the low influence and loading of this index points out that this is not an outstanding feature of those cells, which can be expected in light of the fact that there is a much greater number of faults present in cells where zinc mineralization is unknown. The negative loading of Borrowdale Volcanics is a factor present in the model to counterbalance the high weight of the acidic intrusions existing in the central Lake District, both indexes being intimately related. The negative, coefficient of the No. of Fault-Contact Intersections would, on one hand, act as a minor balancing load of the weight of the faulting indexes previously discussed, and on the other hand would indicate the abnormally low value that this index has in some productive cells as 6, 41, 42, and 53. Finally, the great diversification displayed by the parameters present in the model, assures that the small positive constant included would not exert an important influence in the results. Therefore, except for severely anomalous circumstances highly unlikely to occur, positive estimates due to the constant term are not to be expected from the selected model. (c) Combined Model The combined geochemical-geological model chosen, accounts for 100% of the variance of the response, and is represented by the following equation: Y = 30.79062+0.042270a-0.26475Pb+0.00579Ba-0.58009Ni+0.37812Mn- 0.06051Coal Measures+O.00787Lower Limestone-0.00123Upper Limestone -0.01781Borrowdale Volcanics+0.24436Number of Fault Intersections -0.02442Length of Faults Table 7.12 shows that the last six variables included in the equation have practically no influence on the value of the final R2, but • 1 3 6 reduce the standard error of the estimate, from 0.8727 to the final value of 0.0062 (34% and 0.2% of the mean response, respectively). It is worth noting that this is another example of the complex relationship existing between the variables in a regression equation, where the inclusion of two new parameters such as Pb and Ni change the sign and importance of many coefficients, as is the case of Ga, Coal Measures and Upper Limestone. As may be seen in the structure coefficients, the model is domin- ated by the influence of the Length of Faults, No. of Fault Intersections and Ba, parameters whose importance with respect to zinc production has already been discussed. The influences of Mn, Lower Limestone, and Borrow- dale Volcanics, are in this case similar to that in the two previous models, and hence need not be discussed further. What needs to be explained is the Meaning of the loadings for Pb and Ni, new parameters in this respect, and their influence in the signs of the remaining parameters. The negative loading of Ni, an element of relative importance in the structure of the model, reflects the generally unfavourable nature of the Lake District as a zinc-producing area, and within it points especially to the southern part, where no zinc mineralization is known to exist and where high levels in this element are present. The negative coefficient of Pb, an element relatively abundant in the Pennine region, coupled with its negligible importance in the structure of the model, indicates that it is present in the equation to indicate pertain local peculiar features. Apparently, this coefficient would indicate that, however abundant this element may be in the area, the only anomalous productive cell is 32, and to a minor extent 36 and 106; therefore, more than 75% of the zinc-prod- uctive cells bear non-anomalous contents of Pb and, what is more,- cells 6, 41 and 42 are deficient in this element, features that could explain the negative loading attached to it. The negative coefficients of Ga, is rendered positive by the strong negative weight of Ni, this change being necessary as a counter- 4 balancing effect for the northern part of the Lake District and for the area around cell 49, regions that have had zinc output and which present high contents in both elements. If that balancing feature were not present in the equation, those areas would probably render strong negative estimates, making the forecasts obtained with the model unreliable and very probably with biased residuals. The negative coefficient attached to the Coal Measures represents the scarcity of this unit within the zinc-productive cells. In this case no counterbalancing effect is required, as it was needed in the geological model, because cell 6 - which includes a certain amount of this unit - is low in Ga, and Ba, and has no Lower Limestone; cell 49, the other prod- uctive cell bearing outcrops of Coal Measures, is high in Pb and Ni, and also bears no Lower Limestone outcrops. Therefore, the model as a whole considers the global nature of those cells, it being unnecessary to stress the presence of Coal Measures in them. The negative loading of Upper Limestone is difficult to explain because this unit bears a great part of the most important ore deposits in the Pennines. Since this is a very weak loading, and since the influence of this index in the structure of the model is almostnegligible, it may tentatively be considered as representative of the inexistence of zinc mineralization in many areas where this unit constitutes most of the out- cropping rocks. If this were the case, the negative loading would also be an indication of a counterbalancing effect influencing the productive cells bearing these rocks, and its characteristics would be explained by the remaining parameters in the equation, rendering this index redundant. Finally, as with the geological model, it is thought that the positive constant term present in the equation will not affect the results to a great extent, because of the great diversity of parameters included, which ensures, that positive. estimates would be unlikely to occur due to the constant. 7.3.3.3 Forecast of the potential number of copper deposits per cell Among the copper-producing cells of the area , this index has a mean of 1.63 deposits and a standard deviation of 0.80 deposits. Most of the variables considered are not significantly correlated with it, Acidic Intrusive Rocks being the only parameter having a significant correlation coefficient at the 0.05 level of significance (0.748). As can be expected, a large number of the variables bear negative coefficients of correlation with the response. The models selected for further use with forecasting purposes are summarized in Table 7.13 and Figure 7.3. (A) Geochemical Model The geochemical model chosen accounts for 100% of the variance of the response, and is represented by the following equation: Y = -15.42588+0.47410Fe-0.53576Ga+0.60548V-0.20187Ba-0.16744Ni -0.36336Mn40.12042Mo+0.94475Zn-0.69656Cd Two elements are very important with respect to the weights that they impose in the model, having positive coefficients: Zn and Mo. The very strong positive loading of Zn reflects the high content in this element usually found in the copper-producing cells of the area, as much in the Pennines as in the Lake District; worth mentioning in this respect is that the three cells producing more than £100,000 of copper output, have zinc contents exceeding 500 ppm on average. The great importance of Mo in the model stresses the favourable character of the Lake District as a whole for containing copper mineralization, and within it, of areas underlain by Borrowdale Volcanics. A second group of indexes, that of Fe, Ga, Cd and Mn, have a relative importance in the model, and bear regression coefficients varying in importance and sign. The loading of Fe indicates the favourable nature of the Skiddaw Slates and Borrowdale Volcanics in the Lake District, and in a minor proportion the importance of some restricted areas in the Pennines, • TABLE 7.13 SELECTED MODELS FOR THE FORECAST OF THE NUMBER OF COPPER DEPOSITS PER CELL MULTIPLE P 1.0000 RSO 1.0000 STO. ERROR OF EST. 0.0128 RSO (ADJ.) wpm ANALYSIS OF VARIANCE OF SUN OF SQUARES MEAN SQUARE F RATIO REGRESSION 9 6.545 0.727 4426.776 RESIDUAL 1 0.004 4.000 VARTAUES IN EQUATION VARTARLE COEFFICIENT STD. ERROR F TO REMOVE STRUCTURE COEFFICIENTS (CONSTANT -15.42553 ) FE 1 0.47410 0.02154 484. 3831 0.216 Cl 2 .4.53526 0.01723 112. 6095 0.202 V 5 0.60548 0. 0145 2 1739. 2491 0.015 94 6 e.0.20147 0.00392 2653.7611 0.058 NI 0 -0.16744 0.00219 5920.8027 0.113 MN 9 -0.36336 0.01473 604.7160 0.242 MO 12 0.12042 0.00439 751. 2766 0.417 ZN 14 0.94475 0.01241 5791. 1131 0.355 CO 15 ■0069656 0.00900 5991.1407 0.265 tUMMARY TAPLE STEP VARIAEL 0 MULTIPLE INCREASE F VALUE TO NUMBER ENTERED REMOVED R RSQ ON RSO ENTER OR REMOVE MO 1; 0.4171 0.1740 0.1740 1.6957 2 MN 0.6143 0.3723 O. 20 33 2.6121 3 FE 1 0.7716 0.5953 N nso 3.7713 2N 14 0.4133 0.6614 0.0665 le 1712 NI 0.8568 0.7341 0.07u 1.3629 CO 1: 0.0925 0.7966 0.0624 1.2269 GA 0. 9569 0.9195 0.1230 4.5826 a 94 0.9779 0.9563 0.0368 1.6074 9 V 1.0000 1.0000 0.0436 17 39.2491 (a)GEOCHEMICAL MODEL MULTIPLE P 1.0000 - RSO 1.0000 STO. ERROR OF EST. 0,0161 RSfe (A 0.1.) 1.0000 ANALYSIS OF VARIANCE OF SUM OF S1UA RES MEAN SQUARE F RATIO REGRESSION 9 6. 545 0.727 11040.130 RESIDUAL 1 0.000 0.000 VARIA9LES IN EQUATION VARIABLE COEFFICIENT STD. ERROR F TO REMOVE STRUCTURE CO‘FFICIENTS (CONSTANT 0.77660 ) WILSON 2 ..0.02426 0.00077 998.6205 0.095 LORLST 3 0.01022 0.00018 1164.0169 0.229 MIOLST 4 0.00281 0.00011 693.9510 0.473 1581/1 0 0.18633 0.00403 2142.6729 0.149 SK/008 10 0.00035 2.00001 562.1622 0.401 INTACT 11 0.03843 0.00052 5417.2675 0.748 INTSCT 13 0.00330 0.00031 120.1912 0.191 CNTFLT 15 ...0.02157 (.00100 464.4379 0.397 /NT503 16 e0.12427 0.00436 812.4957 0.465 SUMMARY TABLE STEP VARIABLE MULTIPLE INCREASE NUMBER ENTERED REMOVE° R RSI IN *SO EATER 1 11161 IL 8 0.1491 0.0222 0. 02 22 0. 2545 2 INTACI 11 0.0002 O. 640 3 0.6130 13. 7445 3 TNTRAS 16 0.9413 0.8461 0.24 59 15, 1113 4 50 /WM 10 0.9592 9..101 0 03 39 2.5475 5 001101 13 0.9659 0.5310 O. 01 29 0. 9636 6 901514 2 D. 9741 0. 9489 Oa 0159 1. 2445 7 LOWLST 3 0.9586 D.1774 0. 0285 3.7712 a MIOLST 4 0.9977 0.9953 0. 0180 7 6695 9 CNTFLT 15 1.0001 1.1203 8.00 47 4 64. 4379 (b)GEOLOGICAL MODEL HUI T IPLE P 1.0.100 R00 1.0030 STO. EFRO* OF EST. 0.0000 RSO(ADJ.) 1.0.000 ANALYSIS Or VARIANCE OF SUM OF SQUARES MEAN SQUARE F RATIO REGRESSION 9 6.545 3.727.4894126.945 RESI3UAL 1 0.000 0.000 VARIA4LES IN EQUATION • VARIAD lE COEFFICIENT STD. ERROR F TO REMOVE STRUCTURE. COEFFICIENTS (CONSTANT -15.03576 ) 4 FE 1 .-0.69220 0400002 '93952.5341 0.236 GA 2 0.46093 0.00712 *15183.7923 0.715 NI 8 ...0.14058 0.00001 • 24545.1954 . 0.193 MN 9 0.53459 0.00002 17 47 8 9. 703 6 0.242 MD 12 -0.05262 0.00001 *1 813 3. 0 612 0.417 214 14 0.52661 0.00002 *51565.5945 0.385 cn 15 -0.43014 0.00002 *6 30 65. 561 4 . 0.268 UPPLST 19 0.10838 0.00700 *0 10 6 4. 2342 0.206 SORROW 23 -0.00030 0.00000 • 44935.4145 • 0.096 SUMMARY TOOLE STEP VARIABLE MULTIPLE INCREASE F VALUE TO RUMMER ENTERED REMCVE0 RSQ IN R90 ENTER OR RFM0 00 MO 12 O. 41 71 0.17 4 0 0. 1740 1.8957 2 MN 4 0.6143 0.1773 0. 20 33 2. 6121 3 FE 1 O. 77 16 0.5953 O. 21 80 3.7713 4 2(1 14 0.8/33 0.6614 0. 0661 1. 17/2 5 RI 4 0.8568 0. 7341 0.0727 1.3679 6 Cl) 15 0.8925 0.7956 [40624 1. 2269 GA 2 0.9589 0.9145 0. 12 30 4. 5926 a U7RL ST 19 , 0.9993 0.1986 0.0791 114. 7572 9 BORROW 23 1.0000 1.0300 O. 0014 564/9 35. 4/45 (c ) COMBINED MODEL .. Forecasted numberof copper deposits percell . [fJ' - ~ ~ 0 0 '...".J ~e ( 0,0 V 0 0 01 '~YO J 0:010 0 10 @'O'O ( 0 0:0 0i@ \ ~ - 010 010 0 R-=-toI. 0iO;0 0 0 _,~QjOI0!01 0 10'0 f-- Ii: 0J\,."\ i 0:0:0,0 \Y ~ 01@j 0 GEOCHEMICAL MODEL ~ { ~~ 0 0 "-.../ ,.-.- $10 0 0 0 -'f I 0 / 0 0 KEY TOSYMBOLS )0 0 0:0 0:0 0 o Morethan 10 {. @, 0:0 000 @ 6-10 \ .~0~0!0 --g:0------t-! . :@):01b:0.0:010 0 o 3-5 10?0!o:a 0 10/0/010 o 1-2 '10Y\,{\ @i@l@! Blonk-O \i V 01010 GEOLOGICAL MODEL FIG.7.3 • I as those around cells 35 and 71. The strong negative loading of Cd would indicate the generally unfavourable character to contain copper deposits of the Pennines region and of the Silurian rocks in the southern Lake District, areas where high concentrations of cadmium are especially found. The weights of Mn and Ga, are more difficult to explain, because these elements are generally present in important amounts in the Lake District. In the opinion of the author, these coefficients do not reflect regional trends, but point out the lack of copper mineralization in the western Lake District, an area where those elements are particularly concentrated. Besides, a parallel effect might be stressed in the model by the general deficiency in these elements of the main productive cells (32, 36, 75), when compared to levels found in surrounding areas. A similar explanation can. be postulated for the negative weight of Ni, which in this case would not reflect the Lake District as a whole, but the high concentrations existing in the barren Silurian rocks of the southern part of that area. Finally, two elements that have little importance in the structure of the model need to be discussed: Ba and V. The negative loading of Ba would not indicate regional patterns, but would point out strong deficiencies in this element shown by the copper-producing cells of the area, which with the exception of cells 32 and 71 have average values well below the regional mean of 394 ppm. The positive loading of V would indicate, besides favourable nature of the Skiddaw Slates and Borrowdale Volcanics, the high content present in some productive cells as 32, 64 and 75. (B) Geological Model The selected geological model accounts for 100% of the variance of the response, and is represented by the following equation: • 200 Y = 0.77660-0.02426Millstone Grit+0.01022Lower Limestone+0.00281 Middle Limestone+0.18633Ashgill+0.00035Skiddaw Slates+0.03843 Acidic Intrusive Rocks+0.00330No. of Fault Intersections-0.02157 No. of Fault-Contact Intersections-0.12477Basic Intrusive Rocks As may be expected from the available output figures, the chosen model is dominated by parameters reflecting the influence of the Lake District as a main copper-producing region, a feature that is evidenced in the structure coefficients and in the weights of Ashgill, Acidic Intrusive Rocks, and Skiddaw Slates. It is worth considering in this respect, that the presence of Acidic Intrusive Rocks in the model points out the large number of acidic dykes (quartz porphyries) existing in the central and northern Lake District and not the main acidic intrusive basses of the area, which are rock bodies that do not appear to influence the presence of mineral- ization. Also, the low effect of Ashgill on the value of R2 would indicate that these rocks exert a limited influence in the copper output, manifested mainly through their presence in the main producing area of the field (cell 75). Thus, the inclusion of this index in the equation, more than reflecting its own favourable nature towards'containing copper deposits, would act as an indirect indicator of the presence of the top of the Borrow- dale Volcanic Series, a sequence where deposits similar to those,of the Coniston district may possibly exist. The generally unfavourable character of the Pennines is manifested by the negative regression coefficients attached to the Basic Intrusive Rocks (dolerites and related bodies), weight that is partially counter- balanced by the positive loading of Middle Limestone,a unit that covers extensive areas in the copper-producing cells of that region. The coefficients of Lower Limestone and Millstone Grit do not reflect regional trends, but are a consequence of local phenomena, as is the presence in cells 31, 32, 36 and 41 of minor outcrops of Lower Limestone • 20, 1 rocks, and the general absence of copper ores in the easternmost part of the area where Millstone Grit is an important constituent of the strati- graphic succession. It is worth noting that the negative loading of the latter index is not as strong as could be expected, and reflects the presence of these rocks in minor outcrops in cells 31 d'32. The positive weight of the Number of Fault Intersections reflects the general importance of this parameter as a control of localized enrich- ment. It is worth considering that more than half of the copper-productive cells have strongly anomalous values of this index. This fact is to a certain extent counterbalanced by the value of cell 75, which is the most important area for copper output, and which is abnormally low in this parameter, as compared to the remaining productive cells (it has a value of 5, contrast- ing with an average of 41); this feature would explain why the loading of this index is not very strong. Finally, the negative coefficient of the Number of Fault-Contact Intersections must be considered as an indirect reflection of the favourable nature of the Lake District in this context, since this parameter is generally low in that region, contrasting strongly with the values found in the Pennines, which are generally well above the regional average. (C) Combined Model The combined geochemical-geological model chosen, accounts for 100% of the variance of the response. It is represented by the following equation: Y = -15.03576-0.68220Fe+0.46093Ga-0.14058Ni+0.53459Mn-0.0536Mo + 0.50681Zn-0.43014Cd+0.00808Upper Limestone-0.00030Borrowdale Volcanic& It may be seen in Table 7.13 that the last variables entered in the model did not improve significantly the value of R2, but were maintained n 2 in the equation due to the decrease in the value of the standard error of the estimate that they produced. It is worth noting that this model constitutes an excellent example of the complex relationships operating between the variables in a regression solution, since the addition of two geological variables to the geochemical indexes has produced a reverse in the sign of most of them, and hence the interpretation of the physical meaning of the model needs to be done taking into account this influence, the effects of which are directed to the obtainment of the most balanced model possible. Three main variables appear to be the most important controls of the equation, as indicated by the structure coefficients: Ga, Mo and Zn. The positive weight of Ga, by far the most important index, reflects the favourable character of the Lake District towards containing copper mineral- isation and especially of the northern and central regions within it, which bear high content in this element. The positive loading of Zn reflects high levels of this element present in all the copper-producing cells, a fact that is stressed by its very strong loading, indicating that this element is a good pathfinder for copper mineralization in the studied area. The negative coefficient of Mo is rather puzzling because it,is present in high concentrations in the Lake District, and thus a positive loading could be expected. A possible explanation for the value obtained, can be related to the high concentrations present in the barren Silurian rocks, which also bear high Ga values. Since Ga is very heavily loaded in the model, the unfavourable character of the Silurian needs to be express- ed in the equation by some means, in order to obtain reliable estimates. Apparently, the counterbalancing effect is mainly manifested` through the negative weight of Mo, which would diminish the estimates of the cells underlain by those rocks. This effect would be enhanced and complemented by the negative coefficients of Fe and Ni, elements that are also present in high concentrations in the Silurian, and which - in addition - will 21)3 decrease the estimates of the areas underlain by Skiddaw Slates, which are strongly anomalous in Fe, Ga and Ni. Three other parameters are of intermediate importance in the structure of the model: Mn, Cd and Upper Limestone. The positive coefficient of Mn would reflect the generally favourable character of the Lake District, and of some localized areas in the Pennines that bear mod- erate to high levels of this element; it is worth mentioning that among the latter areas are the districts around cells 25 and 36. The negative coefficient of Cd would reflect the generally unfavourable nature of the Pennines and southern Lake District, areas that present high concentrations of this element. The weight of Upper Limestone is a reflection of the importance of this unit within the Northern Pennine orefield, pointing out the presence of extensive outcrops of these rocks in all the copper- producing cells of that field. The influence of Borrowdale Volcanics in the model is very marginal, this may be assessed from the structure coefficients and from its very low loading. The negative character of the weight is rather surprising, since this unit is known to contain important copper deposits. Apparently, this fact could be better explained as a counterbalancing effect introduced in the model to diminiSh the strong influences of Ga and Mn, elements that are present in very high concentrations in that volcanic rocks,and also as an decreasing effect for the loading of Zn, an element that is very anomalous in cells 32 and 75, cells which contain copper mineralization in the volcanics. 7.3.4 Forecast of average value of expected reserves per deposit The best models for the estimation of the average value of the potential reserves existing in the deposits of each cell, are discussed in the following paragraphs for the three base metals considered in the present research. As was done in the previous section, the geochemical, geological and combined models are given in succession for each metal, in TABLE 7.14 FORECASTED AVERAGE VALUE OF RESERVES PER DEPOSI1 (IN POUNDS X 1000)-NORTHERN ENGLAND LEAD RESERVES ZINC R,_S-6F.VES COPPER RESERVES CELL CMBND. GLOCH. GEOL. CMBND. GEOCH, GEOL. CMBND. GFOCH. GEOLt MODEL MODEL MODEL MODEL MODEL MODEL MODEL MODEL MODEL 1 1795 -507 -99 -370 1701 -570 -34 - -386 60 2 1650 570 ' -99 -435 2221 2-644 38 -697 109 3 1545 106 -88 -79 2026 -1209 287 -684 264 4 949 -858 514 -296 865 -160 146 -339 -3 5 638 271 844 871 942 1421 -12 -798 -245 6 177 145 566 584 595 269 -17 -665 -318 7 912 78 1052 853 -65 1790 21 -808 -15 8 47 83 803 552 205 1133 -19 - -230 32 9 1294 827 -99 -703 1199 -570 -48 -174 60 10 1147 608 -99 -43 1716 -570 -45 -799 60 11 302 480 -99 54 1320 -699 -36 -701 37 12 1516 178 -99 -113 1902 -662 -33 -677 42 13 1015 -292 195 -392 940 -445 -22 -428 -45 14 199 -142 1269 1136 463 3394 -31 -369 -70 15 536 11 1287 1076 451 2592 -17 - -177 22 16 83 930 799 1176 498 20 -6 - -821 40 17 157 1177 560 969 856 -1385 -5 -591 38 18- -573 270 80 446 -90 -1798 -4 -260 47 19 -218 449 -99 -172 807 -1020 -35 -689 27 20 -1002 305 -52 431 43/ -2076 -54 -936 3 21 -955 767 -77 -13 633 -2536 -38 -685 5 22 -379 1093 -22 201 964 -1984 -28 -876 -52 23 417 1398 -81 -159 1216 -703 -27 -960 -22 24 1661 -256 721 586 1203 971 -26 - -738 -84 25 1294 564 744 832 817 935 1 1 1 26 3434 1172 1312 2716 2717 2612 -17 -873 -6 27 1968 791 1356 2382 2036 2861 -10 -745 16 28 134 94 107 -737 -511 -2679 27 -178 51 29 -2475 -255 -42 -1323 -1504 -1241 -24 455 -5 38 1 163 45 -138 -562 -1504 -29 -162 -63 31 -376 -57 549 -99 -801 -742 1 1 -8 32 791 1058 575 29 19 -1699 -26 60 -1269 33 -2038 861 514 769 234 1016 -33 -554 -154 34 -1052 1149 -90 -224 292 -541 -9 -559 60 235 622 35 -442 503 -1218 -13 -546 -167 36 544 902 282 0 11 -604 12 35 -325 37 341 448 539 25 22 -355 -10 -580 -334 33 1555 1107 1001 1759 2034 1738 -12 -842 -51 39 1069 944 625 591 458 -740 15 -638 13 40 -2391 210 -13 -447 -563 -1013 -38 253 3 41 -252 227 -99 195 214 453 22 21 32 42 286 453 136 772 773 412 -2 2 -70 43 769 712 962 405 750 152 21 -320 36 44 -1033 491 521 -422 102 -1077 189 70 165 45 -1059 801 394 451 676 823 -41 -499 47 46- 711 672 52 -451 494 -558 1691 -515 1691 47 257 1144 -86 -714 50 -1339 2243 -372 1979 48 401 853 -31 -1286 -1173 -1190 9 -544 -1115 49 -116 893 484 317 320 -432 -8 -346 -349 50 131 335 186 233 344 t -1586 -7 -524 -64 51 301 653 39 -239 946 -3322 -14 -315 3 52 -631 769 528 -925 525 3775 239 301 485 53 1421 1271 2463 0 -7 -327 -8 6 -230 54 4001 2918 3292 -183 285 -569 -1 0 -29 55 4786 1317 3341 -310 411 -582 -9 -64 -14 561 -683 490 1339 -1071 -612 -647 120 559 88 57 -133 1060 757 1517 1533 1935 -52 -547 33 58 -131 600 232 96 720 -129 174 -807 232 59 38 -76 523 -223 -409 20 -20 -254 -4 60 -36 91 1021 1053 185 1574 -18 -384 22 61 -89 572 341 793 536 -724 -17 -606 36 62 2294 626 833 -295 1622 -837 -26 -798 22 63 1163 1603 1895 -882 573 4605 266 135 574 64 2899 1539 3188 -785 127 -557 -10 18 -415 65 1788 1572 1684 -855 -646 -1104 2557 395 2451 66 1081 371 -384 -1057 -504 -1140 2247 462 2488 67 -2945 -1139 -3572 -2395 -2230 -200 583 1814 605 68 -1767 -831 -2765 -1299 -435 -1997 13 576 62 69 -1611 421 -327 -573 -242 -2619 -4 -2 36 70 1269 532 910 567 1724 33E -21 66 4 71 1319 667 923 0 -9 -12 18 -95 -10 72- 700 851 758 8.36 -141 394 3 -256 -14 73 441 1123 42 -131 1433 -497 -32 -796 80 74 -995 1739 1107 -309 -602 8163 439 -245 945 75 416 . 246 26 -1,40 -1634 -1196 1065 1066 1045 76 -3521 -1057 -5031 -2076 -2110 -699 436 1888 455 77 -2909 -840 -4663 -2354 -1636 -644 7 1761 60 73 .-3101 -761 -4359 -1933 -1522 -644 31 1376 68' ;3-. 3232 -1149 -4729 -1649 -1537 -1097 3000 1317 2882 -592 -111 186 316 651 -551 3376 86 3247 81 620 73 79 143 1213 -2780 -22 -235 27 82 1328 898 209 545 917 -1495 -7 265 -1 63 297 1301 605 1 -1 34 13 -53 13 84 636 1433 345 -322 460 -181 1816 -67 1797 85 -1630 -862 -4871 -1994 -928 -717 739 1562 755 86 -.3020 *343 -4597 -1698 -2023 -625 4 1360 57 57 -2354 -752 -2963 -1584 -1467 -589 -3 1205 51 85 ^3100 -811 -3120 -1682 -1509 -644 -11 1088 42 89 -1989 -963 -3051 -1041 -1481 -755 542 955 561 90 159 14 13 173 1018 -888 -37 29 41 91 77 283 -19 233 996 -590 -32 -237 42 9 2 -215 759 113 249 722 -781 -22 -325 43 93 -782 919 125 518 254 -1212 -15 -514 41 94 -3350 -191 -350 -1592 -2092 -408 2544 1204 2490 95 -1457 251 158 -784 4 -3110 -33 27 47 96 -2526 593 -145 -159 -543 -1955 55 -321 147 97 -314 495 -152 -614 936 -3393 390 -179 457 93 -1068 236 -213 -343 -121 -2140 184 74 255 99 -348 -252 100 -910 -935 -2767 -5 20 50 100 -486 58 1390 1186 -335 3252 -3 263 32 101 -2175 255 1226 634 -337 2603 -14 126 17 102 -699 460 -99 -64 529 -4566 -22 -461 22 103 -1114 4E6 -180 -349 -164 -4527 1686 -99 1672 104 -873 119 -721 -483 106 -3949 -20 440 24 105 -1702 2131 -90 -703 -521 -3659 5 100 4a 106 568 2140 830 3 16 -5 12 12 12 2 4 order to facilitate the comparison between the different approaches that may be followed. Once again, emphasis is placed on the physical signif- icance of the models, which are discussed in terms of the structure coeff- icients and of the nature and importance of the regression coefficients attached to the variables included in them. The overall forecasts for the 106 cells into which the studied area was subdivided, are summarized in Table 7.14. 7.3.4.1 Estimation of the average value of the lead reserves per deposit Among the productive cells this parameter has a mean of £663,100 and a standard deyiation of £1,091,284. The 14 trace elements selected in the present research are not significantly correlated with this index, with the exception of Pb which has a coefficient of correlation significant at the 0.05 level (0.319). Among the geological parameters, only Borrow- dale Volcanics is significantly correlated with the response at the desired level (0.394), most of the parameters bearing, as may be expected, negative coefficients of correlation. The models selected for further use in the forecasting of base metal mineralization in Northern England are.summarized in Table 7.15 and Figure 7.4. (A) Geochemical Model The geochemical model selected explains 33.71% of the variance of the response. It is represented by the following equation: Y = 2304.03683+53.27178Ga+122.50711Pb-144.23845Ni-216.14737Zn+ 175.09459Cd The structure coefficients indicate that the equation is strongly dominated by Pb, and in minor proportions by Cd, Ni and Zn. The contri- bution of Ga to the value of R2 is very small, due to its very low corre- lation with the response and with the remaining elements, an exception being Ni. TABLE 7.11; MODELS 61-P.M.ZTED FOR DU: FORECAST OF THE AVE- RAGE VALUE OF EXPECTED LEAD RESERVES PER DEPOSIT RS O. 3371 MIME R 3.55'6 RSO (ADJ.) 0.2563 STD. TRROR OF EST. 955.4417 ANALYSIS OF VARIANCE OF SUM OF MARES MEAN S'IJARE F RATIO REGRESSION 5 14851591.420 2971318.262 3.254 RESIDUAL 32 29211824.672 912863.895 VARIABLES IN EQUATION VARIABLE =EFFICIENT STD. ERROR F TO REMOVE ST.AUCTURE COEFFICIENTS 1C0NST2NT 2384.03682 ) GA 2 53.27178 24. 83479 4.6712 0.141 PR 4 122. 50711 44. 82466 7.4694 0.549 NI 8 -144.23845 55. 36879 6.7863 0.353 /34 14 ■2164 14737 105. 751'3 4.1776 4.308 CO 15 175.29459 94.64:56 3.4229 0.416 SUMMARY TABLE STEP VARIABLE MULTIPLE INCREASE VALUE 73 SOMBER ENTERED RI MOVED RID IN RS Q INTER 04 REMOVE 20 4 0.3195 0.1115 0.1315 At. 0641 2 NI tw 8.4808 4.1677 4.7592 2.4583 3 GA 2 0.4972 3.2472 0.0865 3.919) 4 IN 14 C.5150 :42661 0.0189 9.8511 5 CO 15 0.5806 2.3371 1.0739 3.4224 (a)GEOCEEMICAL MODEL 5811T1 4LE R 7.9354 1550 0.4030 STD. IRROP OF EST. 579.0214 0000.1.5 0.3513 ANALYSIS OF VARIANCE OF SUM OF SQUARES MEAN MARE F RATIO RE7RE5S/ON 3 17722321.898 593073.965 7.676 *ESIDJAL 34 26271074.172 772678.652 VARTAALES IN EQUATION VARIABLE C3EFFICIENT STO. ERROR F TO -REMOVE . STMUC TU RE COEFFICIENTS (CONSTANT -19.30242 5 VMS) O 1.78427 1.57345 9.7831 • 0.349 SI0.U4N 12 -5.06219 2.53510 4.6802 • 0.1:9 BORROW 12 3.4683! 2.77533 21. (.21 a • 0.620 SUMMARY TABLE STEP VARIABLE MULTIPLE INCREASE F VALUE 71 NUMBER ENTERED REMOVED R 0311 IN PSG EWER OR REMOVE BORROW 12 0.3936 0.1549 0.1549 5.6005 2 UPPL ST 8 0. 5764 3.3323 1.1773 4.2933 3 SILURN 10 0. 6354 30438 0.0715 4.0022 (b)GEOLOGICAL MODEL MULTIPLE P 4.85,3 RSO - '0.7327 110. EFROR OF _11. 62..6163 RSQ (A 0J.) 0.6670 ANALYSIS OF VARIANX OF SUM OF SQUARES MEAN SQUARE F RATIO FEG•tL1SION 7 3e263243.4,9 4611066..1.1 11.245 RESIDU4L Jd 11760192.6,1 332674.469 • IMMIAILBS 10 EQUATION • VARIABLE COEFFICIENT STO. ERROR F TO REMOVE STRUC TORE COEFF/C I CNTS (CONSTANT -1431.21836 ) CU 3 -218.599..9 32.25472 45. 531 5 • 1.112 CO 7 11..97229 41.92447 7.353 . 0.047 MN 9 -224.64213 4..65158 31.4559 . 0.009 LI 10 167.83453 29. 267: 5 41.1959 • 0.083 ZN 14 148.6.331 34.53122 18...19 7 • 0.209 BORROW 26 6.51514 C. 76460 72. 6.263 . 0.460 COCKER 29 59.22421 19. 9372. 8.3240 . 0.117 SUMMARY TIME STEP 63.10°1: MULTIPLE NUm3EP INCR.A SE F vol..: Ti 047E8E3 ,tsoocsa asn IN RSQ _14 ER OR RE10V‘ 1 3o880.0w 26 0.3936 0.1549 3.1249 6.6415 2 CU 3 4.>147 1.2,56 4.1146 3 LI la 5.2385 3.6333 0...14 0. 1301 7.7241 4 oth 9 6.7344 0..394 6.1304 5 2M 9. 9147 14 0.7916 0.6266 2. CA 72 , 7. 4691 6 100(46 29 0. 8168 3.6671 1.44.5 7 CO 7 .3 7263 4.556. 1.2327 4.66it 7. 3>35 (c) COMBINED MODEL I KEY TOSYMBOLS ~ More than2500 @ 1001-2500 o 501-1000 o 1-500 Blank: 0 FIG.7.4 2'1 5 The strong influence that may be expected from the Pennines in the model is manifested through the high coefficients attached to Pb and Cd, elements generally present in high concentrations in that area. The negative coefficient of Ni would reflect the much less favourable chara- cter of the Lake District towards containing rich lead deposits, a region where that element is found in high concentrations in the pelitic sediments. In addition, this loading would counterbalance, up to a certain extent, the high weights of Pb and Cd in some areas such as cells 25 and 38, which bear such amounts in these elements as to render very high spurious positive estimates, but whose importance is diminished by their deficiency in Ni. The negative weight of Zn, an element that is present in rather high levels in the Pennines and which should therefore have a positive loading, is puzzling. It may be assumed that this weight, as well as the positive constant term, is present in the equation as a means of counter- balancing the strong influence of the Pennines, manifested directly through the loadings of Pb and Cd and indirectly by the weight of Ni. In addition, this negative weight would decrease the importance of the Silurian rocks still more, because they have high levels of this element. As indicated, Ga has a limited influence on the structure of the model, pointing out that its inclusion indicates some local conditions rather than regional trends. Its positive weight would indicate the possibility of finding lead mineralization in the Lake District, and within it especially in the Skiddaw Slates and Borrowdale Volcanics, series that are the highest gallium-bearing units of the studied area, and which bear the lead-zinc mineralization present in that region. (B) Geological Model The geological model chosen explains 40.38% of the variance of the response, and is represented by the following equation: 2 S. Y = -99.30042+1.78427Upper Limestone-5.06019Silurian+3.46835Borrowdale Volcanics As may be seen in Table 7.14, the structure coefficients of the model indicates that it is dominated by the two stratigraphic parameters included, which are the rock-units that contain most of the ore deposits existing in the area. On the other hand, the negative coefficient attached to the Silurian rocks and the low influence of this parameter in the value of R2 , clearly indicate the unfavourable character of this unit. Finally, it is worth noting that the latter coefficient, coupled with the strong negative constant term present, secures that only the geo- logically favourable areas are going to render positive forecasts. (C) Combined Model The combined geochemical-geological model selected for the fore- cast of the average value of the lead reserves per deposit, explain 73.27% of the variance of this output index, and is represented by the-following equation: Y = -1431.21836-218.5999Cu+110.97529Co-224.64213Mn+187.85453Li +158.60331Zn+6.51354Borrowdale Volcanics+59.22421Cockermouth Lavas The structure coefficients of the model indicate that it is dominated by two parameters: Borrowdale Volcanics and Zn. The influence of the first of these, as is obvious, reflects its favourable nature towards containing lead mineralization. On the other hand, the positive coefficient of Zn reflects the general favourability of the Pennines in this respect, a feature that is indirectly enhanced by the strong negative loadings of Cu and Mn (the first replaces Pb in the equation) and directly enhanced by the positive loading of Li. The three last parameters have little influence in the structure of the model, indicating that they represent rather localized features. In fact, these three indexes point to the Carbonif4rous Limestone as the main - ■•■ 3 7 lead-bearing stratigraphic unit, since in these horizons the highest con- centrations of Li in the area are found, as well as the lowest concentrations of Cu and Mn. The positive loadings of Co and Cockermouth Lavas, and their influence in the structure of the model, indicate the favourable character of the northern part of the Lake District for the presence of lead mineral- ization. The relative high weight of Co reflects high concentrations in this element in the Skiddaw Slates, rocks that are also high in Li. These enhancing features are 'partly counterbalanced by high Mn and Cu levels in that unit, which would diminish the estimates obtained for that area. It is worth noting that the loading attached to Co would not render positive est- imates in areas high in this element but underlain by barren Silurian rocks, because these areas also have strongly anomalous contents in Cu, which w ould more than counterweight the positive effect of Co. 7.3.4.2 Estimation of the average value of the zinc reserves per deposit This output index has a mean of £422,343 and a standard deviation of £754,755 for the productive cells in the area. The geochemical and geo- logical variables selected in this research are not significantly correlated with it, most of them bearing negative coefficients of correlation. The models selected for forecasting purposes for the whole area are summarized in Table 7.16 and Figure 7.5. (A) Geochemical Model The geochemical model chosen explains 99.98% of the variance of the response and is represented by the following equation: Y = 8633.41873-65.32103Fe+141.72769Ga-154.55276Cu+14.69845Pb-54.69614Ba -65.19871Ni-104.03094Mn+103.08958Li-8-72414Mo+22.26212Zn It may be seen in Table 7.15 that the three last parameters entered in the equation do not decrease the value of R2, but were maintained in the model because they diminish the standard error of the estimate from 257.57 TABLE 7.16 MODELS SELECTED FOR THE FORECAST OF THE AVE- RAGE VALUE OF THE EXPECTED ZINC RESERVES PER DEPOSIT - - MULTIPLE R 0.9999 RSO 0.9915 STD. ERROR OF EST. 23.2286 RSO(ADJ.) 0.9913 ANALYSIS Of VARIANCE OF SUM OF SQUARES WZIN SQUARE F RATIO REGmESSION 10 6834764.75♦ 683478.476 1266.714 RESIDUAL 2 1079.132 529.568 VARIABLES IN EQUATION VARIABLE COEFFICIENT STO. ERROR F TO RENEVE STRULTUR. COEFFICIENTS {CONSTANT 8633.41873 ) FE 1 .65.432103 6.54968 52.3726 0.007 64 2 141.72769 9.53945 220.7322 0.004 CU 3 .154.55276 7.07115 477.71E6 0.204 P8 4 14..9845 3.54205 17.2200 0.068 BA 5 .54.69614 1.83755 885.7172 0.550 NI 6 .65.19871 4.10932 251.7322 0.052 MN 7 .104.03094 2.53156 1688.2908 0.063 LI 8 103.08958 1.98690 2666.86E6 8.367 MO 10 -3.72414 2.79755 9.7250 0.521 IN 12 22.26212 6.86077 10.52E0 0.033 SU2NAFY 'TABLE STEP VARIAPLE truttIrlE INCREASE F VALUE TO NUMEER ENTERED REMOVED *60 IN RSI ENTER OR RE YOVE 1 BA 5 0.5497 0.3021 0.3021 4.7624 2 25 12 0.6126 0.3753 0.0732 1. 1715 3 MC 10 0.7347 0.5298 0.1645 3. 2159 CU 3 3.8258 0.6787 0.1399 3.4594 LI 6 0.5645 0.7474 0.0697 1. 0022 64% 7 3.9395 0.8826 0.1352 6.9119 7 N/ 6 5.9754 0.9515 0.0689 7.0965 GA 2 0.9971 0.9941 0.0426 29.0343 FE 1 0.9997 0.9955 0.0044 0. 6193 10 Pe 4 0.5999 0.9998 0.0014 17.2200 (a)GEOCEEMICAL MODEM MULTIPLE R 0.1411 RSO 0.9020 St Di ERROR Of EST. 206.6101 RS01003.1 0. 1250 ANALYSIS OF 4ARIANSE IF SUM OF sms44:5 1E4N SCUAPS F RATIO RE6RESaIIN 6 b27)722.272 141( 6. 1.171 25.646 RESICLAL 26.2141.67. 42656.271 • VARIABLES IN LOUAT ION • VARIABLE COEFFICIENT SID. ERROR F TO RENEVE : STRUCTURE COEFFICIENTS • {CONSTANT .511.651.24.1 000 faLSTN 3 4.77416 26.9)(1 0.033 LULLST, 4 .3.53231 3.7362 27..0945 . 0.226 UPPLST 6 5.66658 1.61463 129.1512 0.521 SKI040 8 141:1967 1.29312 11. AIt 4 0.024 INTACT 9 130626E2 2.21199 35.'520 0,246 CNTFLT 13 .14.393'5 2.83774 42.41'2 „ 0.032 SUMMARY TABLE STEP VARIAtLE MULTI! LE INCRL AS= F VALUE TO NURSER ENT,It D REMOVES 5 KSO IN RSI ENTER OS 91.3V_ UP PEST 6 0.5119 0.2621 0.2621 3.9.6i CNTFLT 13 2.6753 4.4563 0.1919 3.5042 LOWEST 4 3.7563 2.6153 u.1623 3. 4265 4 MILSTN 5 3.8546 0.7343 0.1120 3.3215 SKIDAW 5 3.86/3 0.7419 J.3115 O. 3117 9 3.6411 0. 9625 0.2209 35.3111 (b)GEOLOGICAL MODEL - - MULTIPLE P 1.015) RSQ 1.0000 STD. ERROR OF EST. 0.0239 0501033.0 1.0010 ANALYSIS OF VARIAN(: OF SUM OF SQUARES MCAN MOPE F RATIO 511)50 SIGN 11 6835563. 900 621442. 173.2517023. 535 RESIDUAL 1 0.011 9.001 VARIAREFS IN EQUATION VAR/ABLE COEFFICIENT STO. ERROR F TO R:NOVE STRUCTURE COEFFICIENTS {CONSTANT 2773.35152 ) CN 3 .13.35574 6.00911 .49966. 687 T 0.204 V 5 1.56026 0.00707 45679. 5122 0.550 RA 6 .49. 74611 4. ae 2.5. 1 .47496. 14C. 7 0.143 NI 8 ^100.63659 0.43.75 •64915.7749 0.052 LI 14 66. 21592 0. 04153 '62582.2472 0.367 MO 12 -3o.991,5 0. 0u410 '.6829. 9935 0.521 AS 13 -7.37581 Co 34346 •32415.2133 0.256 CD 35 84.60417 C. 01699 '69921.1139 0.009 LOWEST 15 -1. 35J39 0.05229 '5 6349. 7591 0.221 UPPLST 20 1.94909 0.42236 '15484.0114 0.512 SKIDAW 22 0.65435 0.00006 '76369.4357 0.024 SUHMAPY TARS STEP TAPIA 910 MUL TIPLE INC ,LIA SC F YALUE 71 HUNTER ENT,PEO 9E904E1 K 505 IN ISO iN730 5:13/5 1 IA 6 0.5497 0.3E21 0.3021 4.742. 2 UPPLST 23 0.7711 0.5346 0.2925 7,2151 3 LI 10 5. 9133 3.8339 0.2330 12.9Z43 4 Mt 9 0,0654 0,03,0 3,0994 11.563, 5 3530118 22 0.9815 0.5732 3.0413 1C. 77 79 6 MO 12 0.9188 0.5777 0.0445 1.2,91 7 C9 15 0.9964 3, 0928 D.0151 10.53J1 e 1.03117 18 0.9987 0.9975 0.0245 7. 290: 9 CU 3 0.9998 0.9997 0,0322 20 9113 10 41 13 1.0015 1.t.Z3 0.0,13 17•482... 11 V 5 1.03,10 1,1105 J. 0104 48679.5122 • .... (c) COMBINED MODEL r-r"-. ~ @!C)® @ ...... -.-->.'" -:.4-- ~ I,N @!@!o! . __ 1- ---r--I--- 0i0:@I~ I------~ ------;----I--- ~ @ @), KEY TOSYMBOLS i (}C)C) Q) Morethan2500 =-.J- 01 ( ~! @) C).@ --f @ 1001-2500 . l\!~; Q C) r-- r-T o 501-1000 ~@; -L I C) I : I o 1-500 I i\ I I /.)1 '-oJ -1 I'~ i I i~ BlonkO - r __~j_l-.-U~ GEOLOGICAL MODEL FIG.7.5 2 to the final value of 23.22 (60.9% and 5.4% of the mean response, respect- ively). The Pennines, the main zinc producing region in the area, is represented in the model by the positive coefficients of Li, Zn and Pb, which indicate broad regional, as well as local trends. This influence is partially counterweighted by the negative loading attached to Ba, an element very important in the structure of the model. The negative loading of the latter element reflects an important feature of the area. The known antipathy Zn-Ba manifested in physical form by the disappearance of the workable zinc deposits as soon as the inner part of the barite zones that can be distinguished in the Pennines are reached (see section 4.2.4). As well, this negative weight has an additional counterbalancing effect on the areas underlain by barren Silurian rocks, which bear high concentrations in this element and of Zn and Ga; therefore, if this counterbalancing effect were not present in the equation, those areas would introduce a degree of unrealibility in the model. The Lake District is represented in the model by the coefficient of Cu, Ni, Mn and Mo, which indicate that the area is not favourable towards containing zinc mineralization, and also the special local unfavourability of some geological units as the Silurian rocks and Borrowdale Volcanics. The strong positive loading of Ga indicates the restricted favour- able character of the Skiddaw Slates to contain most of the zinc-producing deposits of western Northern England (Thornthwaite, Threlkeld, Force Cragg, etc.). Finally, the wide variety of elements and coefficients present in the model, assure that the obtainment of positive forecasts as a consequence of the positive constant term included in the equation is highly unlikely. (B) Geological Model The geological model selected for the forecast of the average value of zinc reserves per deposit, explains 96.25% of the variance of the 2 3 9 response and is represented by the following equation: Y = -570.65624-4.02235Millstone Grit - 3.83231Lower Limestone +5.86658Upper Limestone+1.01967Skiddaw Slates+13.62662Acid Instrusive Rocks-18.39375Number of Fault-Contact Intersections The Pennines directly influence the model through the positive coefficient of Upper Limestone and indirectly through the negative loadings of Millstone Grit and Lower Limestone, parameters that have a twofold implication. On one hand, these weights define the position within the Carboniferous sequence of those horizons most favourable towards containing zinc mineralization (i.e. Upper and Middle Limestones), and on the other hand they confirm the known fact that the workable zinc deposits lie in the Alston Block of the Pennines to the west of the Burtreeford Disturbance, an area almost devoid of Millstone Grit rocks and which has not rendered zinc output where the Lower Limestone forms an important part of the sequence (i.e. at the Escarpment area). The Lake District influence on the model takes place through the loading of the Skiddaw Slates, a unit that bears the most important zinc- bearing ore bodies of north-western England, and through the coefficient of the Acidic Intrusive Rocks. The latter weight, in the opinion of the author, is not related to the main intrusive bosses existing in that area, but to the numerous acidic dykes (quartz porphyries and felsites) present, which are especially abundant in relation to the Skiddaw Slates in cells 41 and 42, where important zinc deposits lie (Thornthwaite, Threlkeld, Force Craggy. Finally, due to its almost negligible influence on the structure of the model, the negative coefficient of the Number of Fault-Contact Inter- sections may be interpreted in terms of very local features. Apparently, as with the geological model for the forecast of the number of zinc deposits per cell, this loading would indicate abnormally low values that the index 2 1 0 has in some productive cells as 6, 41, 42 and 53. (C) Combined Model The combined geochemical-geological model selected explains 100% of the variance of the response and is represented by the following equation: Y = 2773.35152-13.35574Cu+1.56026V-49.74631Ba-100.68659Ni+66.21592Li -36.99155Mo-7.07581As+84.60417Cd-1.35034Lower Limestone+1.84808Upper Limestone+0.88435Skiddaw Slates It may be seen in Table 7.15, that only the first four variables included in the model increase significantly the value of R2 , the remaining variables having been introduced in the equation to decrease the standard error of the estimate from 241.13 (57.0% of the mean response) to 0.02% (0.004% of the mean response). As may be seen from the structure coefficients, the model is mainly dominated by the weights of Ba, Mo and Upper Limestone, and in minor proportion by the loadings of Cu, Li and Lower Limestone. The significance of these parameters, as well as the local influence of Ni and Skiddaw Slates, has been discussed when dealing with the two previous models, and hence need not be discussed further. The significance of the three new indexes included (V, As, Cd), which are present with similar loadings in the geochemical model selected for the forecast of the number of zinc deposits per cell, may be interpreted thus : the low positive coefficient of V points out to relatively high concentrations of this element present in the central and northern Lake District, around cells 32, 41, 42 and 53, and to high concentrations in the Pennines around cell 49, areas that have rendered zinc output. The negative loading of As reflects the general low values that this element has through- out the area, with the exception of a small zone around cell 32. The strong weight attached to Cd needs to be interpreted with care because of its negligible influence on the structure of the model. • 2 1 1. Apparently, that loading does not reflect regional trends ( such as the favourable character of the Pennines in this respect), but points out strongly anomalous contents in this element in cells 32 and 106, both of which have been zinc-producing zones. It is worth noting that the high Cd content of the barren Silurian rocks would not render erroneous positive estimates because that content is more than counterweighted by the negative coeffic- ients attached to Cu, Ba and Ni, elements that are present in moderate to high levels in those rocks. Finally, due to the great variety of parameters included in the model, it is highly unlikely that the positive constant term would be responsible for positive estimates in any area. 7.3.4.3 Estimation of the average value of the copper reserves per deposit This production index has a mean of £111,574 and a standard deviation of £317,244 among the productive cells in the area, figures that clearly indidate the erratic nature of the value of the copper output raised in this region. The only parameters significantly correlated with this index at the 0.05 level are Silurian and Ashgill, both of which bear a coefficient of correlation of 0.998; by far, most of the geological indexes have negative coefficients of correlation with the response, a feature that is shared by many geochemical parameters. The models chosen for further use in the forecast of the value of the copper reserves existing in the area, are summarized in Table 7.17 and Figure 7.6. (A) Geochemical Model The geochemical model chosen to forecast the average value of the copper reserves per deposit explains 100% of the variance of the response, being represented by the following equation: TABLE 7.17 MODELS SELECTED FOR THE FORECAST OF THE AVERAGE VALUE•- OF THE EXPECTED COPPER RESERVES PER DEPWIT MULTIPLE R 1.0000 RSO 1.0000 STD. ERROR OF EST. 0.3332 ASO(ADJO 1.3030 ANALYSIS OF VARIANCE OF SUN OF SQUARES MEAN SQUARE f RAT/0 lEGRESSION 9 1086439.489 111826.665 1006958.672 RESIDUAL 1 0.112 0.111 WARIAILES IN EQUATION SIMUCTUFI COEFF/CILNTS • VARIABLE COEFFICIENT STO. ERROR F TO REMOVE • (CONSTANT -4134.81298 1 CU 3 43.43612 8.07775 312131.2576 . 0.145 09 4 -1.51346 0.08113 341.4847 . 0.266 BA 6 -13.61680 0.04675 84877.2927 . 0.157 CO 7 47.46777 0.07699 558614.1556 • 0.094 In 6 102.64929 0.05154 '66440.7591 . 4.172 LI 20 -42.04477 0.03673 .12630.6026 . 0.326 MO 32 19.52236 2.04171 218877.1792 . 0.403 70 14 28.46573 0.12292 53625.7350 . 0.071 CO 15 -1.42680 0.13016 120.1552 . 0.710 SUMMARY TAPLE STEP VAR/ABLE NUL7IPLE INCREASE c VALUE TO NUMBER ENTERED REMOVED RSO IN RSO ENTER OR -REMOVE 1 AO 12 .0.4235 2.1626 0.1626 1.4499 2 08/ 5 0.7052 0,4973 4.3345 3.3222 3 LI 10 3.6491 0.1200 0.2236 1 .6142 CU 3 0.9113 0.5306 2.1095 • 3.8790 5 CO 7 0.9804 146769 0.1464 31.7155 6 CD 15 0.9937 8.9875 0.0106 3.3993 7 RA 6 0.9969 1.9937 0.0092 2.9735 6 114 14 1.1101 1.7000 0.0062 323.1669 9 PR 4 1.0000 1.2000 0.0000 347.9867 (a)GEOCHEMICAL MODEL MULTIPLE R 1.0020 RIM 4,0030 STD. 0RMON OF LIT. 4.0093 RSOIAD3.1 1.0010 ANALYSIS OF vAR/ANCc OF SUM Of 500A405 mciN SnuAFT F RATIO RE6/1E6510N 9 1004.45.103 1114/6.6/6.52851112.678 89113841 1 1.534 0.900 VARIABLES IN EQUATION VARIABLE CuLFFILIENT SID. ERROR F TO R24062 STRUCIURC COEFFICIENTS (CONSTANT 60.07279 0 MICLST 4 -9.11736 0.00001 325324.4711 .0.201 UPPLST 6 -0.21943 0.33122 7,9679.7408 0.192 845E(30 6 0.53247 1.28172 121391.9513 44115 ASPOIL 8 102.2E271 4.2)254 v3,996..215 0.998 E4309014 9 -3.7224C 0.001,1 v.2727.6302 0.208 INTACI 11 1.41819 0.05073 v65244.1317 0.124 INTSCT 13 ...2.36766 4.02021 v04322.1717 0.509 LENGTH 14 ..5.:5(01 0.06.106 91441.2514 0.520 INTOAS 16 -8.29321 3.04579 v63473.42370 A.643 SUNMAAY TULE SILP VAKIAEL MULTIFLL INCRLA3L F YALU, TJ NUMELR LNTLRLD PLMOVLO K V10 IN ROO ENTEK 6, •LLNOVE ASHOIL 5 0.9963 0.9957 0.9967 26,9.4.. 93 : INT441 11 3.446'9 0.9192 0.0225 25.3394 3 80190W 9 3.9937 C.9994 0.3022 2.9169 4 INT.AS 16 1.0998 0.9996 0.0071 1.5.51 201.12/ 13 3.9999 0.9999 0.0003 12.7052 : OPALS/ 5 1.0000 0.9999 0.3131 3.1E08 7 LENGTH 14 1.04C0 0.9999 0.0464 1.2547 0 VAS,23 b 1.3001 1.0320 0.0210 1.>553 9 51031.51 4 1.3100 1.1206 0.0012 325/34.4741 (b)GEOLOGICAL HODEL MULTIPLE P 1.2700 550 1.0009 STD. ERPOR of E6T. 4.67.!7 810(004.) 1.0010 ANALYSIS OF VARIANCE OF,) SUM OF SOU4145 MEAN SOUAFE F RATIO RFS/L.:55DM 10,4440.I94 1119.6.277Z11/2164.347 RLS/DUAL 1 0.005 3.145 VARIAbLES IN EQUATION VAR/ADLE 10007101101 STU. ERROR F 70 REMLVE STRUCTURE COEFFICIENTS (CONSTANT -167.13112 ) CA 2 0.66021 0.00997 4424.16:9 0.054 80 4 7.0915(. 4.01272 21036.56.4 0.2(8 PA b 0.31996 0.0,302 1,42.2094 4.157 CO 7 3.55(19 2.01151 45127.4493 0.094 LI 10 -2.14222 3.404,2 49353.2735 0.326 AS 13 -1.37315 0.00994 128E2.70(3 0.051 BASE90 20 3.73217 0.20609 11313.1647 0.116 ASMGIL 22 116.6459/ 1.41181 *97942.3017 0.998 /61003 25 0.67473 0.0417. 154511.0143 0.124 SUhmAF) / AXE STEP 240/APLE EN.LTIILL INCREASE F VALUE TO NU.AFE.R LMTLRLD LEMOVLO R 11S0 IN ISO ENTER 00 RF.v40., 1 ASHGIL 22 3.9933 0.9467 3.9967 2679.4493 2 1472C1 25 0.9996 0.9992 0.3025 25.3394 a P3 4 3.9997 4.9455 J.0233 3.4975 4 CO 7 3.9909 0.9996 u.3231 Wihn 5 LI 14 4.9499 0.9999 0.4002 3.4375 6 .5ASLR0 20 0.9999 0.0999 0.0041 2.89.3 7 v6 13 1.0002 1.0022 0.2011 6 04 6.915, 2 1.349) 1.22J0 3.1011 5.0001 JA 6 1.4220 1.4443 0.21.0 1592.274, c)COMBINED MODEL • Forecasted average value ofcopper reserves per deposit-in£xIOOO I KEY TO SYMBOLS @ M~rethan2500 ® 1001-2500 o 501-1000 o 1-500 Blank: 0 FIG.7.6 2 1 2 Y = -4134.81298+43.43612Cu-1.51348Pb-13.61880Ba-57.46777Co+102.64929Ni -42.04477Li+19.52236Mo+28.46573Zn-1.42680Cd It may be seen in Table 7.16 that the increase in the value of R2 due to the last four variables entered (Cd, Ba, Zn, Pb) is negligible; however, these variables decrease the standard error of the estimate from 68.13 to the final value of 0.33 (61.0% and 0.2% of the mean response, respectively). As could be expected, the model as a whole reflects the preponder- ant nature of the Lake'District as the main copper-producing region in the area. This influence is mainly manifested through the very strong positive coefficients of Ni and Cu and by the loading of Mo, elements that are present in high concentrations in that region, especially in cells 32, 64 and 75, which are the areas that have rendered the highest copper outputs (the latter cell contains the Coniston District), The generally unfavour- able character of the Pennines towards copper mineralization is manifested through the very high negative coefficient of Li, and by the weights of Pb, Ba and Cd, elements normally present in high concentrations throughout that area; the loading of Li, in addition, indicates the unfavourable nature of the northernmost part of the Lake District in this respect, an area that is strongly anomalous in this element. Two elements that have little influence in the structure of the., model (Co, Zn) need to be interpreted cautiously, since in this case they do not indicate regional trends, but point out local features: the negative weight of Co reflects its low content in the Borrowdale Volcanics, as opposed to the remaining geological units that constitute the Lake District, which bear high cobalt concentrations; it must be remembered that the main copper-bearing deposits in that area lie in those volcanics. The positive loading of Zn reflects the fact already pointed out, that high contents in this element are normally found in the productiiie cells, especially around • 2 1. 3 cells 32, 36 and 75, only areas that have rendered more than £100,000 of copper ore. (B) Geological Model The geological model chosen for the forecast of the average value of the copper reserves per deposit, explains 100% of the variance of that production index, and is represented by the following equation: Y = 60.87279-0.01738Middle Limestone-0.01943Upper Limestone+0.53242Basal Conglomerates+102.88O78Ashgill-0.O2240Borrowdale Volcanics +1.41879Acid Intrusive Rocks-0.36768Number of Fault Intersections -0.05581Length of Faults-8.89326Basic Intrusive Rocks It may be seen in Table 7.16, that Ashgill accounts for most of the value of R2 because of its high correlation with the response. The remaining variables present were allowed in the equation to diminish the standard error of the estimate to its final value of 0.009. The structure coefficients of the model indicate that it is dominated by the presence of Ashgill, a parameter that bears a very high positive loading. This weight must be considered with care, since besides reflecting the minor presence of copper ores at Brygill mine in levels of this unit, it reflects the unique presence of this parameter in cell 75, which is the highest productive cell in the whole area. Therefore, the importance of this index must be regarded more as an indication of the presence of the top of the Borrowdale Volvanic Series in the vicinities, than as an indication of a favourable nature of the unit itself. The importance of the Lake District as copper-producing region is furthermore emphasized in the model by the coefficients of Acid Intrusive Rocks and Basal Conglomerates. The former weight would reflect the abund- ant minor acidic dykes present in the central and northern parts of that area, and not the main acidic bosses which until now have proven barren. The positive loading of the Basal Conglomerates indicates a local feature r 2 L4 of the Lake District: the presence of this unit in cells 31 and 32, which have had a small to intermediate copper production. The generally unfavourable character of the Pennines and of the Carboniferous rim surrounding the Lake District towards copper mineralization is manifested in the equation through the negative coefficients of the Middle and Upper Limestones and of the Basic Intrusive Rocks (Whin Sill and other similar rocks especially abundant in the Pennines). The negative coefficients of the faulting indexes included in the equation, are related to the fact that the copper-producing cells of the Pennines, which rendered a rather small output, are invariably strongly faulted, contrasting with the productive cells in the Lake District which bear only a few faults. It is worth noting in this respect that the copper production,contrasting with the lead and zinc outputs, does not have a definite relation with the amount of faulting, since even though a high number of fault intersections favoured the formation of copper deposits, the value of the output that was obtained from them was not necessarily higher than the one obtained where the faulting parameters are not especially important. A possible connection between this feature and the shifting of copper veins by faults, a fact that has been noticed in the Lake District and which may have resulted in the missing of veins at some mines, could be tentatively postulated as an explanation for that lack of definite relation. No satisfactory explanation has been found for the negative load- ing attached to the Borrowdale Volcanics. It is possible that this weight may be present in the model as a. means of counterbalancing the combined influences in some areas of the parameters previously discussed, especially the effects of the Ashgill and Coniston rocks and of the Acid Intrusive Rocks, which lacking a counterbalance would render very high positive estimates for some areas, introducing a degree of unreliability in the fore- casts and probably a bias'in the residuals. 2L3 Finally, it must be considered that the great variety of parameters included in the model, assures that positive forecasts would be unlikely to arise from the positive constant term contained in the equation. (C) Combined Model The combined geochemical-geological model chosen for further fore- casting purposes, explains 100% of the variance of the response, and is represented by the following equation: Y = -167.13110+0.66820Ga+2.09150Pb+0.31932Ba+0.65019Co-2.14620Li -1.37305As+0.732l7Basal Conglomerates+1O6.63581Ashgil1+0.16473 Acid Intrusive Rocks In Table 7.17, where the details of the model are given, it may be seen that once again most of the value of R2 is explained by Ashgill, the remaining variables being present in the model in order to decrease the standard error of the estimate to its final value of 0.07 (0.06% of the mean response). The comparison between this model and the geochemical one is another excellent example of the complex relationship operating between variables in multiple regression problems. It may be seen, that the inclusion of the geological parameters with the geochemical indexes, has called for a counterbalancing effect for the strong influence of the geo- logical indexes, and for the disappearance of Cu, Mo and Zn, effects that have been translated in a change on the sign of the coefficients of several of the geochemical indexes. The influence and physical meaning of the loading attached to Li, Basal Conglomerates, Ashgill, and Acid Intrusive Rocks, are the same as that in the two previous models, and hence need not be discussed further. The remaining parameters may be separated into two groups. On one hand, the locally influencing loadings of Ga, Co, and As, and on the other hand the more regional weights of Pb and Ba. The weights of Ga, Co 2 I 3 and As, represent the favourable nature of the Borrowdale Volcanics towards containing copper mineralization, since this unit bears high contents of Ga and Co, and average levels of As. Besides, those indexes would also point out to the favourability in this context of certain zones of the Skiddaw Slates, such as cells 31 and 32, which bear high Ga and CO and average As. The positive coefficients of Pb and Ba reflect some high concen- trations of these elements present in the Pennines in cells 37 and 71 (Ba), and 25 and 26 (Pb). It is worth noting that in the geochemical model these loadings were replaced by the strong positive weight attached to Zn. Finally, it is worth noting that the negative constant included in the model, again secures that only the anomalous areas would render positive estimates. 7.3.5 Combined Forecasting Models for Potential Base Metal Reserves In the following paragraphs, the methods employed for the forecast of the base metal reserves existing, in each of the cells in the area are discussed. The analysis is centered on the different paths that can be followed, once the estimates of the number of deposits existing in each area and the average value of their reserves has been obtained by means of the models previously indicated. The comparison between the results attained with each of the paths followed is made by examining the coefficients of correlation estimated between those results and true output figures available for the different productive cells concerned in each case. 7.3.5.1 General considerations and methods of estimation As indicated previously, three types of base metal output were considered in the present research: lead, zinc and copper. This sub- division was made with the idea that the design of a model that could accurately forecast the total potential reserves of the area was unlikely to be successful because of the intricate relationship existing between • 2• 7 the different types of product obtained at each mine, a relationship that does not only depend on the geological characteristics of the deposits worked, but is also dependent on other factors difficult to quantify. A typical factor of the latter kind is the state of metals market at any one time, which would render economic the beneficiation of certain type(s) of ore and uneconomic the treatment of other type(s) which may have been mined due to the characteristics of the deposit and mining methods; in this latter case, the by-product ores were discarded and thus were not considered in the statistics of production. Once the forecasts for the number of potential deposits and average value of their reserves was determined for each metal in each cell, two paths - each of which include several alterantives - can be followed to estimate the potential value of the total reserves of each kind existing in the cells: (1) The two estimates can be simply multiplied or (2) An equation relating those parameters to the total production can be determined for the whole area by means of multiple linear regression, thus obtaining weights for each output index, which would be applied to the respective forecasts for each cell. In the present research, an investigation was performed on the advantages of using one or other method, the final results obtained in each case being compared with the actual production figures available. The correlation coefficients obtained for the different models designed are summarized in Table 7.18. As may be seen in Table 7.18, much better results were obtained with the regressed forecasts than with those attained by simple multipli- cation of the indexes. This fact is valid for all the models designed, indicating the need for a certain differential weight to be applied to the estimated indexes, a loading that is a direct consequence of the varying influence that those indeXes have on the total output. TABLE 7.18 COEFFICIENTS OF CORRELATION BETWEEN ACTUAL OUTPUT FIGURES AND FORECASTS BASED ON SIMPLE MULTIPLICATION OR MULTIPLE REGRESSION OF ESTIMATES OF OUTPUT INDEXES LEAD OUTPUT ZINC OUTPUT COPPER OUTPUT Combined Geochem. Geol. Combined Geochem. Geol. Combined Geochem. Geol. Model Model Model Model Model Model Model Model Model Simple Multiplication 0.603 0.509 0.014 0.287 0.676 0.261 0.757 0.973 0.757 Mutliple Regression 0.825 0.569 0.489 0.989 0.814 0.985 0.993 1.000 1.000 TABLE 7.19 COEFFICIENTS OF CORRELATION BETWEEN ACTUAL OUTPUT FIGURES AND FORECASTS OBTAINED BY MULTIPLE REGRESSION OF ESTIMATES OF OUTPUT INDEXES Alternative LEAD OUTPUT ZINC OUTPUT COPPER OUTPUT Combined Geochem. Geol. Combined Geochem. Geol. Combined Geochem. Geol. Model Model Model Model Model Model Model Model Model (1) 0.825 0.569 0.489 0.989 0.814 0.985 0.993 1.000 1.000 (2) 0.838 0.584 0.518 I 0.989 0.864 0.998 0.993 1.000 1.000 '2 38 Once the foregoing alternative was decided upon, two possible paths were investigated in similar fashion, in order to assess the best procedure to follow when negative estimates of the output indexes were obtained with the models discussed in sections 7.3.3 and 7.3.4. The alternatives examined were the following: (1) Simple regression or Forecast = A+B E(Av.Value)+B E(No.Dep.) 1 2 (2) Simple regression and Forecast = 0 if E(Av.Value) or E(No.Dep.) = 0 The correlation coefficients obtained by comparing the results of each alternative with the actual production figures, are summarized in Table 7.19. It may be seen that, however similar the coefficients may be, it appears desirable to consider a null forecast when negative estimates of the output indexes are obtained (alternative 2). Therefore in the following discussion on the potential reserves that may be forecasted for each metal in each cell, the forecast was considered to be zero whenever the estimated output indexes were equal or less than zero. 7.3.5.2 Potential lead reserves The estimation of these reserves was done according to the following equation: Y = -3633.53161+963.17030Number of Deposits per Cell+5.84509Average Value of Reserves per Deposit In actual output figures, this model accounts for 80.35% of the variance of the total lead otuput; the relationship between the fore- casts obtained and the total actual figures of production is that of Table 7.19 (alternative 2). It may be seen how the equation greatly stresses the importance of the estimated number of deposits with respect to the estimated average value of their reserves, an index which has a low weight and also a low influence in the structure of the equation. An average productive cell in the area would have a forecast of £3,878,664, as opposed to a forecast of £4,343,305 obtainable by simple multiplication of the mean indexes. Considering that the average production of the lead productive cells in the area is about £6,553,000, it may be concluded that the forecasts obtained by applying the indicated weights are very conservative, rendering estimates that are on average 41% below the actual mean production. The coefficients of correlation between the selected indexes and the total output figures are 0.765 for the Number of Deposits and 0.630 for the Average Value of Reserves. These coefficients point to the known fact that the lead production in the area was in general dominated by a large number of medium to small sized operations, rather than by a few large mines. Thus, the structure of the model is dominated by the number of deposits existing in each cell, a feature that reinforces the convenience of using indirect output indexes for the estimation of reserves, over the use of global production figures. The estimated potential lead reserves for each cell are summarized in Table 7.20 for the combined, geochemical and geological models designed. Figure 7.7 graphically represents the forecasts, subdivided into selected categories according to their value. It is worth noting that more than half of the cells bear zero estimates, and that in general the forecasts obtained with the combined model are somewhat higher than those obtained with the other two models. 7.3.5.3 Potential zinc reserves The potential zinc reserves existing in each cell were estimated according to the following expression: Y = -1147.80625+828.07310Number of Deposits per Cell+1.15055 Average Value of Reserves per Deposit Considering the actual output figures available, this model accounts for 97.84% of the variance of the total zinc output. The amount of that variance explained by each of the models designed, is given in 0 GEOCHEMICAL MODEL ~ ~ @ @) @@ 0 rJ ~' 0 ~ @ @!0 (I @> _(@l~l~~ __ - KEY TO SYMBOLS - tz- 010i@i@ 0'@1@1@ /0 0 I 010 @ @) Morethan10,OOO ( 0 !®I @)I@ @ ®>10 @)500l-10,OOO @ 1\ iC®l®!@ 01001~OO ~ 0i0~@!@' ~_=- I o 1-1000 !\ 1~ II. /J o 00 -~r ~'0(( @ Blank:O 'WI )i~ @ GEOLOGICAL MODEL ·1 FIG.Z7 Table 7.19 (alternative 2). It may be seen how the importance of the number of deposits is also stressed in this case, with respect to the average value of their reserves, an index which has a very low loading. An average productive cell would render an estimate of £636,784, as opposed to a forecast of £1,068,527 which would be obtained by giving equal loadings to both output indexes. Thus, the forecasts obtained with this model would be on c. the lower side of the mean output, since they would render estimates that are on average 45% lower than the actual average production figures of the productive cells in the area. The Number of Deposits per Cell has a correlation coefficient of 0.952 with the total zinc output, as compared to a coefficient of 0.408 of the Average Value of the Reserves. These coefficients stress even more than in the case of lead, the fact that the production of zinc in the area has been dominated by a large number of mines, few of which produced important amounts of this type of ore (only at Nenthead and Thornthwaite the value of the output exceeded Elm). The forecasted potential zinc reserves for each cell are summarized in Table 7.20 for the different models designed and are graphically represented in Figure 7.8. It is worth noting that even though a large number of cells bear a zero estimate, those with positive forecasts vary between 27 and 52, figures that greatly superate the actual number of producive cells in the area (13). Also worth noting is that the estimates obtained in this case, are higher for-the geological model than those obtained with the combined or geochemical models. 7.3.5.4 Potential copper reserves The potential copper reserves were forecasted for each cell according to the following equation; GEOCHEMICAL MODEL KEY TO SYM QLS @ More than10,000 @SOOl-10,OOO 01001-5000 o 1-1000 Blank:O FIG.Z8 22 1 Y = -34.29393+25.07606Number of Deposits per Cell+1.98552Average Value of the Reserves per Deposit In real production terms, this model explains 99.97% of the variance of the total copper output,the amounts of that variance explained by each of the models designed being indicated in Table 7.19 (alternative 2). An average productive cell would render an estimate of £221,538, as opposed to £181,865 that would be obtained by simple multiplication of the individual output indexes. Considering that the average copper output in the productive cells of the area is £228,272, it may be concluded that the model would render estimates fairly similar to the actual production figures, those estimates being on average only 4% lower than the mean production values. The model used for forecasting the copper reserves differs widely from those used for the forecast of the other two base metals considered. In this model, whichever the apparent importance of the indexes could be, the value of the Average Value of the Reserves per Deposit is more import- ant than that of the Number of Deposits per Cell, a feature that arises from their respective correlation coefficients with the total copper out- put (0.999 and 0.226, respectively). This fact points out that the copper production in the area, as opposed to the lead and zinc outputs, has not been dominated by a large number of mines, each producing minor amounts of ore, but that it has been mainly carried out at a few places which rendered substantial amounts of ore (in relative terms). It must be noticed in this respect, that of the 11 copper-productive cells in the area, 6 rendered output from only one mine, 3 from two mines and 2 from three mines. This feature suggests the scattered nature of the concentrations of copper ore in the studied area. The potential copper reserves estimated for each cell are summarized in Table 7.20 for each of the forecasting models designed. Figure 7.9 is KEY TOSYMBOLS @) More than2500 @1001-2500 o 501-1000 o 1-500 Blank:O FIG.7.9 2 22 a graphical representation of those forecasts, subdivided into selected value categories. It may be seen how a large number of cells bear zero estimates, a situation especially noticeable in the case of the geochemical model. However, the number of cells with positive estimates largely exceeds the actual number of productive cells in the area (11). Also worth noting is the fact that the estimates obtained with the combined model are generally higher than those attained with the other two models. 7.4 DISCUSSION OF RESULTS 7.4.1 General Considerations In the following paragraphs, a review is made of the results - attained by means of multiple linear regression for the forecast of potential base metal reserves in Northern England. The results obtained by converg-' ent regression of selected output indexes are evaluated in general terms, in order to assess the validity of the forecasting technique employed. The significance of individual results is not discussed in this,section, that aspect being dealt with in Chapter 8, where the whole forecasting procedure is evaluated and compared with other forecasting methods.- When analyzing the results obtained in section 7.3.5, which are summarized in Table 7.20, it must be remembered that they were obtained following a convergent regression path that considered the estimation of the potential number of deposits existing in each cell and of the average value of the reserves contained in those deposits, estimates whidh were combined by the application of statistically significant weights obtained from actual production figures. These last estimates were accepted (or entertained) as significant forecasts, which explain varying amounts of the variance of the respective responses (lead, zinc, or copper production). In order to assess the validity of this converging method, its results were compared with those which may be achieved by straightforward TABLE 7.20 FORECASTLD EASE METAL POTENTIAL RE!',ERVES (IN POUNDS X 1000)-NCRTHERN ENGLAND ESTIVATIUN EASED ON MULTIPLt:. R,:.GR":SSION OF PRODUCTION INJEXES LEAD RESERVES _ ZINC PiSEkVES COPPER .6St.RVES CELL: CMBND. GEOCH• GEOL- CMBNO. GEOCH GFOL. OMEN°. GcOCH. GEOL. MODE MODEL MODEL MODEL MODEL MODEL MOCE MODE MOOLL i 0 o 0 0 104 2 0 0 o o 0 201 3 0 a 523 4 0 55520 0a o a0 0 5 0 9712 5933 0 4430 0 6 0 6435 1181 1193 0 0 7 385 0 8777 491 0 0 5 0 8- 0 4927 0 0 8345 0 331 0 0 106 10 0 0 0 11 0 0 6734 0 0 49 12 a 0 a 0, 64 1T 0a 4539 0 o 0 a 14 0 15960 0 0 12793 0 15 892 7251 13755 3016 ';F,03 6232 0 16' 355 7112 5188 7293 5777 0 0 17 427 16401 2060 1633 0 0 0 18 2491 0 0 0 0 0 19 0 0 0 16069 0 0 20- 0 0 0 56330 0 0 21 0 0 0 2345 8 0 0 22- 0 0 5397 16293 0 - 0 23 0 0 0 4611 0 0 24 1111 0 12476 4512 9330 2311 0 25 3952 20124 15992 11403 11354 11524 0 26 3368 20314 16063 2807 2806 2634 0 27 2178 16399 14616 3066 0 3828 0 28 129 5244 0 0 0 29" a o 0o 0 0 a 30- 0 3844 0 0 0 0 31- 0 4411 0 0 0 0 32 255 4560 5629 1375 1353 0 16 0 33 0 7233 8541 16544 0 0 34 0 0 0 1996 0 iv* 35 1941 2281 0 20810 0 0 36 2426 22176 10144 0 0 0 6 11 0 37 1561 10508 11456 539 534 0 0 33' 1631 15604 12443 5312 0 3289 0 39 975 13363 3335 2421 34034 0 6 0 43 4559 0 0 0 0 0 41 o 0 737 756 1102 3 3 59 42 5542 0 2223 2225 1415 0 43 0 0 3761 0 0 143 0 65 44 4231 971 0 173 0 353 148 333 45 0 902 8537 2491 1513 0 0 93 46 0 0 0 0 0 0 0 3353 47 8953 D 0 0 0 0 0 3980 48 771 7635 0 0 0 0 0 0 0 49 17663 6564 47 47 0 0 0 0 50 130 5857 35 0 0 0 0 0 0 51 337 993 3361 0 0 0 0 0 0 52 4315 0 0 0 22106 497 620 1252 53 1079 0 14019 0 0 0 0 28 0 54 2332 16806 0 0 4645 0 0 0 0 55 2662 0 0 0 6450 0 0 0 0 56 6065 11058 0 0 0 276 1265 219 57 0 9023 8295 9762 3548 0 0 66 56 0 0 10622 0 0 0 0 471 59' 356 0 10497 0 0 1234 0 0 0 60 37 10154 4944 6916 880 0 0 0 61 0 3922 7543 0 0 0 0 0 62 0 0 .0 0 0 0 0 25 63 0 0 0 0 19200 532 296 1494 64 1503 5775 0 0 0 0 0 51 0 65 1343 10493 6436 0 0 0 5083 878 4946 66 276 0 0 0 0 0 921 5019 67 . 0 0 0 0 0 1176 0 1249 68' 0 0 0 0 0 0 0 191 69 0 0 0 0 0 0 0 107 70 842 10156 11087 0 0 0 0 71 0 71 1207 4453 13477 0 0 0 0 0 0 72 836 5699 15009 4765 0 2280 0 0 0 73 0 0 0 0 0 0 0 156 74 0 0 0 0 39144 941 0 2479 75 4111 0 0 0 0 2130 2133 2084 76 0 0 0 0 0 902 0 302 77 0 0 0 0 0 0 3557 109 © 0 2717 123 a 8 8 8 0 0 0 2585 5621 BO 0 4485 5312 0 0 0 142 6477 81 0 1048 3584 0 0 0 0 0 82 996 10444 7439 1694 41263 0 0 0 0 83 401 7236 9566 0 0 0 58 0 0 84 6726 0 0 0 0 3625 0 3643 85 0 0 0 0 0 0 3097 1512 86 0 0 0 0 0 0 2750 106 57 0 0 0 0 0 0 2476 116 BS 0 0 0 0 0 0 2133 96 89 0 0 0 0 0 0 0 1140 90 900 3599 2995 7831 0 0 0 , 80 140 91 650 1314 0 7560 0 0 0 ' 0 13o 92 0 3246 8013 0 0 0 0 146 93 0 2420 8235 16725 0 0 0 0 94 0 2478 5071 0 0 0 0 0 96 0 0 0 0 0 0 0 0 97 1152 0 0 0 0 0 0 1070 95 2649 0 0 0 0 0 172 637 99 0 0 0 0 0 0 110 238 100 3442 14206 4026 0 7183 0 561 0 101 0 12930 3531 0 3573 3 0 0 102 0 0 0 21711 0 0 0 0 103 0 0 0 0 0 0 0 0 104 2722 0 0 0 0 0 1025 14 105 11890 0 0 0 0 0 0 166 106 2556 19939 8046 3 Q 0 14 14 14 regression of the different geological and geochemical parameters, against the actual production figures available for each metal. The comparison between both types of result was mainly focussed on the amounts of variance of the actual production figures explained by them, and on the value of the standard error of their estimates, parameters that give a good evaluation of the forecasts, as related to the real production obtained in the different areas. 7.4.2 Direct Forecast of Lead Reserves The multiple regression of the selected geochemical and geological variables against the total lead output, variable that has a mean of £6,553,710 and a standard deviation of £13,306,956 among the productive cells of the area, rendered the following models: (A) Geochemical Model Y = -15188.78124-943.68332Cu+873.77281Pb-569.53284Ba+932.23061Li (B) Geological Model Y = 2333.11886-21.94132Millstone Grit+23.91924Upper Limestone (C) Combined Model Y = -4481.66279+1155.00434Ga-1287.86075Cu+611.31191Pb-511.34569Ba +1483.65306Co-1878.07096Ni-1736.65226Mn+2331.93461Li+1087.31671Mo -932.31061As-611.09511Permian-23.67857Millstone Grit+1218.90665 Ashgill-30.78147Skiddaw Slates+533.79O34Number of Fault Inter- sections-52.53598Length of Faults Details of these models are given in Table 7.21, where the param- eters that allow their interpretation in similar terms as those previously used, are fully displayed. It is worth noting the resemblance between these models and those indicated in Section 7.3.5, in the sense that similar positive or negative weights are attached in both cases to many of the variables, a feature especially evident for the geochemical components of TABLE 7.21 SELECTED MODELS FOR THE DIRECT FORECAST OF LEAD RESERVES MUL(1PLc A 9.01E9 Rsn 0.3801 STO. 4.K.604 IF t.al. 11499.1796 R19(443.) 0.1960 ANALYSIS OF VmM144Lc 040N SCUAKE F RATIO OF son or AUAKLs K,G1.-lon • e499.3)159.701 /9"db 6.097 aLs.LWAL 33 40/4736769.112 122992083.609 84.1.166/L6 IN EQUATION • VAXAAUL. CV/FE...ILO S TO. 4.11tOnt F TB RON .1..... STRUCTURE COFFFICIFHTS • I . . - . (.0140001 •3198.78124 ) . 0.377 LI) 3 -943.61331: 42/.4,145 0.6222 • Fl. 4 073.(7.11 .0.4 39426 ....117.7 • 0.559 ult 6 ..669.63244 565.61906 4.6117 . 0.369 0.390 L1 Iv 932. Cii 61 359. 8415. 0.721. . ... 5UNNAR3 TA6LE STEP VARIA611 NULT If LE INCRE A SC F VALuE 10 Min tiLR 0.3,4.0 it.MuVE.D R RSO IN •RS9 ENTER OR RLMUVL • Pu 4 0.3450 0.1190 0.1190 4.9629 2 bit 6 0.4929 0.2450 0.1264 5.7410 3 L1 i0 3. 6353 4.2S62 J.0455 2.06.2 • CU 3 J•6169 6.3505 ..6943 5. o .32 (a)GEOMENICAL MODEL MULTIPLE A - 0.4961 PS0 D. 241 2 STD. ERROR OF EST. 11879.2171 RSO (ADJ. ) .7.2/11 -- ANALYSIS OF VARIANCE • OF SUM OF SQUARES MEAN SQUARE F RATIO REGRESSION 2 1612724953.319 806362476.660 5.714 RESIDUAL 35 4939052964.496 1411/6798.986 VARIADLES IN EQUATION VARIABLE COEFFICIENT STD. ERROR F TO REMCVE STA UCTU92 CO. FFIC. :N71 (CONSTANT 2333.11886 ) KILSIN 5 -21.94132 11.90901 3.3944 . 0.272 UOPLST 6 23.91924 7.35296 10.5671 6.935 SUMMARY TABLE STEP VARIABLE MULTIPLE NUMBER INCREASE F VALUE TO ENTERED REMOVED R RSO IN 211 ENTER OR REMOVE UPPLST 6 0.4160 0.1730 2 0.1730 7.5329 MILSIN 5 0.4961 0.2462 0.0731 3.4944 (b)GEOLOGICAL MODEL MULTIPLE R 0.9056 RSO 0.6833 STD. ERROR OF 1ST. 7490.2247 RSQ(ADJ.) 0.8202 ANALYSIS OF VARIANCE OF SUM OF SQUARES MEAN SQUARE F RATIO REGRESSION 16 5373605/26.598 33585)320.412 5.486 RESIDUAL 21 1178172791.217 56103466.248 VARIABLES IN EQUATION VARIABLE COEFFICIENT STD. ERROR F TO REMOVE STRUCTURE COEFFICIENTS (CONSTANT -4461.66279 ) . CA 2 1155.00434 502.74083 5.2779 0.036 CU 3 ■1267.86075 669.58071 3.6994 0.229 PO 4 611.31191 333.00174 3.3700 8.380 BA 6 •511 34569 257.05773 3.9570 0.251 CO 7 1483.65306 613.59825 3.3230 0.047 NI 8 .4878.07096 796.23982 5.5633 0.928 MN 9 -1736.65226 491.45065 12.4872 0.032 LI 10 2331.93461 411.20979 32.1592 0.266 NO 12 1047.31671 431.41939 6.3520 0.126 AS 13 -932.31061 403.97137 5.3262 0.147 PERRIN 17 -611.99511 /95.69350 9.9013 0.115 Mf LSTN 19 ■23.67857 10.93436 4.6695 0.149 ASHGIL 25 /210.90665 593.36074 4.2199 0.092 SKIOAN 27 ■30.76147 11.33043 7.3805 0.236 INTSCT 31 533.79034 137.29525 15.1155 0.151 LENGTH 32 52.53596 14.65115 12.5579 0.133 SUMMARY TABLE STEP VARIABLE MULTIPLE INCRZA SE F VALUE NUMBER ENTERED REMOVED R RIO IN RSO ENTER OR REMOVE 1 PR 4 0. 3450 0.1190 0.1190 4. 8629 5. 7310 2 BA 6 0.4929 0.2430 0.1240 3 INTSCT 31 0.5592 0.3127 O. 0698 3. 4523 AS 13 0.6107 0.3730 0.0602 3.1696 4 2. 7982 5 NILSEN 19 0.6507 0.4234 0.0504 6 LI 10 0.6675 0.4727 O. 0493 2. 5985 0.7770 0.6035 0.1311 9. 9237 7 SISIOAH 27 1.7711 6 NO 12 0.7916 0.6266 0.0226 9 MN 9 0.8061 0.6495 0.0232 1. 5577 10 LENGTH 32 0.8196 0.6717 0. 5219 1. 8042 11 PER0404 17 0.8381 0.7025 0.0307 2.6565 12 GA 0 0.8474 0.7181 O. 0157 1. 3882 13 CU 3 0.8681 0.7536 O. 0355 3.4535 14 ASHG IL 25 0.8753 0.7714 O. 0178 1. 7955 15 NI a 0.8898 0.7917 0.0203 2.1421 16 CO 7 0.9056 0.0202 O. 0785 3.3230 (c)COMBINED MODEL 2 2 4 the combined model . In Table 7.22, a comparison is made between the results achieved with these equations and those obtained by convergent regression, for the three kinds of models designed. It may be seen how the results of the convergent models are systematically better than those obtained by direct regression, except for the R2 of the combined model which has a higher value in the latter case, though its standard error is higher. These results indicate that the regression technique employed in the present research, which makes use of indirect production indexes in an attempt to localize the forecasts, is a valid and significant way of fore- casting lead reserves. Moreover, it may be concluded that, in this case, the use of combined geochemical-geological indexes greatly improves the estimates, more than doubling the amount of variance of the total lead out- put explained and halving their mean quadratic deviation (standard error). It is also worth noting, that in all cases the geochemical models rendered better results than the geological ones, explaining a higher proportion of the variance of the response with a lower standard error. In this respect it is worth remembering that the value of R2 used in the comparison is independent of the number of variables present in each of the original models, since it reflects a degree of correlation between the forecasts and actual production figures, the forecasts being,in all cases, obtained from the regression of the two production indexes against the total lead output figures available. 7.4.3 Direct Forecast of Zinc Reserves The multiple linear regression of the total zinc output, variable with a mean of £1,440,153 and a standard deviation of £3,203,520, against the selected geochemical and geological parameters,gave the following best equations: '4 TABLE 7.22 COMPARISON BETWEEN SIMPLE AND CONVERGENT REGRESSIONS FOR THE FORECAST OF LEAD RESERVES (Standard Error as % of mean response, R2 as percentage of variance explained) Combined Model Geochemical Model Geological Model R2 St.Error R2 St.Error R2 St.Error Simple 78.9 5.8 30.5 9.2 24.6 14.0 Convergent 71.4 1.5 37.4 7.1 26.1° 7.8 TABLE 7.24 COMPARISON BETWEEN SIMPLE AND CONVERGENT REGRESSIONS FOR THE FORECAST OF ZINC RESERVES (Standard Error as % of mean response, R2 as percentage of variance explained) Combined Model Geochemical Model Geological Model R2 St.Error R2 St.Error R2 St.Error Simple 95.2 3.3 86.4 1.7 98.9 76.1 Convergent 98.4 8.4 98.4 8.4 98.0 TABLE 7.26 COMPARISON BETWEEN SIMPLE AND CONVERGENT REGRESSIONS FOR THE FORECAST OF COPPER RESERVES (standard Error as % of mean response, R2 as percentage of variance explained) Combined Model GeoChemical Model Geological Model R2 St.Error R2 St.Error R2 St.Error Simple 100.0 0.0 100.0 10.0 100.0 0.0 Convergent 98.6 391.2 100.0 0.0 100.0 0.0 TABLE 7.27 TOTAL POTENTIAL RESERVES AS FORECASTED BY SIMPLE AND CONVERGENT REGRESSION MEANS (R2 as percentage) Combined Model Geochemical Model Geological Model R2 T-value R2 T-value R2 T-value Simple 33.6 1.049 32.0 . 0.481 26.3 0.214 Convergent 77.2 0.624 37.6 0.390 32.1 0.261 E.4, 4 0.1 0.1 (A) Geochemical Model Y = -19681.99178-1498.46211Fe+395.37271Pb+157.37318V+758.90654Ba +91.77878Co+681.53771Ni+2866.19392Mn-1378.48237Mo-1358.46887As -6047.18470Zn+8410.50428Cd (B) Geological Model Y = 5110.37452-9.13967Millstone Grit+7.010510Upper Limestone +20.59971Acid Intrusive Rocks+125.91074Number of Fault Inter- sections-19.76717Length of Faults (C) Combined Model Y = 31795.88037+91.78461Fe-782.40855Pb+174.68533V-339.43469Ba -768.31171Co+1060.73636Ni-126.20569Coal Measures+34.03047 Lower Limestone+14.03938Middle Limestone+11.64175Upper Limettone -5.98259Length of Faults Details of these models are given in Table 7.23. It may be seen how the variables included in these models and their weights, are fairly similar to those present in the equations designed for the estimation of the individual indexes of zinc output; especially striking is the similarity between the geochemical and geological models and those for the forecast of the number of zinc deposits per cell. This feature confirms the conclusion attained in Section 7.3.5.3, where the importance -of the number of deposits as a controlling factor of the zinc output was evident. A comparison between the results attained using the total zinc output as response, and the ones obtained by convergent regression, is made in Table 7.24. Two points are worth noting from that table: (1) The coefficients of correlation between. the forecasts and the response, are higher for the convergent models, with the exception of the geological one which is marginally lower in the former case; (2) The standard errors of the estimates are lower for the models built with total output as response, excepting the geological model which has a markedly lower error in the 0 TABLE 7.23 SEGF.CTED MODELS FOR THE DIRECT FORECAST OF ZINC RESERVES •-- WILTIELP P 1.0001 run 1.4000 51.O. F0711P OF r.57. 2'1.0835 RSOTA9J.) 1.0000 ANALYSIS OF VARIANCE n7 non Or snun7-1 MEAN SONAR.: F R1TIO PECIESSION 11 123149497.509 1111 +444.774 17'13.6,6 RESIDUAL 1 629.184 629.194 8441491AS IN EQUATION VARIABLE C0:FF=3M STO. ERROR F TO REMOVE STRUCTURE COEFFICIENTS !CONSTANT .9641.901'. 1 PE 1 ■1419.48211 1.2.39111 1 4647. 7211. 8.008 09 4 145, -.7271 t6.359', 58/. 140, 7 0.045 V 5 157.37418 17.78169 151.9961 0.159 94 6 758.11994 6.39 746 14475.5049 8.575 CO 7 91,77978 8.94267 107. 7253 8.122 NT 8 641.9,771 16.9,525 1629. 163 7 0.224 MN 4 2864.19312 16.75641 29751.1165 0.016 MO 12 -1374.44'37 9.11949 32948.677 1 0.285 AS 17 ..1398..5117 /6.04311 7205. 1/59 0.236 TN 14 -6C+.7.17•40 34.73875 30303. 5573 4.150 CS 15 443 J. 5j420 45.53937 34034. 1671 0.071 SW/NARY TAPLE STEP VAQ/A9L 9 MULTIPLE ENPR-.4R7 F VA LOS 19 NU59ER ENT:423 REMC09.9 RS1 TN RS1 :NTSR OR R11001 1 57 6 0.5747 0.7311 9.3393 9. 4357 2 co 7 2.9918 9.3593 3.2149 9.3061 3 NI 4 0.9141 2.6530 0. 39 77 7.39'5 4 RN 9 0. 4457 0.'545 3.1316 4.8943 5 V 3 0.4'194 0.7150 0.0154 0.2154 6 01 15 3.9945 0.90'1 1.0392 9.2756 7 IN 14 0. 9704 0. 0107 0.0105 V. 279r 8 .40 12 0.9989 20251 9. 0155 0.3550 9 MN 9 0. 9'89 9.8260 -9.•3911 0.9224 /0 on 4 0. 5174 2.5.0 , 1.1157 5.3326 11 914 9 0.9422 00877 .0460 1.2294 57 el: 1 0.9314 9.9532 0. 9755 4.0999 13 17 13 1.1909 1.0371 2.2159 7318. 1119 (a)GEOCHEMICAL MODEL MULTIPLI R 0.9654 RS9 0.9119 STO. cktu.,, OF c:T. 1094.4514 RSO(AOJ.) 0.8033 ANALYSIS OF VAR' nPCF OF SON OF s4J,0L, 11774 34UAFt F RATIO RL6R.S500N 5 114765691.5'-9 22901/1e. 225 19.162 KESIDUAL 7 8334920.1.7 1157146.724 VAPIAOLLS 340 L °OAT INN VAP/ A Olt CC -FFICILNT bT9. ER.COR F TO 41119E STRO67URF COEFFICIENTS (CONSTANT 6119.37492 ) 4.2 4.72.9 MILSTN 3 ..9.13467 3197 0.254 UPPLST 6 7..011 1.61393 13.4399 0.256 INTACT 9 20.54971 11.66163 3.9023 0.255 /HTSCT 11 12,.91074 19.21253 42.9.1 4 0.323 LENGTH 12 •19./9727 2.43351 69.9317 0.523 SUMMAPY TARLC STEP VAPJAILL MOLTTILL INCR1 ASS F INALU9 Tu MASER ENTL9...2 re MOULD k 550 IN ?SO 3917,2 OF' P4330E. 1 LENGTH 12 3.5048 0.2549 6.2943 3,7612 2 IN MT 11 0.9662 0.7503 0. 4956 19.9464 3 UPPLST 6 1.9322 0.3509 0.1156 8.1449 4 .11L2116 3 3.94.) 5.6949 0.0263 1.5731 9 INTACT 9 3,9'.^4 0.9313 1.3371 .31 33 (b)GEOLOGICAL MODEL • MULTIPLE R 1.0005 RSO 1.0000 STO. ERROR OF EST. 49.7389 RS9(403.1 1.0000 ANALYSIS OF VARIANCE -I OF SUM OF MAPES MEAN SQUARE F RATIO REGRESSION 11 123148047.736 11195277.067 4525.252 RESIDUAL 1 . 2473. 956 2473.956 VARIABLES IN EQUATION VARIABLE COEFFICIENT STD. ERROR F TO REMOVE STRUCTURE COEFFICIENTS (CONSTANT 31795.88037 ) FE I 91.71461 8.44609 118.0940 0.008 PEI 4 -782.40855 10.36486 5698.2334 0.045 V 5 174.60533 8.29281 443. 7220 1.159 BA 6 .339.41469 4.83992 4916.5327 0.575 CO 7 -7613.31171 13.26358 3355.4699 0.022 NT 6 1160.73636 17.76146 3566.6280 0.224 COALNS 16 -126.20569 2.27319 2405.5515 0.061 LOWLST la 34.03047 0.55344 3780.8448 0.181 mIDLST 19 14.03938 0.28670 2398.0061 0.166 UPPLST 20 11.64175 0. 2090 9 2582.4345 0.748 LENGTH 26 -5.98259 1.19875 906.1859 0.502 SUMMARY TABLE STEP VARIABLE MULTIPLE INCREASE F NUNREP VALUE TO ENTERED REMOVED R RSO IN RSQ ENTER OR REMOVE 1 BA 6 4.5747 0.3303 O. 3303 5 4258 2 MIDI. ST 19 0.6462 0.4176 0.0873 3 LENGTH 26 1.4987 0.7120 0.5070 0. 0594 1.6317 4 COALMS 16 0.7731 0.6978 5 0. 0908 1.8052 V 5 0.8145 0.6634 0.0656 6 P9 4 1.3646 0.0535 0.7285 0. 0651 1.4385 7 100112 10 0.8732 0.7625 0.0340 0.7164 e FE 1 0.9002 0.8104 0.0479 9 UPPLST 20 1.0116 0.9615 0.9245 0. 1141 4.5344 10 NI 8 0. 9657 11 0.9326 0. 00 50 0.2317 CO 7 3. 0.0674 (0 ).... HOE 1..-INED MobEL 3155.4699 i convergent model. *.■ , e.." Since no systematic differente- may be distinguished between both types of model, the analysis of the results must be performed taking into account the relative importance of the statistics obtained. On one hand, it may be observed that the amount of variance explained is very high in all cases, varying the respective values between less than 1% and 12%. On the other hand, the standard error of the estimates are low in all cases, with the exception of the direct geological model, the differences of the most significant values varying between 5 and 6%. In the opinion of the author, the observed differences are in most cases so marginal that the indistinctive use of either type of model would render similarly significant regional results. However, the use of convergent regressive means appears to be desirable, if results with full local significance are wanted, since the zinc production in the area is highly dependent on the number of deposits worked, a feature that can only be assessed and weighted by indirect forecasting methods. Therefore, in the final evaluation of multiple linear regression as a means of forecasting base metal mineral- ization, the results obtained by indirect methods are preferred to those attained by straightforward regression of total zinc production figures. 7.4.4 Direct Forecast of Copper Reserves The following models were obtained by multiple regression of the selected geochemical and geological parameters against the total copper output, a parameter that - among the productive cells of the area - has a mean of £228,272 and a standard deviation of £634,284: (A) Geochemical Model Y = -8619.86129Cu-30.34078Ba-122.75012Co+206.87180Ni-78.80164Li +42.92621Mo+54.81425Zn ti 7 (B) Geological Model Y = 80.85680+0.09508Middle Limestone+209.24999Ashgill+1.05257Acid Intrusive Rocks+0.07572Length of Faults-81.54923Number of Fault Intersections (C) Combined Model Y = -308.13212-0.94658Ga+5.06637Pb+3.34956Co+1.24983Mo-4.48959Cd +218.07560Ashgill+1.19017Acid Intrusive Rocks-0.04866Number of Fault Intersections+0.09208Length of Faults Details of these models are given in 'Table 7.25. Comparing the variables and loadings present in these models with those of the equations selected for the forecast of the individual copper production indexes, it may be seen that there is a strong resemblance between these and the expressions chosen to estimate the average value of the copper reserves per deposit, a feature that is strongly evident when comparing the respect- ive geochemical mdoels. This fact confirms the conclusion attained in Section 7.3.5.4, where it was considered that, regarding copper output, the average value of the production of the depotits existing within a cell, was more important for forecasting purposes than the number of deposits worked in that cell. A comparison between the results attained by direct regression of the total copper output and those obtained by convergent means, is done in Table 7.26, where it may be seen that the amount of variance of the actual copper output explained by the models is in all cases higher than 98%, and that, excepting the combined model, the standard error of the estimates of the convergent models are lower than those of the direct regression, the differences ranging from 4% to 10%. Three points may be concluded from the comparison. Firstly, the use of either type of geological model would render fairly similar results, since the difference in the standard error of the estimates is not great TA4LE 7.25 SELECTED MODELS FOR THE DIRECT FORECAST OF COPPER RESERVES . _. . - - mainvir. P 0.9997 inn 0.3395 STO. ERROR OF EST. 26.5933 RSICADJ.1 0.9984 ANALYSIS OF VARIANCE OF SUM OF SIUAPES 4004 SIUARC F RATIO PFGRESSION 7 4021 150.572 574435.796 812.264 RESIDUIL 3 2121.610 701.293 . VARIAILES IN EQUATION VARIABLE COEFFICIENT STI. ERROR F TO REMOVE STRUCTURE COEFFICIENTS (CONSTANT •6619.86129 ) CU 3 89.58554 3.04758 864.1007 0,139 RA 6 -30.34078 3.19459 90.2035 0.163 CO 7 -122.75012 4.32741 804.6161 0.103 NI 8 254.47140 3.54195 3411.2740 0.173 LI 10 -76.55164 2.89475 741.9922 0.312 MO 12 . 42.92521 2.45044 306.7639 0.411 25 14 54.81425 4.48866 149.1E63 0.091 SUNHARY TAUS STEP VAPIAPLE MULTIPLE INCREASE NUMBER ENTERED REMOVED F VALIt To RSI IN PSO ENTER 02 2E4OVE 40 12 0.4115 0.1593 0.1693 2 NI 8 1. 934; 0.7105 0.5049 Q. 3355 5. 4711 3 , CO 7 0.5504 4 0,7325 0.2176 5. 4394 CN 3 0.9205 0.0474 5 1.1749 4.9111 LI 10 0.9361 0..725 0.1251 6 24 22.59°" 14 0.9/16 0.9536 O. 611? 7 IA 6 2. 7,57 0.9197 1.9499 1.91 9".7 3 (a)GEOCHEMICAL MODEL _ MULTIPLE R 0.9159 RSI 0.9195 SID. ERROR 07 EST. 9.0984 RSI(ADJ.) 0.9998 ANALYSIS OF VARIANCE OF SUM OF SQUARES 6100 SQUARE F RATIO REGRESSION 5 4022252.650 004450.530 8210.429 RESIOUAL 5 489.996 67.979 • VARIABLES IN EQUATION VARIABLE COEFFICIENT 870. ERROR F TO REHM : STRUCTURE COEFFICIENTS • (CONSTANT 80.85660 ) 11101ST 4 0.09510 0.01431 44.15(1 • 0.176 ASSAIL 8 209.24999 1.66152 15660.56E4 • 0.996 151001 11 1.0526/ 0.08661 141.11.5 . 0.093 LENGTH 14 0.0'572 0.02613 8.4012 . 0.501 LG1NT 16 01.54923 18.11064 20.2576 • 0.750 SUMMARY TABLE F VALUE TO STEP 1145I8ELE MULTIFLE INCREASE HUNKER ENTERtO REMOVED R PSO IN RSI ENTER OR REMOVE 1 ASHGIL 6 0.9960 6.9920 0.9920 1110.5397 2 INTACI 11 0.9993 0.9982 0.0067 40.9658 3 MSOLST 4 0.9997 0.9994 0.0007 7.5686 4 LCINT 18 4.9998 0.9997 0.0003 5.6013 0.0002 0.4002 5 LENGTH 14 0.9999 0.9999 _ (b)GEOLOGICAL MODEL HNLTIRLF P 1.0013 RS'l 1.0000 SIB. EPPCR OF EST. 0.0071 RVI(A0J.) 1.0000 ANALYSIS OF 447TANCI OF SUN OF SOUARFs 4704 79)3040 F RATIO PEGPESSTON 4023172.187 44'02.P.231.7854354.073 F.Esm111 1 0.000 7.000 VARIABLES IN E9UATION VARIABLE COEFFICIENT STS. ERPUR F TO REMOVE STRUCTURF COEFFICIENTS (CONSTANT -308.17212 I GA p 0.76164 '11042. 7259 09 4 0.00132 .48142.715' ::21: CO 7 3.34958 0.10111 *15415.7251 HO 12 1.24981 (.010,1 .62767.6476 2::74. R9 05 --!:!4!:5!! 1.70213 R5E099.5734 0.?33 72 518.37561 8.011'.9 g6R174.1457 ;1,7IT-g 1.19117 0.07009 4245E1.1892 ,(1,71ri ' INTSCT 27 -0.94860 7.30119 64432.4276 0.496 ERNGTM 28 0.09258 7.00102 917016.4899 0.501 SUMMARY TAPER STEP VARIAPEF MULTIPLE INCREASE F VOLIT TO NUMBER 64109E1 RENUTI R R59 IN 079 ENTER OR 'E401/7, 1 ASHSIL 22 0.9960 0.9919 1108.9757 2 TITACI 25 0.9993 9.9987 O.0567 40.6751 3 Ry 4 :::::: 4 CI 15 .,1.5170 :::g; INN: 5 LIMITS 28 0.9999 5.02at 2.9.146 6 INTSCT 77 0.9999 1:0).i94ii 7.0091 7 CO 7 0.9999 0.9199 0.0000 ;1.1 18n: a 49 ta 1.0209 1.0700 0.0171 5.31'9 9 GA ? 1.6000 1.0000 0.0000 2201042.7259 (c) COMBINED MODEL • 2:S enough at such low values, as to render the direct model unsatisfactory. Secondly, the use of converging regression for the geochemical variables appears desirable, because even though the obtained values of R2 are similar, a decrease of 10% in the standard error of the estimate may be obtained by this means. Thirdly, the results of converging combined model must be regarded with caution, since even though this model explains a very similar amount of variance as the direct model, the standard error of its estimates are very high. This fact arises from the high forecasts obtained with that model, which 'may be interpreted as either representing that the model is unsatisfactory and unsuitable for the purposes aimed at, or that the copper output in the area has been much smaller than what it should have been from a statistical point of view. In the latter case, large amounts of untouched reserves may possibly lie in several areas, their value amounting to several times the total production obtained in all the mines. Taking into account the foregoing conclusions, and the erratic nature of the copper output which has been raised in the area (as evidenced by the very high standard deviation of the total copper production), it may be stated that the covergent use of indexes which stress the importance of local features, appears extremely desirable, and even necessary for the meaningful forecast of copper reserves. The results attained using combined geochemical-geological convergent models, need to be examined with extreme caution, because the forecasts are likely to be high in almost all cases, contrasting with the general low values of the output. Summing up, it may be concluded that the comparison between results obtained by straightforward and convergent regression methods, indicates that the latter method, which makes use of indirect indexes of of production as a means of forecasting base metal reserves, is a perfectly valid alternative for the estimation of such reserves. Its results in • 2 2 most cases are statistically better and more significant than those obtained by the former method, having in addition the advantage of introducing a greater local weight in the forecast, a factor especially important if meaningful local estimates are desired, as is the case in most mineral exploration problems, as opposed to problems related to mineral endowment of extensive areas, when emphasis is on the obtainment of regionalized results, as free of local influence or noise as possible. 7.5 INVESTIGATION ON THE DESIGN OF MODELS FOR THE FORECAST OF COMBINED TOTAL AND LEAD-ZINC POTENTIAL RESERVES 7.5.1 General Statement of the Problem As indicated previously, a complex relationship exists between the amounts of different types of ore raised and beneficiated in any mining district at any one time, a relationship that is strongly influenced by extra-geological factors practically impossible to quantify in accurate terms. This fact makes the design of models for the forecast of combined reserves highly unlikely to be successful, if absolute production values are used as response, while building-up the models. Since in many instances global forecasts of potential reserves are required for an area (e.g. for the allocation of exploration expend- iture), in the following paragraphs an attempt to establish a model for the forecast of such reserves is discussed, firstly for total combined reserves and later for combined lead-zinc reserves. 7.5.2 Forecast of Combined Total Potential Reserves The multiple regression ,of the geochemical and geological indexes selected in the present research against the total output, variable with a mean of £7,154,743 and a standard deviation of £15,086,407 among the productive cells of the area, rendered the following models: 2 1 (A) Geochemical Model Y = 5444.28177+1254.62065Pb-965.80692Ba-1379.77357Co+1009.78727Li (B) Geological Model Y = 49345.50169+27.63027Upper Limestone+22188.38989Number of Fault Intersections-30598.74O4OLength of Faults (C) Combined Model Y = -8893.36965+1168.78988Ga-1408.45735Cu+780.03807Pb-583.62022Ba +1639.09847Co-1998.05214Ni-2017.33589Mn+2632.44063Li+1269.72242Mo -1032.94065As-77.95338Permian-26.13728Millstone Grit+1563.16191 Ashgill-31.31201Skiddaw Slates+699.02926Number of Fault Inter- sections-69.53076Length of Faults These models explain 36.02%, 30.98% and 81.64% of the variance of the response, respectively, (unadjusted for the number of variables in the equation). If these models are compared with those discussed in Section 7.3, it may be seen that they have a strong similarity with the ones designed for the forecast of lead indexes, a fact that reveals the strong influence that the output of this metal has on the combined production of the area. Furthermore, it may be seen that the similarity is especially evident in the models designed to forecast the number of potential deposits per cell, a feature pointing out the importance of this production index, as compared to the average value of the output per deposit. It is worth noting that the influence of the copper and zinc outputs is represented only in the combined model, where they are reflected by the loadings of Ga, Ni, Millstone Grit and Ashgill. By regressing the total output against the production indexes of the metals that compose it,the following equation may be obtained: TABLE 7.28 FORECASTED BASE METAL COMBINED RESERVES(IN POUNDS X 1000)—NORTHERN ENGLAND ESTIMATION BASED ON MULTIPLE REGRESSION OF OUTPUT INDEXES OF COMPONENT METALS COMBINED TOTAL RESERVES COMBINED LEAD—ZINC RESERVES CELL CMBIND. GEOCH. GEOL. CM3NO. GEOCH. GEOL. MODEL MODEL MODEL MODEL MODEL MODEL 1 6560 0 0 o 0 2 0 0 0 0 0 a ' 3 0 213 0 0 0 0 4 0 0 9210 0 0 5499 5 15492 3956 37580 12581 2299 29E86 6 11070 7807 21718 8327 6903 7427 7 11785 28572 37556 13766 19267 26317 8 0 0 40578 0 0 27295 9 17558 0 0 164 0 0 10 20716 0 0 5432 0 0 11 3104 15727 0 0 7724 0 12 43 62 0 0 0 0 0 13 10995 0 1784 4449 0 888 14 5813 0 71444 12228 0 65780 15 19930 0 55740 23763 0 47983 16 26292 23207 19079 26517 18499 1407 17 18156 12272 2354 17653 13086 0 18 0 42801 12100 0 31140 0 19 0 29007 0 0 17063 0 20 0 88390 0 0 56651 0 21 0 45027 1994 0 30120 0 22 0 38641 0 0 26454 0 23 4394 27454 0 0 15870 0 24 17685 32375 26098 20675 24099 24291 25 57112 42360 40487 54179 39480 37550 26 50022 48000 49230 58587 50648 45740 27 37072 40575 55368 47344 37807 48833 28 0 36191 0 0 23736 0 29 0 411 25775 0 0 14700 30 11691 28708 0 7391 16371 0 31 1281 36733 0 399 27080 0 32 1601 2793 3259 4444 5580 0 33 6557 31491 20387 9709 22457 16961 34 718 5838 0 0 4435 0 35 5577 42729 0 1725 32691 0 36 15887 14066 3128 19453 17541 0 37 7659 11273 9991 13619 10011 3478 38 37388 26606 39241 39395 27745 33949 39 15555 72681 6983 17505 56494 0 40 0 0 31797 0 0 21800 41 561 3184 2292 897 3431 2847 42 11982 16707 6031 12037 16763 4463 43 3945 0 0 9789 0 303 44 0 4179 0 0 5547 0 45 8346 12071 12181 2997 9528 12905 46 2576 0 0 0 0 0 47 2492 0 0 0 0 0 48 0 21717 9160 0 22959 0 49 6515 15550 11905 12329 17977 0 50 0 8978 21661 0 8425 1242 51 16514 0 0 7352 0 0 52 0 0 56563 0 0 69500 53 6085 0 7220 7869 1184 3501 54 144 21564 0 2592 20057 o 55 337 5033 0 5681 10230 0 56 2343 0 5216 2705 0 6663 57 23714 37968 33332 17137 27335 34119 58 13175 0 2258 6975 0 2792 59 9219 36870 17651 7637 22318 10719 60 16437 16356 38181 19414 11639 27369 61 23024 296 2082 18811 0 0 62 430 0 0 0 0 0 63 0 60464 0 0 78453 64 0o o o 0 0 a 65 0 6941 0 9884 65 0 0 0 0 o 0 67 o a 0 0 68 0 o 0o a 0 o 69 0 0 0 0 0 0 70 13091 0 23323 11748 0 12648 71 11696 5299 21055 8985 3598 10375 72 24923 104534 21471 22439 78894 19555 73 7721 0 0 0 0 0 74 0 76176 112234 0 55714 140495 75 0 19655 0 0 13064 0 76 0 71077 0 0 47976 0 o 0 0 a , o o a 0o 8 0 80A 13210 n 0 10607 0 0 81 10699 0 0 5780 0 0 82 18312 83355 0 15985 68118 0 83 1499 1443 10082 3812 5207 8265 84 0 0 0 0 0 0 85 0 0 0 0 0 0 86 a 9779 0 o 4237 0 87 0 a 0 o 0 o 35 0 0 0 a 89 0 7346 0 0 0o 0 90 27165 0 0 19558 0 0 91 25261 0 0 18055 0 0 92 20370 0 0 1269+ 0 0 93 17650 26172 0 9726 21369 0 94 0 o o a 95 0 0 0 a 0o 0 96 0 5952 2750 0 0 0 97 10770 0 0 0 0 a 98 13788 0 0 6 820 0 0 99 5074 0 0 2963 0 0 100 21163 9054 61940 20304 9521 5663 101 0 0 52796 0 0 441.13 102 0 47565 0 0 31380 0 103 0 0 0 0 0 0 104 8571 0 0 0 0 0 105 0 106802 0 0 80882 3 105 2026 14252 5888 2462 14429 6283 2 3 1 Y = 2159.55983+3.65201Av.Value of Lead Output+12.73590Av. Value of Zinc Output+752.08217Number of Lead Deposits+1255.69929Number of Zinc Deposits-1501.85826Number of Copper Deposits This model explains 94.43% of the variance of the metal output in the area, mainly being influenced by lead and zinc production indexes, variables that bear coefficients of correlation with the total output greater than 0.6. The influence of the copper output is negligible and local, the main purpose of the copper index present in the model being to counterbalance the strong positive constant term included. The silver production indexes, which were considered in this case because the total output includes silver values, proved to be independent of the response and hence of no use in the present case. It is worth considering that, according to that equation, an average productive cell of the area would render £7,323,700, a value that is 2% over the mean total production of the area. The forecasts obtained with the latter model are compared in Table 7.27 with those attained using the total output as response, in all cases the statistics referred to being actual total production figures. It may be seen how in that table, the convergent method of regression renders mcuh better estimates than the simple regression of total output figures, in all cases the values of R2 greater and the values of t for the mean differences being lower in the former case. Therefore, it appears that if combined potential reserves are required for an area, the use of weighted output indexes could, up to a certain extent, overcome the difficulties of designing such models, when the total reserves are to be estimated from various production values whose relationship is highly dependent on extra-geological factors very difficult or impossible to quantify. The total potential reserves forecasted for each cell in the area 2 32 by means of the annotated convergent model, are summarized in Table 7.28 and Figure 7.10, where the forecasts are graphically represented according to selected value categories. 7.5.3 Forecast of Combined Lead-Zinc Potential Reserves According to the results attained in the previous section,a model for the forecast of combined lead-zinc reserves was designed by means of convergent regression of production indexes of the component base-metals, a model that is represented by the following equation: Y = -2860.48451Av.Value of Lead Output+12.89211Av.Value of Zinc Output+757.53770Number of Lead Deposits+983.29242Nutber of Zinc Deposits This equation explains 93.69% of the variance of the combined lead-zinc output. All the variables are significantly correlated with the response at the 0.05 level, bearing coefficients of correlation greater than 0.59. Therefore, they all influence the structure of the model in a similar fashion. It is worth noting that an average productive cell would render, according to that model, an estimate of £7,085,210, a value that is only 1% less than the actual average lead-zinc production in the area. The forecasts of the combined lead-zinc reserves for the cells into which the area was subdivided, are summarized in Table 7.28, and are graphically represented in Figure 7.11, according to selected value categor- ies. The R2 between those forecasts and the actual production figures are 0.6480 for the case of the combined model, 0.4610 for the geochemical model, and 0.2070 for the geological mdoel, values that are much lower than the respective ones of the combined total output (see Table 7.29). As a final point regarding the models designed for combined reserves, it must be indicated that they would not render conservative estimates, as the models of the individual base-metals composing those KEY TO SYMBOLS ~ More than25000 @500125000 01001-5000 o 1-1000 Blank: 0 FIG.7: 10 Forecasted lead-zinc combined reserves-in Ex 1000 ofs),® 0 wo'oo:000 oci op® ®,® o® r 100®0® 7®i o * * o'-o[ ** GEOCHE MICAL MODEL 0 00100 0000T 0 0 CY* ® 00 KEY TO SYMBOLS 0, 0 0 0 0 More than25000 00 -100000 (05001-25000 * * 1001-5000 1-1000 0 Blank: 0 ® GEOLOGICAL MODEL COMBINED MODEL F I G. 7 11 M 233 combined reserves would. Therefore, the forecasts obtained by the use of these models, though statistically valid, need to be considered with caution, and their values should, if possible, be checked against those obtained with the individual elements, forecasts that in the opinion of the author are more reliable, since they are not so affected by extraneous factors as those representing combined reserves. 2 34 CHAPTER 8 EVALUATION OF REGIONAL STREAM SEDIMENT GEOCHEMISTRY AS A MEANS OF FORECASTING MINERAL POTENTIAL 8.1 INTRODUCTION In this chapter, a final evaluation of the forecasting method employed is done, by comparing the results attained by means of the different models designed, with empirical models obtained from the analysis of conventional geological and geochemical information, and with models designed from the analysis of the distribution of the output in the area. A quantitative approach that considers the use of multiple discriminant analysis is also taken to analyze the efficiency-of each model: In addition, the employment of factor analysis as a technique to use prior to multiple regression is discussed, in an attempt to obviate possible anomalies of the models due to the high intercorrelations existing between the variables. 8.2 OTHER METHODS OF FORECASTING BASE METAL MINERAL POTENTIAL 8.2.1 Qualitative Estimation of the base metal mineral potential of the area Two kinds of information are available for the area to obtain qualitative estimates of its mineral potential: conventional geological data, and the regional geochemical reconnaissance that constituted the raw- data for the present research. A brief review of the main conclusions that may be obtained from the analysis of both kinds of data, follows. 8.2.1.1 Estimates based on conventional geological information The mineral potential of the area has been examined by Jones (1941), Dunham (1944, 1948, 1958), Varvill (1954), and Eastwood (1958), on 2 3 5 the basis of the geological factors known to have controlled the emplace- ment of the mineralization that was worked in the Northern Pennines and Lake District orefields. (A) Northern Pennines Orefield The analysis of the distribution of the ore-shoots known in this field shows that very likely most of the the easily accessible ore bodies have been discovered. However, in most districts there is a striking concentration of mines in the lower slopes of the main valleys, while only few veins are known in the higher terrains (Dunham, 1944, 1948). This fact implies that little exploration has been carried out in the watersheds, thus rendering these areas as exploration targets, especially where favour- able horizons are known to be concealed beneath younger formations, and where known mineralized fractures may be reasonably expected to intersect the watersheds. Of those watershed areas, Dunham (op.cit.) indicates six with high possibilities of containing mineral deposits: (a) Killhope Law in the Durham-Northumberland border; (b) East Allen-Rookhope-Derwent; (c) Middlecleugh-Wellhope; (d) Greenlaws-Langdon Beck; (e) Middle Fell in Alston; and (f) Stanhope Burn-Eudon Burn covering the north-eastwards continuation of Boltsburn Vein. In addition, four other areas are suggested, on the basis of the continuity of the main vein systems of the field: (1) Eastwards continuation of the Coldberry-Wiregill complex; (2) Westernmost part of the swarm of veins in Swaledale; (3) Eastern side of the Grassington Moor mining district; and (4) North-eastwards contin- uation of the Sharnberry vein to the southeast of Bollihope. Taking a more regional approach, the following main watershed areas may be regarded as exploration targets in this field (Figure 8.1): 23 3 (A) Tyne-Weardale watershed between Burnhope Seat and Bolts' Law (Cells 36-25-26-27). (B) Tyne-Teesdale watershed from Cross Fell to Burnhope Seat (Cells 35-36). (C) Weardale-Teesdale watershed from Burnhope Seat to Middleton Common (Cells 36-37-38-49). (D) Teesdale-Swaledale watershed from Winton Fell to Dalton (Cells 70-71- 72). (E) Swaledale-Wensleydale watershed from Great Shunner Fell to Bellerby (Cells 81-82-83). (F) Wensleydale-Wharfedale watershed from Bukden Pike to Great Whenside (Cells 91-99). (G) Wharfedale-Nidderdale watershed from Great Whernside to Greenhow Hill (Cells 99-100-106). (H) Wharfedale-Ribblesdale watershed from Malham Tarn to Cracoe (Cell 105). (I) Eden-Tyne and Eden-Teesdale watersheds between Gilderdale Forest and Warcop Fell (Cells 24-35-36-47-48-59). (J) Eden-Swaledale watershed from Winton Fell to Abbotside Common (Cells 70-69-8)). In addition, there are still other areas in the field that might be considered to contain undiscovered ore deposits. These areas are mainly valleys within the known mineralized districts, where important ore bodies may be found in connection with limestones lying beneath the Great Limestone. In this respect, Dunham (1959) suggests trials in the Melmerby Scar and Tynebottom limestones, units that are -concealed under younger cover over much of the area. As well, the exploration of areas where the Whin Sill outcrops could be considered worthwhile, taking into account that some ore-shoots in these quartz-dolerites rendered great productivity at Settlingstones, Stoneycroft-Greyside, Cowgreen, and Closehouse mines. In this case, the • 217 relation of quartz-dolerites to faults with a throw greater than the usual in the mineralized faults of the field, apparently should be looked for. From the available information, it can be stated that the favourable areas in this respect would lie in cells 4, 5, 6, 7, 13, 14, 23, 24, 35, 36, 37, 47, 48, 49, 50 and 58. Finally, it must be remembered that only few deposits were flooded while still in ore, and thus the possibility of finding new ore bodies at depth cannot be discarded. This aspect of the exploration of the field, obviously cannot be ascertained from the available 1"/lmile geological maps. (B) Lake District Orefield The establishment of clear-cut exploration criteria for this field is a difficult task, because the mineralization in that area is typically hydrothermal and does not show strong and defined controlling features. In the absence of clear lithological or structural controls, it becomes very hard to indicate areas favourable to contain mineralization,from the conven- tional geological maps. Taking into account the shape of the known ore bodies and the little amount of work that has been done in many of them, Eastwood (1958) concluded that the only favourable areas that may be pointed out to contain base metal mineralization, are: Thornthwaite-Barrow-Yewthwaite (Cells 42 and 53), Threlkeld (Cell 42), and Coniston (Cell 75), the first two probably containing lead-zinc deposits and the latter copper mineralization. At this point, it appears worthwhile to review the possibility of using as indicators of mineral potential ("metallotects"), some geolog- ical features that are not normally considered when the possibilties of the area are examined, but which clearly showed influence in the geological models designed in this research. The analysis of the parameters included in the geological and combined models designed, shows that, in addition to the known stratigraphic controls, some other geological features could be 2`3 8 used to analyze the mineral potential of the area: the number of fault intersections, the length of faults, the number of fault-contact inter- sections, and the presence of acidic intrusive rocks. The first of those features is a favourable indicator for all types of mineralization in the area, while the second appears to be a negative metallotect. The remaining faulting index is a negative feature for zinc and copper mineralization, and the acidic intrusive rocks are a favourable index for zinc and copper deposits. Regarding the number of fault intersections, considering a regional average of 22 intersections per cell and a standard deviation of 23 intersections, the following areas may be indicated to be anomalous: Alston area (Cell 25), West Cumberland (Cell 29), Carboniferous rim surround- ing the Lake District (Cells 21 and 30), and central Lake District (Cells 51, 53 and 56). Four of these areas are anomalous in this respect, because faults are easily detectable in the sedimentary terrain that constitutes them (Cells 21, 29, 30 and 51); another area (Cell 25) conincides with the most important lead-zinc producing region, a feature that could be expected. However, the value attained by this parameter in the remaining cells (53 and 56) cannot be explained and thus the presence of ore deposits in the Borrowdale Volcanics of those areas could be suggested. Other areas bearing a high number of intersections (more than 46) are cells 31 and 32 in the Lake District, and cells 37, 71, 72 and 79 in the Pennines, a group of cells worth considering as exploration targets of secondary order because the value of the parameter is not related to regional fault-systems or other easily understandable features. Taking into account the foregoing discussion, and considering that the average length of the faults in the region is 0.93 miles, it may be indicated that - among the annotated favourable ateas - cells 25, 53 and 56 have faults of average length less than 0.6 miles, a fact that confirms 239 the favourability of those areas towards containing mineral deposits. This feature is even more stressed for the two last cells, by the very low number of fault-contact intersections that they have (0 for cell 53 and 12 for cell 56), as compared to the regional average of 27 intersections. Regarding the presence of acidic intrusions, as indicated in Chpater 7, its favourable nature related to zinc and copper mineralization refers to the acidic dykes existing in the central Lake District, and not to the main granitic bosses of the area. In this case, cells favourable to containing mineralization of the annotated types are: 30, 31, 41, 42, 43, 51, 52, 53, 54, 55, 63, 64, 65, 66, 67, 74 and 75; Among these, the most important,according to the number of dykes that they contain, are cells 41, 42, 63, 64, 66 and 75. As well, it is worth considering that cell 66, besides having a large number of dykes, is in a similar strati- graphic setting as cell 75, which contains the Coniston copper district; therefore, the possibility of finding copper-bearing deposits in that area is worth considering. Summing up, it may be concluded that in the Northern Pennine ore- field the most favourable areas lie in the main watersheds, in areas where the Great Limestone and other underlying limestones as Melmerby Scar and Tynebottom lie covered by younger formations, and where it may be expected that some of the lengthy mineralized structures of the field may be inter- sected. In addition, minor speculative targets may be considered in relation to the outcrops of the Whin Sill, especially where these rocks are associated to faults with a larger throw than normal in the mineral- ized fractures of the field. On the basis of the foregoing exploration targets, the most favourable areas for undiscovered ore bodies are the following (in decreasing order of importance): cells 36, 35, 37, 38, 49, 47, 48 and 24. No clear exploration targets can be.envisaged for the Lake District orefield, due to the little knowledge available regarding the 2 4 0 factors that controlled the emplacement of the mineralization. However, according to the shape of the known deposits and the amount of mining carried out, areas that possibly contain undiscovered ore bodies are cells 42, 53 and 75, the first two probably containing lead-zinc deposits and the latter copper ore bodies. In addition,to the former, the following areas may be considered favourable towards containing base metal mineralization, on the basis of the value attained in them by parameters found to be related to mineral- ization while building up the geological and combined models: area around Alston (cell 25), zone of Borrowdale (cell 53), and area around Shap (cell 56), all of which bear a number of fault intersections which cannot be explained on the basis of their regional geology; secondary targets in this respect are cells 31, 32, 37, 71, 72 and 79. The favourability of cells 53 and 56 towards containing base metal deposits, is further evidenced by the low value that unfavourable geological parameters (length of faults and number of fault-contact intersections) attain in them. The presence of acidic dykes appears to be a favourable metallo- tect for zinc and copper deposits, the areas with greater possibilities in this respect being cells 41, 42, 63, 64, 66 and 75. It must also be considered that cell 66 is in a similar geological setting as cell 75 which contains the Coniston copper district; thus, the possible existence of copper ores in that cell is suggested by these facts. The different favourable areas that may be considered on the basis of the annotated guides for exploration, are summarized in Table 8.1 and Figure 8.1. It may be seen, that the areas with higher probabilities of containing undiscovered ore bodies are the following (in decreasing order of importance): cells 37, 47, 25, 36, 35, 38, 49, 48, 24, 72, 31, 66, 56, 51, 52, 53, 55 and 75.. Finally, it must be considered that ore bodies lying within the TABLE 8.1 CELLS FAVOURABLE TO CONTAIN BASE METAL MINERALIZATION, SELECTED ACCORDING TO CONVENTIONAL GEOLOGICAL INFORMATION Type of geological indicator Watersheds Whin Sill Acid Intrusive No. of fault length outcrops Rocks intersections of faults 24 4 30 25 25 25 5 31 31 47 26 6 41 32 51 27. 7 42 37 52 35 13 43 56 53 36 14 51 71 55 37 23 52 72 56 38 24 53 73 66 47 35 54 75 48 36 55 76 49 37 63 77 69 38 64 85 70 47 65 86 71 48 66 ' 93 72 49 67 98 80 50 74 99 81 58 75 82 83 91 99 100 105 106 Areas Favourable for Base Metal Mineralization as Selected From Geological lnformation KEY t----++----t---+-+--.3t:-:::~._--''_i_'''''--_t___Y-____+--____if_--t_--_r_--~--_1 ~FAVOURAaLE WATERSHEDS ,-" .... "OTHER WATERSHEDS ~ WHIN Sill OUTCROPS ~ ACIDIC DYKES ... ~~~R~~~~I~~~~R~~:~NX+S (@ f1~t~t~s"~gi~~JF ~,.... rr:- ..~I,--=---+-.,,;._ ..... , __-+ +-~-_+_ ~>--- ~ --+-+l_~_"\_:_~"+'_':_,, ""~--l-+---t_- .--______1 \ ~"'" I' @ /@ I A .. ~ I ''''- I -.----- ItI' /I }\ I -+-+--@-;~ \r---R,--- ,., /1 t~ l \ \ .~f----1----\-+----+----l----1 ( ~J ...... ,~ o 10 20 j ;'eMPf,:e; ,. H~n:' Fig.8.1 1 known mining districts at depths beyond those reached by the mine workings, may possibly exist in several areas, but their presence, as is obvious, cannot be ascertained from the available geological information. 8.2.1.2 Estimates based on regional geochemical data A qualitative appraisal of the base metal mineral potential of the area can be made be means of the regional geochemical information that constituted the raw-data for the present research. Traditionally, this analysis is done with the help of the basic statistical parameters of the individual elements, the areas being classified into background or anomalous depending on certain prefixed statistical criteria. The most used of these criteria uses the mean and standard deviation as yardstics to select probable and possible anomalous areas, the anomalous threshold being normally defined as X + 2s, where X is the geometric or arithmetic mean, depending on the frequency distribution displayed by the element. Accepting the foregoing criteria for the separation of -anomalous samples, maps were prepared for the whole area by means of the PLTLP program, where the elements were plotted unsmoothed according to class intervals selected in standard deviation units. On the basis of those maps, and taking into account the conclusions reached in Chapter 6 regarding the relationship between individual elements and mineral deposits, the following qualitative estimation of the base metal mineral potential of the area may be made, on the basis of individual elements: Barium • This element has a log-normal distribution, with a geometric mean of 225 ppm and a standard deviation (logarithmic)of 0.345. Its frequency distribution (Figure 8.2) shows that the stream sediments of the area constitute a background population at levels below 780 ppm, and an anomalous population at higher levels. The regional distribution of• barium shows the presence of 73 anomalous sites, 17 of which lie in the Lake District 2 42 representing mostly lithological influences; the remaining 56 sites lie principally in the Alston Block region, and in the Pennine Escarpment. Considering that barium is related to mineralization of the Northern Pennine type (galena-sphalerite-barite-fluorite veins and flats), the following areas could be considered favourable towards containing such mineralization: Probably Anomalous: Cells 13, 23, 24, 35 (2 sites), 36, 37 (3 sites), 46 (4 sites), 47 (2 sites), 48 (5 sites) 59, 70, 72 (2 sites), 93, 99, 106 (2 sites). Possibly Anomalous: Cells 7, 24, 25, 35, 36 (2 sites), 37, 38 (2 sites), 47, 48 (3 sites), 49, 50, 58, 59, 71, 72, 83, 92, 103, 106. In addition, 6 very anomalous sites in•the Lake District could , be related to mineralization, and therefore are worth mentioning. These sites lie in cells 31, 32 (4 sites), and 42. Cadmium As indicated in Chapter 6, cadmium has a very complex frequency distribution that does not fit normal or log-normal curves. Its mean value is 0.7 ppm and its standard deviation 1.2 ppm. Its frequency distribution (Figure 8.3) shows a background population at values below 2.5 ppm, and an anomalous population over that value. Accepting this threshold, the following cells could be considered favourable towards containing lead-zinc deposits:, Probably Anomalous: Cells 25, 26, 32 -(4 sites), 34, 36, 54, 56, 72, 82, 85, 103, 105, 106.. Possibly Anomalous: Cells 6, 26, 39, 54, 72, 74 (3 sites), 75, 86, 100, 104, 105, 106 (2 sites). Copper This element is log-normally distributed in the area, with a "." .... It. 10 S~ .0 '0 10 0.1 0.1 0.01 10000. ~"""""~TrT...,.....,--,M!. ...... ,l> .... 51 ••, .• ------.._--- .'-'j'-.-.h~--;-.-. [. ,: ... j ... ,... 1 • I . . .. ' I . ~ .:' 1 rj ... ~-~ -.-.-. . : 1: .: i I .! J. I IJ i ',.' ·1':::· I· I 10! . i !. 1. .. I "I Figurea.~ I· I I .. I ! I 'J lJ oL.. ,_:-J .~j .J._~_: L..L__1_.~. .. L...__ L.: .~_:J_ ... _ L:..:... L~ .. ;... ~_ .. L.: .... L:_:.1. .'1:.. .J._...... 1..:.: L~J ... !.:_L.l: : '. ..·,. ..1·, ... geometric mean of 13 ppm and a standard deviation (logarithmic) of 0.436. Its frequency distribution when plotted logarithmically (Figure 8.4) shows a fairly smooth passage from the background population to the anomalous one, with a threshold that may be established at 68 ppm. The spatial distribution of copper values shows the presence of 51 anomalous sites in the area, most of them lying in the Lake District. Of these sites, 24 may be considered due to industrial contamination, the reamining sites possibly representing copper mineralization. According to that distribution, the following areas may be considered favourable towards containing copper ores: Probably Anomalous: Cells 32 (4 sites), 42 (2 sites), 54, 64, 75, 84 Possibly Anomalous: Cells 31 (2 sites), 32 (3 sites), 41 (2 sites), 43, 63, 64, 75, 79. Iron Iron has a gaussian distribution in the area, with a mean value of. 3.5% and a standard deviation of 1.7%. Its frequency distribution (Figure 8.5) shows a clear background population at values comprised between 2.4% and 4.7%, and a sub-anomalous and anomalous population at levels greater than 4.7%. A threshold of 7.0% may be accepted to define the anomalous region. Of the whole population, 64 sites bear anomalous values, most of them lying in the Derwent Basin of the Lake District. Since this element was found to be related only to mineralization in the Pennines, all but 9 of those sites can be eliminated from a mineral exploration point of view. The remaining sites are related either to Whin Sill outcrops or to the Carboniferous Limestone Series, and therefore could be considered as indicators of potential mineralization. In this respect, the following areas can be considered as favourable: Probabl Anomalous: Cells 18, 36, 100 2 44 Possibly Anomalous: Cells 15, 24, 25, 38, 48 (2 sites) Lead Lead is log-normally distributed in the area, with a geometric mean of 37 ppm and a standard deviation (logarithmic) of 0.535. Its frequency distribution (Figure 8.6) shows a clear background population at levels below 540 ppm, a value that may regarded as threshold for the anomalous values. The spatial distribution of lead values shows the presence of 50 anomalous sites in the area, only one of which could be considered as belong- ing to features other than lead-zinc mineralization. Since this is one of the best elements that may be considered to define potentially favourable areas for base metal deposits, the following areas might merit further investigation in that respect: Probably Anomalous: Cells 7 (2 sites), 18, 26, 27, 28, 31, 32 (4 sites), 36 (2 sites), 38, 39 (5 sites), 47 (2 sites), 49, 50, 54, 70, 76, 84, 99, 106. Possibly Anomalous: Cells 6, 15, 25, 26, 27, 32, 38, 46 (2 sites), 47, 49, 50, 54, 59, 65, 82, 84. Lithium Lithium is distributed in the area almost following the- gaussian law, with a mean of 63 ppm and a standard deviation of 39 ppm. Its frequency distribution (Figure 8.7) shows a clear background population bearing values up to 61 ppm, a sub-anomalous region with values comprised between 61 and 135 ppm, and an anomalous population over that figure. The regional distribution of this element shows the presence of 65 anomalous sites, most of them lying in the Alston Block of the Pennines and in the northern Lake District. Apparently, most of the high values in the Lake District are due to lithological effects, and thus, only the probably anomalous sites should be regarded important from the mineral C;Rt PAPERS CHR'STCHURCH NZ 2 H 1 , $ ' , T F. ; 'rl 1 Frequency distribution , of , 1 Iron I ' •1 r .11 I r7:Jr 1 t ' - -77'- 1 ri I $ - - ' T -rt H - - • L - - 1 ' - •' orre.r+rr 1 • - , 1 Figure 8.5'__H. ' $' $ t ", i • , $ 1 , ■ 1 ■ • ... '. - ..j...___ 1 1 1 1 t 1, ; : f; : ,$, ,.....,.L. . . -1: 1' 1. 1. $ $ _ , _ - 1 .1 tit4 exploration point of view in that area. The remaining sites may be related to mineralization, and thus might merit further investigation. Bearing these facts in mind, the following areas may be regarded favourable towards lead-zinc mineral deposits: Probably Anomalous: Cells 16, 26, 31 (4 sites), 32 (3 sites) 37, 39, 42 (3 sites), 43, 84. Possibly Anomalous: Cells 25, 26 (4 sites)', 36 (2 sites), 37, 38, 39, 49 (5 sites), 59 (3 sites), 71. Molybdenum This element has a complex distribution in the stream sediments of the area, with a mean of 0.8 ppm and a standard deviation of 1.5 ppm. Its frequency distribution when logarithmically plotted (Figure 8.8), shows two populations: A background population at values lower than 2.2 ppm, and an anomalous population bearing higher levels. Within the latter group, two sub-populations may be distinguished, separated at the 11 ppm level; the lower of these may be considered to represent possibly anomalous values and the other probably anomalous values. The spatial distribution of molybdenum in the area shows 38 anomalous sites, 6 of which may be due to industrial contamination arising from populated centres (Lancaster, Port Carlisle, Barrow-in-Furness, etc.). Considering only the remaining anomalous sites, the following areas may be regarded favourable towards containing copper mineralization: Probably Anomalous: Cells 4, 13, 32, 52, 56 (2 sites), 63 (2 sites), 64, 65, 75, 76, 85, 97, 103, 106. Possibly Anomalous: Cells 14, 52, 54, 56 (2 sites), 63, 64 (2 sites), 67, 75 (2 sites), 85, 94, 103 (2 sites). Zinc As indicated in Chapter 6, zinc has accomplex distribution in the stream sediments of the area, not conforming to the gaussian or log- 2 1 3- gaussian curves. Considering a mean of 172 ppm and a standard deviation of 339 ppm, a regional threshold of 850 ppm may be tentatively accepted for the anomalous values. The regional distribution of zinc values shows the presence of 31 anomalous sites in the area, most of which lie in the Pennines region. Accepting the annotated threshold, the following areas may be considered worth investigating from a mineral exploration point of view: Probably Anomalous: Cells 26, 32 (4 sites), 36, 39 (2 sites), 54, 82, 86, 92, 99, 103, 104, 106 (2 sites). Possibly Anomalous: Cells 6, 25, 26, 31, 36, 37, 48, 56, 61, 67, 81, 105. As it was indicated in Chapter 6, in addition to individual elements, three factors of the components solution computed for the data of the present research can be considered to be related to mineralization, and thus could be used to produce qualitative estimates: Factor Cd-Zn-Pb: This association would reflect the lead-zinc mineral- ization of the region, but it is in places obscured by a slate-greywacke component of the samples, which tends to diminish the value of the factor scores for this association in many areas. Regarding as favourable towards lead-zinc mineralization all those sites having scores greater than 0.5, the following areas may be selected: Cells 55, 71, 72 (8 sites), 74 (2 sites), 75 (4 sites), 82 (4 sites), 83 (6 sites), 99 (2 sites), 103, 104 (10 sites), 105 (18 sites), 106 (2 sites). Factor Ba-Pb: This negative factor is considered to represent in the area an association that may be termed "Northern Pennines-type mineralization", that is veins and flats formed essentially be galena, sphalerite, barite, and/or fluorite. Accepting that factor scores lower than -0.5 could represent favourable areas for the presence of this type of mineralization, the following cells may be selected in this respect: 0 2 1 7 Cells 25, 26, 28, 32, 36 (8 sites), 37 (9 sites), 46 (5 sites), 47 (2 sites), 48 (8 sites), 49, 59 (5 sites), 71 (3 sites), 72, 84 (2 sites) , 106 (4 sites). Factor Mo-Cu-As: This is a mixed factor representing several features of the area, among which copper mineralization is one. The interpretation of the scores representing this factor, need therefore to be done cautiously, if they are to be used for the selection of areas favourable for copper ores. If values greater than 0.5 are considered, the following cells may be chosen in this respect: Cells 32 (4 sites), 43, 47, 53, 54, 56, 58, 64 (4 sites), 65 (4 sites), 75 (2 sites), 76 (2 sites), 78, 83, 88, 94 (9 sites), 95, 103 (2 sites). The different areas that may be selected as favourable towards containing base metal mineralization in the studied region, are summarized in Table 8.2 and Figure 8.9, on the. basis of the foregoing discussion. It may be seen in that table that the areas most favourable from the lead-zinc potential point of view are cells 25, 26, 32, 36, 72, 99 and 106; of secondary importance in this respect are cells 6, 37, 38, 39, 48, 49, 59, 71 and 82. The areas most favourable for copper mineralization are cells 32, 54, 64, and 75, and in minor proportion cells 43, 56, 65, 76, 94 and 103. Finally, it is worth mentioning that, on the basis of the previous selection of areas and of the one done with conventional geological data, it may be concluded from the qualitative analysis that the most favourable areas from the lead-zinc view point are cells 25, 36, and 72, cell 75 being the most adequate area in which to explore for copper-bearing deposits. Note that cell 25 has been the most important lead-zinc producing area of the region, that cell 75 has been the most important copper producing cell of the region, and that cells 36 and 72 have produced more than Um and E4m in lead-zinc ores, respectively. TABLE 8.2 CELLS FAVOURABLE TO CONTAIN BASE METAL MINERALIZATION, SELECTED BY QUALITATIVE ANALYSIS OF REGIONAL GEOCHEMICAL DATA Type of Geochemical Guide Lead - zinc mineralization -,Copper Mineralization Factor Factor Factor Pb Zn Cd Ba Li Fe Cd-Zn-Pb Ba-Pb Cu Mo Mo-Cu-Pb 6 6 6 6 16* 15 55 25 31 4* 32 7* 25 25* 7 25 18* 71 26 32* 13* 43 15* 26* 26* 13* 26* 24 72 28 41 14 47 17* 31 32* 23* 31* 25 74 32 42* 32* 53 18* 32* 34* 24* 32* 36* 75 36 43 52* 54 25 36* 36* 25 36 38 82 37 54* 54 56 26* 37 39 35* 37* 48 83 46 63 56* 58 27* 39* 54* 36* 38 100* 99 47 64 63* 64 28* 48* 56* 37* 39* 103 48 75* 64* 65 31* 54* 72* 38 42* 104 49 79 65* 75 32* 56 74 46* 43* 105 59 84 67 76 36* 61 75 47* 49 106 71 75* 78 38* 67 82* 48* 59 72 76* 83 39 81 85* 49 71 84 85* 88 46 82* 86 50 84* 106 94 94 47* 86* 100 58 97* 95 49* 92* 103* 59* 103* 103 50* 99* 104 70* 106* 54* 103* 105* 71 59 104* 106* 72* 65 105* 83 70* 106* 92 76* 93* 82 99* 84* , 103 99* 106* 106* * Contain probably anomalous sites Al1B;l0 }i'''·iVOU:Lj3LB FOH BJ~J.c; r·lliT.iJJ i·!Il~iliL..LI:6ATIOH ,AS SELBC'l'BD BY QUALITATIV.c: Al~ALY3IS OF llliGIONAL GEOCHEI·iIC~~j DATA ~. C!1. CI • @ )r-.: g .. 0 0 o a ->, - • • ~ o 0 0 ~ 0 OD 0 K 4-~--'O- ~ li. 4 + i -";fl rtO 18 II GEOCUEMICAL 0°F~LJ INDICATOR f il~"'-@i • @ -'B@!a O-- ~ o Pb p. D 0 o . 0 00 0 . 0 0 o • 2n / .6. .6.AJ @) Cd gG iii Be • -.. o Li 0 b 0 0 o 0 00 0 .6. o Ba ! .6. .6._---3 + • t) @I 0 .-- o Fe ( · i o .~ 6 Cu A +lL-A + .A + +0· . :. ... Mo \ • • 0 0 o .@: -, 0 00 0 o Factor Cd-2n-Pb 6~~ '\.....j.-... A • Foetor Ba-Pb 0 ·0- ~o + factor Mo-CIt'"As - 0 .6. A + A + +6 + '1 @ \- B • r:.a "'I 0 0 ~ I ~A }) + \.-) @ 1/ 0 f~ ~\ ° 0° C ~i A~ + A ~ 0- \!J 0- @ o-~ eo eJi@: ) 0 0 tf A+ A. o 10 20 I AREAS FAVOUHliBU FOR BASE NETAL r·IIN~RJiLIZn.TION ,AS SELEC'l'ED BY ST.h.TISTICAL AliALYoI3 OJ!' THE FRl~QIENCY DISTRIBUTIOn OF OUTPUT VALlES @ @ @ ~ @ ® @ lead,zinc and copper ores @Lead and zinc ores @ @ @ @ f o Copper Ores . OIG'G @ @ / I I 0,® @ @ @ @ @ @ FIG.8.10 2 4 8 8.2.2 Forecasts based on the analysis of the frequency distribution of output values A quantitative estimation of the base metal mineral potential of the region can be made on the basis of the analysis of the distribution of the output indexes selected in this research. Such an approach gives a rough idea of the amount of ore that may be expected to exist in the whole area, without indication of where that ore may lie. Considering the favourable areas to contain base metal mineral- ization indicated in the preitious section, it may be assumed that copper mineralization may be expected to exist in 42 of the 106 cells, and that lead-zinc ores may be expected to be found in 61 cells. Accepting the conclusions reached in Chapter 5, where the distribution of the output indexes was found to be log-normal in the studied area, the following estimates may be made, on the basis of the statistics indicated in Tables 5.4 and 5.5. Lead Reserves The average number of lead deposits in the productive cells of the area was found to be 6.55, their average output being £988,260. Therefore, the total number of lead-bearing deposits that may be expected in the 61 cells with possibilities, is 399, with present total expected value of their reserves of £394,315,740. In addition, these deposits would have silver contents whose value equals £14,558,540, rising the total present value of those reserves to £408,874,280. The 95 per cent confidence limits for those predictions, according to the normal curve, are: Expected number of lead deposits 183-610 Expected value of silver reserves : £ 6,672,180- 22,240,600 Expected value of lead reserves : £180,851,580-602,838,600 Total expected value of the reserves : £187,523,760-625,079,200 0 2 1 9 Zinc Reserves The average number of zinc deposits is 2.53 in the productive cells, rendering those deposits an average production that may be valued at £530,940. Thus, the 61 cells selected may be expected to contain 154 deposits with a total present expected value of their reserves of £82,380,760. The 95 per cent confidence limits for those estimates, according to the t-curve are: Expected number of zinc deposits: 18-286 Expected value of zinc reserves : £9,618,920-153,392,840 Copper Reserves The copper-productive cells in the area have an average number of• deposits of 1.63, their average production being valued at £119,570. Consider- ing that copper deposits can be expected to exist in 42 cells, the total number of such deposits that may be expected is 68, with a total present- expected value of their reserves of £8,130,760. According to the t-curve, the 95 per cent confidence limits for those forecasts are: Expected number of copper deposits: 13-118 Expected value of copper reserves : £1,554,410-14,109,260 Considering the area as a whole, it may be concluded that, according to the qualitative estimates done in the previous section, 31 cells are favourable towards containing lead, zinc, and copper ores; 30 cells would only contain lead and zinc ores; and 12 cells would only contain copper ores (Figure 8.3). Therefore, the following combined estimation may be made: Main cells (Lead, zinc and copper ores) Expected number of lead deposits z 203 Expected number of zinc deposits : - 78 Expected number of copper deposits : 51 2 54 Expected value of lead reserves £200,616,780 Expected value of silver reserves : 7,401,380 Expected value of zinc reserves 41,715,320 Expected value of copper reserves : 8,252,630 Total expected value of reserves : £255,831,550 Average expected value of reserves per cell : £8,252,630 Secondary cells (lead and zinc ores) Expected number of lead deposits : 196 Expected number of zinc deposits : 75 Expected value of lead reserves : £193,698,960 Expected value of silver reserves : 7,146,160 Expected value of zinc reserves 40,120,500 Total expected value of reserves : £240,965,620 Average expected value of reserves per cell: £8,032,187 Minor cells (copper ores) Expected number of copper deposits : 17 Expected value of copper reserves : £2,032,690 Average expected value of reserves per cell: £169,390 TOTAL EXPECTED VALUE OF RESERVES FOR ALL 73 CELLS: £498,829,680 WEIGHTED AVERAGE OF EXPECTED VALUE OF RESERVES PER CELL: £6,831,641 If actual production figures are considered, the following con- clusions may be drawn from the previous quantitative estimations: (a) With respect to lead reserves, 147 deposits with reserves valued at £108m could still be lying undiscovered in the area. These deposits would contain in addition, silver contents that may be valued at £4.6m. (b) A total of 119 zinc-bearing deposits with reserves valued at £63m, could be expected to exist untouched in the 61 cells favourable towards containing this type of deposit. r 2A, 4 1_` (c) With respect to copper mineralization, 47 deposits bearing reserves valued at £5.6m may be expected to exist in the 42 cells that are favour- able in this connection. (d) Accepting the previously indicated figures, the average value of the reserves that may be expected in the zinc and copper deposits, is similar to the value of the reserves in deposits exploited until now. On the contrary, lead deposits would be on average smaller than those worked up to the present, with an average present value of their reserves that may be estimated at £730,000,an amount that is 27% less than the actual average value per deposit (£988,000). (e) The mineral endowment of the favourable areas would be £24,821 per square kilometre, a value that is composed of £14,784 of lead reserves; £8,630 of zinc reserves; £767 of copper reserves; and £640 of silver values contained in the lead ores. Regarding the localization of this mineral wealth, 6.0 base metal deposits may be expected to exist in each of the 31 most favourable cells,rendering a rate of expectation of one deposit per 16.6 square kilometres; another 30 cells would have 4.4 lead or zinc deposits each, with a rate of expectation of one deposit per 22.7 kilometres; and finally, still another 12 cells would have 1.6 copper deposits each with an expectation rate of one deposit every 62.5 square kilometres. 8.2.3 Quantitative forecasts using a combination of factor and regression analysis As indicated when reviewing the previous work regarding the fore- cast of mineral potential, in many cases the use of a combination of multi- variate statistical techniques has rendered very good results. One of the most used, combinations, is the one that considers the initial employment of factor analysis, and a subsequent multiple regression of factor scores representing the selected solution. The use of such a combination of techniques is justified, when the ti -t2 number of independent variables is to be reduced, when there is a need to identify theoretical variables that could be related to output indexes, or when strong collinearities between the independent variables impedes the significant application of regression analysis. Since the possibility of reducing the number of independent variables is in most cases a tempting proposition, and since the variables used in the present research are highly correlated , investigations on the use of factor analysis prior to multiple regression were performed, in order to: Attempt to eliminate the possible influence that the unorthogonality between the variables has on the models; to reduce if possible the number of independent variables; and to obtain the best possible expression of the geology-production relationship, a fact that would allow more accurate and reliable forecasts. With the annotated purposes in mind, an orthogonally rotated factor analysis was performed on three kinds of data: (a) Geochemical data represented by all the samples collected in the area; (b) Geochemical data represented by scores type A; and (c) Geological data. In each case, solutions were chosen, scores were computed, and these were averaged for each cell, and the averages were regressed against the output indexes indicated in Chapter 5. 8.2.3.1 Forecasts based on geochemical factors As indicated, factor scores representing two types of data were calculated for the geochemical data. Firstly, the scores for the orth- ogonally rotated factor solution discussed in Section 6.5 were estimated for the six factors contained in it, for each sample collected in the area. These scores were averaged for each cell, and those averages were regressed against the• selected output indexes, with the following results: (A) Average value of reserves per deposit The six factors present in the solution are not significantly correlated with this output index expressed in terms of lead, copper or A ) 3 zinc production. No significant equation could be found for the cases of lead and zinc, and for the case of copper a very poor equation explaining 58.67% of the variance of the response was found. If this equation is compared with the general model designed (Table 7.17), it may be seen that nothing could be gained in the present case by expressing the 14 original variables in terms of 6 factors, the forecasts that could be obtained being much more unreliable and inefficient than those of Table 7.14. (B) Number of deposits per cell This output index is also uncorrelated with the factors defined. No significant equations could be found for the cases of lead and copper reserves, and for the case of zinc the best model attained explained 56.39% of the variance of the response. If that result is compared with the corresponding one of Table 7.12, it may be seen that this is markedly worse, thus rendering unjustified the use of factors instead of the original - variables to forecast the number of deposits per cell. Taking into account the discouraging results attained, those investigations were discontinued, and another _approach was chosen to investigate the problem. In this latter approach, the correlation matrix of the scores type A for each cell (see chapter 5) was taken as the starting point of the factorization. Even though in this case the eigen-structure of the system and screegraph showed that the best solution to choose contained only four factors, solutions containing 2 to 6 factors were computed, scores were obtained for each of them, and these were regressed against the chosen production indexes. (A) Average value of reserves per deposit No significant equation was found for the forecast of lead reserves, except for the model designed with a six-factors solution which rendered an equation explaining 13.64% of the variance of the response. Three significant equations were found for the forecast of zinc reserves, • 2 4 the best of which explained 60.10% of the variance of the response; the latter model was also obtained using as independent variables the scores of the six-factors solution. Finally, only one significant equation was found for the forecast of copper reserves, a model that also corresponds to the six-factors solution, and which explains 84.15% of the variance of the response with a standard error of 163.05. If these results are compared with those of the general geochem- ical models designed (Tables 7.15, 7.16, 7.17),it may be seen that they are worse, indicating that raw-data give a better reflection of the relation- ship geochemistry-output, than factors computed on them. (B) Number of deposits per cell The best equation found to forecast lead deposits corresponds to the five-factors model, explaining 27.66% of the variance of the response. No significant equations could be attained for the cases of zinc and copper deposits. If the only significant result obtained is compared with that of the general geochemical model (Table 7.15), it may be seen that it is less significant, rendering worse forecasts. Considering the poor results obtained, factorization of geochem- ical data as a step prior to multiple regression analysis, was discontinued. 8.2.3.2 Forecasts based on geological factors With the main purpose of reducing the number of independent variables, the geological data employed in the present research were standardized and factorized, and the scores resulting from that manipulation were regressed against the selected output indexes. As with the geochem- ical data, the solutions chosen were orthogonally rotated component solutions; they contained 3, 6, 9, 12 and 15 factors, although the eigenstructure of the data and the screegraph suggested that the best solution to choose was the one containing 9 factors. The results obtained by regressing the 2 ,d111 factors against the output indexes were the following: (A) Average value of reserves per deposit The best equations obtained were in all cases attained by the use of the 15-factors model. The lead reserves rendered an equation with an R 2 of 34%, and a standard error of the estimate of 887.56. The zinc reserves rendered an equation explaining 79.02% of the variance of the response, with a standard error of 352.35, and the copper reserves rendered an equation explaining 99.58% of the variance of the response with a standard error of 12.22. Comparing these results with those of the general geological models (Table 7.9), it may be seen that the equation for lead is slightly worse in the present case, that the one of zinc is markedly worse,and that the one for copper output has a much better R2 but a markedly higher stand- ard error of the estimate. (B) Number of deposits per cell As with the previous production parameter, the best results were also obtained when the 15-factors model was used. The forecast of lead deposits gave an equation that explains 19.38% of the variance of the response, with a standard error of the estimate of 8.35. The best equation found for the estimation of zinc deposits explained 93% of the variance of the response, with a standard error of 1.34; and the regression performed to forecast the number of copper deposits rendered the best equation containing 9 variables and explaining 100% of the variance of the response, with a standard error of 0.0012.. If these results are compared with those of the geological models indicated in Table 7.9, it may be seen that the geological models discussed in Chapter 7 are more efficient and significant than those in the cases of the number of lead and zinc deposits. On the contrary, in the case of the number of copper deposits, the factorized model gave much better results 2 1 I than the raw-data. A careful weighting of the results attained with the factorization of the geological data, against the results of the geological models built up with the raw-geological data, and against the difficulties in interpret- ation posed by the factorized models, leads to the conclusion that factor- ization of the geological data prior to the regression analysis is not a very adequate tool to use in the present case for forecasting purposes. This fact is especially so, if it is considered that the main aim in using the technique with these variables, is to reduce the number of independent variables, a premise that in no case is achieved. Therefore, after these investigations, the use of factorized geological models was abandoned. 8.2.3.3 Discussion of results The causes for the little use that can be made in the present case of factor analysis, are complex. On one hand, statistical causes could be argued, which would indicate that the method as it is normally used is not suited for the purposes aimed at in this research. On the other hand, the behaviour of the variables could be explained in terms of their geological nature (as opposed to their statistical nature), and by • the complex structure of their relationship, which would be fundamental in obtaining a clear expression of the geology-mineralization relationship. Several hypotheses can be tentatively entertained in this context. In the opinion of the author, the most important of these is that it may be assumed that although factors are meaningful while visualized from a regional point of view, when they are applied to localized geological features (as mineralization) their meaningfulness cases to exist, possibly as a result of the lack of connection between the different factors. That is, it may be postulated that when dealing with regional geological vari- ables, the presence of strong relationships between them is more an advan- tage than a hindrance, if localized features are to be investigated. That hypotheis points towards two characteristics of the geolog- ical features: Their fundamental dependence on the geological system (environment) as a whole, and their localized dependence on particular relationships displayed by the parameters that constitute the system (i.e. local controls). Therefore, the use of independent pieces-of information that are part of the whole system but do not define it (i.e. are necessary though not sufficient conditions), is not likely to reveal at its best the minor components of the environment, such as mineralization. Other hypotheses that may be brought forward to explain the behaviour of the factors, are related to the nature of the technique itself. Factor analysis, as all the statistical techniques that make use of correlation matrices, is a method highly sensitive to the number of samples included in the analysis, especially when the frequency distributions of the variables are not smooth, and very high or low values are likely to occur in some observations. In this case, factor scores would also be variables depending on those features of the population, and thus would be distorted by averaging, rendering much meaningful information the greater the number of samples included in the analysis. The annotated fact indicates a strong disadvantage that factor analysis appears to have for the purposes aimed at in this research, and which is related to the fact that the forecasts need to be calculated on a subset of the whole population (control cells or training set). If- factorization is performed with the observations of the control cells, the resulting scores cannot be successfully applied to a study area, when the resulting model is extrapolated. On the other hand, if factorization is performed on the whole set, and only the scores of the control area are used during regression, this partitioning would introduce errors in the results obtained, since the factors appear to lose consistency when the set is separated into sub-sets. Apparently, this fact is fundamental in giving results much worse than could be expected. In addition, the geological and geochemical data as used for purposes of forecasting, present the problem of the constant sum, that is the variables tend to add to 100 in each observation, rendering in many cases non-zero correlations or trends that are not a result of real inter- relations among the variables, but are the result of a constraining effect produced by the fact that the value of a determined variable in an obser- vation is not independent, but is fixed by the values of the remaining variables. Miesch (1969), Chayes (1960, 1962), and other researchers, have pointed out this problem, for which no clear solution has been devised yet. Another probable cause for the inefficiency of factor analysis in this case, is related to the type of variables that the scores represent. When a solution is rendered into a space matrix (scores), background noise produced by non-significant loadings present in the factor, would distort the actual value of the factor in the observations, thus giving theoret- ical variables that depart from what may be considered the optimum value of the solution for each observation. Unfortunately, this departure from the optimum value is not systematic, and thus its, importance is in many cases hard to assess and even to realize (see in this respect Chapter 6). Alternatives to obviate the previous shortcomings, but which were not investigated in the present research, include the use of the variance- covariance matrix and not of the correlation matrix as starting point of the analysis, the estimation of communalities by multiple regression prior to the analysis, the expression of the- values of each variable in an observation as ratios between that variable and other variables under investigation, and the use of the significant loadings only, while calcul- ating the factor scores. The aforementioned are considered the most important arguments that can be postulated to explain the behaviour of the factors computed in • 259 the present case. Those arguments indicate that, at least in the realm of mineral exploration, factor analysis should be used with extreme care, until further investigation to clarify several obscure aspects of the technique are performed. 8.3 EVALUATION OF REGIONAL GEOCHEMISTRY IN THE FORECASTING OF MINERAL POTENTIAL Several methods can be envisaged to evaluate the efficiency of the forecasting models designed in this research on the basis of regional geochemical data. Taking into account the very good quality of the geo- logical data employed in the design of the remaining models, it is considered that the best approach that can be taken is to compare by different means the efficiency of the various models, and to analyze the results of the comparison in the light of the present duality optimum geological information= non-optimum geochemical data. That is, if the efficiency of the geochem- ical models approaches that of the geological models, and if the addition of geochemical data to geological information improves the forecasts, the use of regional geochemical information should be considered adequate fot the purposes of forecasting mineral potential of broad regions. In the following paragraphs, the evaluation is done in two stages Initially, a qualitative-quantitative approach is taken, where the fore- casts obtained by multiple regression are tested against the empirical and quantitative models obtained in the preceeding section. Later on, the efficiency of the models is discussed in statistical terms, by comparing statistics inherent to the models and by the use of multiple discriminant analysis. 8.3.1 Qualitative-quantitative evaluation of the •eochemical models The estimates obtained in the previous section indicated that 73 of the 106 cells of the area should be considered favourable towards • 260 containing base metal mineralization. Of those cells, 12 would only contain copper ores, 30 would only contain lead and zinc ores, and 31 would have lead, zinc,and copper ore bodies. The models built by means of multiple regression gave positive estimates for the following number of cells, as grouped into the same three categories: Combined Models: 53; Geochemical Models: 72; Geological Models: 89. The respective departures from the optimum qualitative estimates are 27%, 1% and 21%. The total number of cells with positive forecasts that coincide with cells selected qualitatively, is the following: Lead and Zinc Reserves Copper feserves Combined Models 38 (63%) 10 (24%) Geochemical Models 43 (69%) 18 (44%) Geological Models 39 (64%) 24 (58%) If the above figures are expressed in terms of the respective total number of cells with positive forecasts, a measure of the degree of success of the models designed may be obtained: Lead and Zinc Reserves Copper Reserves Combined Model 76% 58% • Geochemical Model 80% 64% Geological Model 73% 48% As may be seen, the geochemical models are the ones that do best as compared with the qualitative estimates. It may also be seen, that the combination of geochemical and geological data improves the efficiency that is obtained with the latter type of information. Considering only those cells that coincide in the regressed and qualitative forecasts, the following number of deposits may be forecasted in them by multiple regression and by the analysis of the distribution of the actual production figures: 261 Lead Deposits Zinc Deposits Copper Deposits Regression Simple Regression Simple Regression Simple Anelysis Estimate Analysis Estimate Analysis Estimate Combined Model 236 249 118 86 15 16 Geochemical 278 282 196 109 36 29 Model Geological 298 255 110 99 106 39 Model The deviations of the first group of forecasts with respect to the second group are: • Lead Deposits Zinc Deposits Copper Deposits Combined Model 5% 37% 6% Geochemical Model 1% 77% 24% Geological Model 17% 11% 171% As may be seen, the geochemical models do fairly well in fore- casting the number of deposits that may be expected in the favourable cells, with the exception of the model for the prediction of the number of zinc deposits, which gives higher estimates than what could be expected from the distribution of the known ore bodies. It is worth remembering in this context, that many deposits that do not register zinc output, might have had such ores, but due to economic or other reasons these ores were not beneficiated, and thus were not included in the statistics of production. It is also worth noting, that the geological model renders much higher estimates for the number of copper deposits than could be expected. Therefore, the forecasts of that model need to be viewed with care, when areas favourable for copper mineralization are selected. Considering the same cells as before, the present value of the reserves that may be expected according to the regressed models and to the distribution of the actual output, is the following (values in thousands of sterling pounds): 2 62 Lead Reserves Zinc Reserves Copper Reserves Regressed Simple Regressed Simple Regressed Simple Model Estimate Model Estimate Model Estimate Combined Model 233,229 323,944 63,122 100,572 10,788 1,893 Geochemical 274,736 322,361 104,848 165,638 25,839 4,304 Model Geological 294,501 305,241 58,843 118,096 40,302 12,674 Model The deviations of the regressed models with respect to the values estimated from simple statistics are: Lead Reserves Zinc Reserves Copper Reserves Combined Model 38% 59% 470% Geochemical Model 17% 58% 500% Geological Model 4% 101% 218% These figures indicate that the geochemical models do reasonably well as compared to the other models when total values of lead and zinc reserves are considered. Regarding copper reserves, the estimates are much greater than what could be expected, indicating that care must be exercised when that model is viewed in the light of defining areas favour- able for copper mineralization. It is worth noting in this respect, that the value of the copper reserves forecasted by all the models, are much higher than the one that may be estimated from the distribution of the actual production figures. This fact suggests that the copper production has been much smaller than what would be statistically expected, thus indicating the probable existence in the area of undiscovered copper reserves, which greatly surpass in value the production that has been raised until now. A final comparison between both types of forecast may be obtained by relating the total expected value of the reserves lying in the coincident 263 cells, to the number of deposits that may be forecast in those cells, thus rendering a measure of the expected average value of the reserves per deposit. The value attained by the latter index in both types of forecast for the different output categories considered, is the following (values in thousands of sterling pounds): Lead Reserves Zinc Reserves Copper Reserves Regressed Simple Regressed SiMple Regressed Simple Model Estimate Model Estimate Model Estimate Combined Model 1372 973 851 733 718 118 Geochemical 1159 974 844 961 717 148 Model Geological 1024 981 1073 594 380 325 Model The deviations of the regressed models with respect to the simple estimates are the following: Lead Reserves Zinc Reserves Copper Reserves Combined Model 41% 18% 508% Geochemical Model 18% 12% 384% Geological Model 4% 86% 20% This comparison once again indicates that the geochemical models do fairly well when forecasting lead and zinc reserves, as compared to the qualitative forecasts, and that the estimates for copper reserves are much higher than what could be statistically expected. Summing up the results of the previous comparison, the following points may be stated: (a) Regarding the identification of cells favourable for_base metal mineralization, the geochemical models are the best of all the models designed, with a rate of success of 80%, for the identification of potential lead or zinc-bearing areas, and a 64% rate of success while identifying areas favourable for copper mineralization. In both cases, the combination of geochemical and geological data renders better results than the use of • 4 geological data alone. (b) Regarding the forecast of the number of the different base metal deposits that may be expected in the area, the geochemical models Appear to be better than the geological ones for forecasting the number of lead and copper deposits; in those cases, the combination of geochemical and geo- logical data greatly improves the estimates. In the case of the number of zinc deposits, the geochemical models perform worse than the other models, rendering estimates much high estimates than could be statistically expected. It cannot be ascertained if the latter fact is a consequence of a real defect of the model, or if it is a consequence of defects in the statistics of output, which would indicate much fewer zinc-bearing deposits than really exist. In this respect is is worth considering that, as a way of example, it was not until the last stages of exploitation of the ore bodies in the Lake District, that it was realized that many of the "lead" deposits contained sphalerite as their main constituent; therefore, many of the ore bodies of that area are not considered in the statistics as zinc- bearing deposits, although they contained important amounts of zinc ores. (c) Regarding the value of the forecasted reserves, it may be concluded that the geochemical models do reasonably well in the case of the lead and zinc forecasts, but give grossly high estimates when the value of the copper reserves is predicted. Apparently, this fact is not a defect of the geo- chemical model, but is a feature shared in a greater or lesser extent by all the models designed, thus suggesting that the production of copper has been much smaller than could be expected from the geological and geochemical characteristics of the area. Therefore, the probable presence of important undiscovered copper reserves may be inferred from the foregoing feature of the models, rendering unreliable the estimates based solely on the consider- ation of the statistical distribution of the actual copper output. • 2 6 5 8.3.2 Evaluation of the geochemical models in terms of their basic statistics As indicated in Chapter 7, when dealing with the general theory of multiple regression analysis, two basic statistics inherent to regression models may be used to evaluate their efficiency: The multiple correlation coefficient and the standard error of the estimates. The first of these, if squared and expressed as a percentage, indicates the amount of the var- iance of the phenomenon under investigation which is explained (i.e. accounted for) by the model, and the second statistic may be visualized as the mean deviation of the estimates from the true mean of the observations of the dependent variable. As was also indicated, the value of these statistics is highly dependent on the number of parameters included in the model, and therefore they need to be standardized in a convenient way in order to compare models that have different numbers of independent variables in them. In this research, the parameters were standardized by means of an expression devised by Golberger (1967) for the case of the multiple correlation coefficient, and by expressing the standard error as a percentage of the mean response, If absolute production figures are considered, the following statistics may be obtained from the models designed: Lead Reserves Zinc Reserves Copper Reserves 2 R St. Error R2 St. Error R2 St. Error Combined Model 68.3 114.4 100.0 3.4 100.0 0.003 Geochemical Model 38.0 169.2 100.0 1.0 99.9 11.6 Geological Model 26.3 179.2 93.2 7.6 99.9 4.3 These figures indicate that the geochemical models perform better in all respects than the geological models, if lead and zinc reserves are considered. Regarding copper reserves, even though both types of model explain a similar amount of the variance of the response, the standard error 6 of the geochemical estimates is much greater than the one of the geological estimates, and thus the former estimates must be considered worse. This fact, as already indicated, is related to the very high estimates that the geochemical model gives for copper reserves. In this case, it may also be seen that the addition of geochemical information to geological data, greatly improves the estimates obtained with the latter type of information. This tendency is so marked, that in no case would the geological models be considered as the best for forecasting purposes. If the forecast of the number of deposits per cell is considered, the following statistics may be obtained from the models designed: Lead Reserves Zinc Reserves Copper Reserves R2 St. Error R2 St. Error R2 St. Error Combined Model 67.6 83.5 100.0 - 0.2 100.0 0.0 Geochemical Model 39.6 107.3 100.0 0.1 100.0 0.7 Geological Model 23.9 120.5 100.0 1.2 100.0 0.5 These figures indicate that for lead and zinc reserves, the geo- chemical models perform much better than the geological ones, and that for copper reserves the latter perform slightly better. It is also evidenced in this case, that the combined models are in all instances better than the geological models, and that the latter cannot be chosen in any case as the best representatives of the parameters-mineralization relationship. Regarding the forecast of the average value of the reserves per deposit, the following statistics may be obtained from the models: Lead Reserves . Zinc Reserves Copper Reserves R2 St. Error R2 St. Error R2 St. Error Combined Model 66.7 94.5 100.0 0.005 100.0 0.06 Geochemical Model 25.6 144.0 99.9 5.5 100.0 0.3 Geological Model 35.1 132.5 92.5 48.9 100.0 0.008 These statistics indicate that all the three models have similar • in laY Eli 4-1 g efficiency in forecasting the average value of the copper deposits. Geo- chemical models are more efficient than geological models for estimating the value of zinc reserves, and are less efficient for predicting the value of lead reserves. However, the addition of geochemical data to geological parameters, greatly improves the forecasting efficiency of the latter regard- ing lead and zinc reserves. Considering that convergent regression of production indexes is postulated in the present research as the most efficient method of forecast- ing, the performance of the individual models may be further assessed by comparison of the final predictions obtained by convergent regression, with the actual output figures of the productive cells. That comparison may be done by means of three statistics: (a)The correlation coefficient squared and expressed as a percentage; (b)The index of forecasting efficiency o. IFE ((1-V77172) x 100), a statistic that is also expressed as a percentage indicating the reduction obtained with the models in the errors of the predictions, as compared to predictions based on chance alone; and (c) the standard error of the estimate expressed as percentage of the mean response. The computed statistics are the following: Lead Reserves Zinc Reserves Copper Reserves R2 IFE St.Error R2 IFE St. Error R2 IFE St. Error Combined Model 71.4 48 104 98.4 87 27 98.6 88 32 Geochemical 37.4 21 158 98.4 87 27 100.0 100 0 Model Geological 26.1 14 174 98.0 85 31 100.0 100 0 Model From these figures it may be concluded that the geochemical fore- casts obtained by convergent regression of production indexes are, in all cases, more or less equally efficient to the geological estimates, and that the combined models increase the efficiency of the indiVidual parameters in most cases. 238 Regarding the indicated statistics, it must be considered that they do not reflect how the individual predictions behave, but only reflect the behaviour of the mean forecast against the respective mean production. Summing up the results of the previous comparison, the following points may be concluded: (1) Regarding the forecast of the total value of the reserves and of the number of deposits per cell, the geochemical models perform better in all respects than the geological models, if lead and zinc reserves are considered. For copper reserves the geological models perform better than the geochemical ones, probably as a result of the very high estimates rendered by the latter. In most cases it may be seen that the combination of geochemical and geological parameters greatly improves the efficiency of the estimates,. a tendency that is so marked that the geological models would in no case be chosen as the best to use for the purposes of this research. (2) With respect to the prediction of the average value of the reserves per deposit, all models are similarly efficient when copper reserves are considered, the geochemical model being more efficient than the geological one regarding zinc reserves, and less efficient when estimating lead reserves. In this case, the forecasts are also improved by the combination of geological and geochemical information. (3) Considering the final results of the research, which were obtained by convergent regression of production indexes, it may be concluded that the geochemical forecasts are equally efficient as the geological predictions, and that the combination of both types of information improves the forecast- ing efficiency of individual parameters in most cases. 8.3.3 Evaluation of the geochemical models on the basis of multiple discriminant analysis Discriminant functions are used for the study of_samples from populations located at different places of a multidimensional space, with • 23- 9 the purpose of establishing criteria that allow their separation. The main objective of the technique is to develop one or more combinations of the variables that define the observations, such that they constitute orthogonal theoretical variables which capitalize upon differences among the populations , by minimizing the ratio of the differences (distances) between the multivariate means of the populations to the multivariate variance within the groups. That is, an orthogonal set of axes is sought, along which the clusters (populations) show their maximum separation with the minimum deformation of their original structure. A comprehensive account of the technique may be found in Krumbein and Graybill (1965), Hope (1968), Cooley and Lohnes(1971), Koch and Link (1971), Davis (1973), and in general in most modern textbooks dealing with multivariate techniques of statistical analysis. Applications to geolog- ical and geochemical problems may be found in Cameron and others (1971), Howarth (1971a,1971b), De Geoffroy and Wignall (1970), and Castillo-Mui-loz (1973). Two main ways of operating with multiple discriminant functions may be envisaged: The first considers the establishment of criteria for the separation between selected populations known a priori to be different, the analysis of the significance of the separation, and the localization of the best reduced-rank model to describe the differences-between the groups; all these aspects lie under the scope of discrimination. A second way of operating is to establish discriminant functions for known groups, and to use those functions as a means of evaluating the probability of a new observation belonging to any of the groups known a priori. The latter approach, which was used in this research to classify the forecasts of the different models on the basis of actual production populations, falls under the scope of classification methods, the class- ification being based on the computation of diScriminant scores, variables • 2 7 0 that are finally used for the estimation of probabilities of classification. In this case, the observations may be considered as having equal probability of belonging to any group, or a priori knowledge about the populations is used, and a priori probabilities of existence are assigned to each group. Obviously, the last way of operating, which is a combination of discriminant and Bayesian analysis, renders the best results. However, in many instances the assignation of a priori probabilities to each group may be dangerous, because it implies that the behaviour of the phenomenon under investigation is totally known, which in many instances is not so. In the present case, a priori probabilities could be assigned to each prod- uction group on the basis of the frequency distribution of the known out- put; this assignation would imply that the known distribution accounts for all the reserves existing in the productive cells, that is, it would mean that all the reserves in those cells have been raised, no ore being left in them. In the opinion of the author, this would be a very dangerous opinion to sustain, especially when important amounts of ore (mainly copper and zinc ores) may be suspected to exist in several of those cells.. There- fore, in the present analysis the observations were considered as having equal probabilities of belonging to any of the output groups distinguished. The main objective of using multiple discriminant analysis in this case, was to analyze the behaviour of individual forecasts, as opposed to the analysis of the behaviour of the model as a whole, done in the previous sections. For this purpose, the following procedure was . implemented: (a) The productive cells of the area were subdivided into two groups for each of the output categories distinguished (lead, zinc, copper). The distinction was done on the basis of the present value of the output, the cells being separated in the following groups (output values in thousands of sterling pounds): • 2 7 1 GROUP 1 GROUP 2 Output Category Value No. of Samples Value No. of Samples Lead Productive Cells 1-10,000 29 >10,000 9 Zinc Productive Cells 1-500 9 >500 4 Copper Productive Cells 1-150 9 >ISO 2 That is, the first group represents low-productive cells and the second group represents high-productive cells. (b) Three sets of discriminant functions were calculated for each output category, on the basis of the variables included at any stage of the cal- culation of the geochemical, geological and combined models. The signif- icance of the discriminant models was assessed by means of the Mahalanobis' d2-statistic, which measures the generalized distance between the multi- variate means of the groups as a function of the ratio of their multivariate means to variances. The functions obtained and their d2-statistics are summarized in Table 8.3 for each of the nine cases analyzed. (c) On the basis of (b), discriminant scores were calculated for each observation, and the probablities of their belonging to either group were estimated, to obtain a measure of the discriminant efficiency of the models (Table 8.3). (d) Subsequently, discriminant scores were computed in each case for the 106 cells that constitute the population used in this research, and the probabilities of their belonging to either group were calculated. The function with the highest probability was considered the best classification that could be assigned to each cell, as long as that probability exceeded 0.7; if both probabilities were lower than that figure, the cell was assigned to a "barren" category. (e) Once the cells were classified according to (d), contingency tables were prepared, where the classified observations were tabulated against the output category corresponding to each of them according to the forecasts TABLE 8.3 MAIN FEATURES OF DISCRIMINANT FUNCTIONS FOR THE CLASSIFICATION OF PRODUCTIVE CELLS INTO HIGH AND LOW (y1 = Low output category; y = High output cateory) 2 Type of Reserves Type of No. of Discriminant Mahalanobis Degrees Model Variables Efficiency D-Square of Freedom Lead y = 86% 339.56 68 Combined 17 1 y = 77% 2 Geochemical 10 y = 86% 231.53 40 1 y = 66% 2 Geological 5 Y = 79% 232.63 20 y = 55% 2 Zinc Combined 18 y = 88% 285.42 72 1 y = 75% 2 Geochemical 14 y =77% 119.70 56 1 y = 75% 2 . 12 y = 88% 179.57 48 Geological 1 y = 75% 2 Copper Combined 16 y = 100% 178.53 51 1 y = 100% 2 Geochemical 12 y = 77% 157.22 39 1 y = 100% 2 Geological 13 y = 77% 275.59 39 1 y = 100% 2 • 2 7 2 obtained from the different models designed. Following the indicated procedures, nine discriminant models were examined, rendering the contingency tables indicated in Table 8.4. In those tables, the efficiency of each model is calculated as the ratio of coincidence between both classifications to the total number of cells. According to those results, the following overal efficiency may be estimated for the different types of model: Combined Model : 76.4% Geochemical Model: 70.3% Geological Model : 70.0% These figures indicate that the rate of successful forecasting for the geochemical models is similar to the rate of the geological models, and that the combined models render the best results, with an important increase in the rate of success that may be achieved using individual sets of parameters. Regarding the behaviour of individual forecasts for each of the output categories distinguished, the following points are worth noting: (a) The geochemical models perform well when fWecasting lead or copper reserves, but their performance is less than average when forecasting -zinc reserves; (b) The geological models are at the best of their efficiency when forecasting lead and zinc reserves, but are very poorly efficient when forecasting copper reserves; (c) The combined models are the best to use to forecast copper or zinc reserves, but their performance in predict- ing lead reserves is rather poor as compared to the other models. Taking into account that the number of barren cells greatly exceeds that of mineralized cells, a second approach was taken for the evaluation of geochemical models, this time to anaylze the efficiency of the positive forecasts, which would ultimately be the predictions that would be used in mineral exploration. For this purpose, a procedure TABLE 8.4 CONTINGENCY TABLES OF FORECAST CLASSIFIED INTO OUTPUT CATEGORIES BY MULTIPLE DISCRIMINANT ANALYSIS LEAD RESERVES ZINC RESERVES COPPER RESERVES Combined Model Combined Model Combined Model Forecasting Forecasting Forecasting Category Category Category Barren 1 2 Barren 1 2 Barren 1 2 Discrim- Discrim- Discrim- inant Category inant Category inant Category Barren 54 2 0 Barren 62 0 0 Barren 76 0 0 1 20 14 3 1 6 1 7 1 9 4 4 2 1 3 9 2 2 1 17 2 4 3 6 Efficiency: 72.8% Efficiency: 75.5% Efficiency: 81.1% Geochemical Model Geochemical Model Geochemical Model Forecasting Forecasting Forecasting Category Category Category Barren 1 2 Barren 1 2 Barren 1 2 Discrim- Discrim- Discrim- inant Category inant Category inant Category Barren 48 0 0 Barren 58 0 12 Barren 63 2 3 1 13 20 5 1 10 1 6 1 2 6 5 2 0 10 10 2 9 1 9 2 3 2 10 Efficiency: 73.5% Efficiency: 64.1% Efficiency: 74.5% Geological Model Geological Model Geological Model Forecasting Forecasting Forecasting Category Category Category Barren 1 2 Barren 1 2 Barren 1 2 Discrim- Discrim- Discrim- inant Category inant Category inant Category Barren 45 0 ■0 Barren 67 0 6 Barren 41 5 4 1 13 27 5 1 14 0 2 1 7 3 9 2 0 3 13 2 4 0 13 2 9 14 14 Efficiency: 30.1% Efficiency: 75.5% Efficiency: 54.7% TABLE 8.5 CONTINGENCY TABLES OF POSITIVE FORECAST CLASSIFIED INTO OUTPUT CATEGORIES BY MULTIPLE DISCRIMINANT ANALYSIS LEAD RESERVES ZINC RESERVES COPPER RESERVES Combined Model Combined Model Combined Model Forecasting Forecasting Forecasting Category Category Category 1 2 1 2 1 2 Discrim- Discrim- Discrim- inant Category inant Category inant Category 1 16 3 1 1 15 1 4 4 2 3 9 2 1 19 2 3 6 Efficiency: 80.6% Efficiency: 55.5% Efficiency: 58.6% Geochemical Model Geochemical Model Geochemical Model • Forecasting Forecasting Forecasting Category Category Category 1 2 1 2 1 2 Discrim- Discrim- Discrim- inant Category inant Category inant Category 1 28 5 1 1 11 1 7 5 2 2 10 2 1 16 2 3 13 Efficiency: 84.4% Efficiency: 58.6% Efficiency: 71.4% Geological Model Geological Model Geological Model Forecasting Forecasting Forecasting Category Category Category 1 2 I 2 1 2 Discrim- Discrim- Discrim- inant Category inant Category inant Category 1 27 5 1 1 11 1 7 10 2 3 13 2 1 16 2 15 17 Efficiency: 83.3% Efficiency: 76.1% Efficiency: 48.9% • 273 similar to the one previously indicated was followed, but in this case the assignation of each positive forecast to a category was done choosing that category with the highest probability, irrespective of the value of that probability. By this means, another set of contingency tables was obtained in similar fashion as before (Table 8.5). From those tables, the follow- ing overall efficiencies may be estimated for the different types of model: Combined Model : 74.3% Geochemical Model: 73.5% Geological Model : 67.7% From the above results it may be seen that the overall success of the geochemical models to forecast the favourable cells is greater than the'success of the geological models, and that the combination of both types of information renders in general the best results. Regarding the behaviour of the positive forecasts for each category considered, the following points are worth mentioning: (a) As for the classification of the whole group of cells, the geochemical models perform well when forecasting lead and copper reserves, but have a perform- ance below the average when predicting zinc reserves; (b) The geological models present their best efficiency when forecasting lead or zinc reserves, but are poorly efficient when forecasting copper reserves;, (c) The combined models designed perform worse than the remaining models when fore- casting favourable cells, with the exception of copper predictions when the model does better than the geological one, but well below the efficiency of the geochemical model; (d) In general terms, it may be seen that the efficiency of the models for the forecast of zinc and copper` reserves diminishes when only the positive cells are considered, while in that case the models for the forecast of lead reserves increase their efficiency. The latter fact indicates that the models to predict zinc and M 2 7 4 copper reserves have a better resolution for distinguishing between barren and potentially mineralized cells, than the lead models. However, the efficiency of the former two types of model to distinguish between high and low-mineralized cells, is less than the one of the models to predict lead reserves, thus giving a similar and balanced final result. Probably, those differences in partial efficiency could be a result of the contrasting number of mineralized cells available for the definition of the production groups, which in the cases of copper and zinc are fairly low (13 and 11, respectively). In the opinion of the author, the foregoing analysis of the efficiency of individual forecasts, is not enough when dealing with mineral exploration problems, because that analysis takes into account only the rate of success of the models, disregarding the nature of the failures. That is, the analysis only gives an answer to the problem of assessing how good the models are, but does not answer the problem of how bad the failures are. The latter problem is fundamental in mineral exploration, because its resolution allows a clear picture of the risks involved, in the sense that it gives a measure of the possible losses in capital and in opportun- ity that may be incurred by the application of the different models for the selection of target areas. In order to investigate that problem, a procedure similar to the one indicated previously was followed, but in this case contingency tables were computed using a success-failure system of scores, assigned to the forecasts on the basis of the following conventions, which are based on the consideration that the discriminant classification is correct: • 4 2 7 5 Forecast as Compared to Discriminant Classification Score Justification Barren Forecasts Coincident Classification +5 One category above -1 Loss of minor opportunity Two categories above -2 Loss of major opportunity Forecasts Group I Coincident classification +5 One category above -1 Probable loss of opportunity One category below -3 Minor loss of capital Forecasts Group II Coincident forecast +5 One category below -3 Minor loss of capital Two categories below -4 Severe loss of capital On that basis, the contingency tables indicated in Tables 8.6 and 8.7 were constructed, for all the forecasts and for the positive forecasts. From those tables, the following scores may be assigned to each model: All Forecasts Positive Forecasts Model Success Score Failure Score Success Score Failure Score Lead - Combined 385 40 125 12 Geochemical 390 38 190 17 Geological 425 31 200 18 Zinc - Combined 400 72 100 46 Geochemical 340 95 85 34 Geological 400 52 80 15 Copper - Combined 430 32 50 15 Geochemical 395 43 90 18 Geological 290 67 120 45 • TABLE 8.6 CONTINGENCY TABLES OF SCORED FORECASTS AS COMPARED TO CLASSIFICATION OF CELLS BY MULTIPLE DISCRIMINANT ANALYSIS LEAD RESERVES ZINC RESERVES COPPER RESERVES Combined Model Combined Model Combined Model Forecasting Forecasting Forecasting Category Category Category Barren 1 2 Barren 1 2 Barren 1 2 Discrim- Discrim- Discrim- inant Category inant Category inant Category Barren 270 6 0 Barren 310 0 40 Barren 380 0 0 1 20 70 9 1 6 5 21 1 9 20 12 2 2 3 45 2 4 1 85 2 8 3 30 Geochemical Model Geochemical Model Geochemical Model Forecasting Forecasting Forecasting Category Category Category Barren 1 2 Barren 1 2 Barren 1 2 Discrim- Discrim- Discrim- inant Category inant Category inant Category , Barren 240 0 0 Barren 290 0 48 Barren 315 6 12 1 13 100 15 1 10 5 18 1 2 30 15 2 0 10 50 2 18 1 45 2 6 2 50 Geological Model Geological Model Geological Model Forecasting Forecasting Forecasting Category Category _ Category Barren 1 2 Barren 1 2 Barren 1 2 Discrim- Discrim- Discrim- inant Catego inant Category inant Category Barren 225 0 0 Barren 335 0 24 Barren 205 15 16 1 13 135 15 1 14 0 6 1 7 15 27 2 0 3 65 2 8 0 65 2 r8 14 70 TABLE 8.7 CONTINGENCY TABLES OF POSITIVE FORECASTS AS COMPARED TO CLASSIFICATION OF CELLS BY MULTIPLE DISCRIMINANT ANALYSIS LEAD RESERVES ZINC RESERVES COPPER RESERVES Combined Model Combined Model Combined Model Forecasting Forecasting Forecasting Category Category Category 1 2 1 2 1 2 Discrim- Discrim- Discrim- inant Category inant Category inant Category 1 80 9 1 5 45 1 20 12 2 3 45 2 1 95 2 3 30 Geochemical Model Geochemical Model Geochemical Model Forecasting Forecasting Forecasting Category Category Category 1 2 1 2 1 2 Discrim- Discrim- Discrim- inant Category inant Category inant Category 140 15 1 5 '33 1 35 15 2 2 50 2 1 80 2 3 65 Geological Model Geological Model Geological Model Forecasting Forecasting Forecasting Category Category Category 1 2 1 2 1 2 Discrim- Discrim- Discrim- inant Category inant Category inant Category 1 135 15 1 0 15 1 35 30 2 3 65 2 0 80 2 15 85 2 Et Several ways may be envisaged to analyze.those scores (ratios, partial percentages of optimum, etc.). In this research it was considered that the best way is to regard the failure scores as penalties that should be discounted from the success scores, rendering a final score that would give a precise indication of the value of the model as a fore- casting tool. By this means, the following final scores may be assigned to each model (models given in descending order of efficiency and scores expressed as percentage of the optimum): Model All Forecasts Model Positive Forecasts Copper - Combined 75% Lead - Geochemical 76% Lead - Geological 74 Lead - Geological 75 Lead - Geochemical 66 Lead - Combined 72 Copper - Geochemical 66 Zinc - Geological 61 Zinc - Geological 65 Copper - Geochemical 51 Lead - Combined 65 Copper - Combined 41 Zinc - Combined 61 Zinc - Geochemical 35 Zinc - Geochemical 46 Copper - Geological 30 This listing shows that when all the cells are considered, the geochemical models perform rather well when predicting lead and copper reserves, but perform below the average when estimating zinc reserves. The geological models give good results when estimating lead or zinc reserves, but their forecasts are poor for the case of copper ores. Combined models render good results when predicting copper reserves, but do not perform as well as the remaining models when lead and zinc reserves are to be forecasted. When only the positive forecasts are considered, it may be seen that all the models for the forecast of lead reserves are very efficient, while the models for the prediction of zinc and copper 2 7'7 reserves are much less accurate. Once again, the geochemical models give a clear differentiation between high and low-mineralized cells for the cases of lead and copper, but have poor resolution for zinc reserves. Geological models are efficient in separating lead and zinc reserves, but have very poor resolution in distinguishing cells with different copper potential. Combined models are efficient in differentiating lead reserves, but do not perform as well as the remaining models for the forecast of zinc and copper reserves. Summing up the results of the latter analysis, which is considered the most logical way to assess the mineral exploration potential of the models designed, the following conclusions may be drawn: (a) The geochemical models are efficient in differentiating barren areas from areas with copper and lead potential; within those areas, these models are very efficient for distinguishing the ones with low potential from those with high potential. The efficiency of these models to distinguish barren areas from areas with zinc potential is below average. (b) The geological models are very efficient for predicting areas with lead and zinc potential, and for distinguishing within them those with the most important possibilities. Regarding the prediction of copper reserves, the efficiency of these models is very poor. (c) Combined models are efficient to separate barren areas from areas with zinc and copper possibilities, though they do not perform well in differentiating them according to their potential. For the case of lead reserves, these models do not perform as well as the remaining models. • 2 7 8 In order to obtain a complete picture of the efficiency of the models designed, the analysis of their overall success-failure rate appears worth performing. Using similar scores as before, the following overall efficiencies may be estimated: All Forecasts Positive Forecasts Combined Models 67% 48% Geochemical Models 59 58 Geological Models 60 55 These figures indicate that on the whole, the geochemical models perform similarly to the geological models, and that the combin- ation of geochemical and geological information gives the best results to separate, within a broad region, the areas that are likely to be barren from the areas that are likely to contain base metal mineralization. In addition, it may be concluded that the best general way to analyze the forecasts is to use combined models to separate barren, from mineralized areas, and to use geochemical models to separate-within the latter-those that have high potential from the ones with low potential. 8.7 FINAL EVALUATION OF THE MODELS DESIGNED In the preceeding section, several ways of evaluating the efficiency of the geochemical models designed, as compared with the other types of model, were discussed. The conclusions attained from the different kinds of evaluation performed, indicate that, in general terms, the best models to use for the forecast of the base metal potential of the area, would be combined models, supported by predictions obtained by means of geochemical models. However, it was also concluded that the efficiency of the different models was not consistent for the different types of reserves to forecast, but it varies within fairly broad limits. Worth remembering 2 7 3 in this respect, is the low efficiency of the geochemical models to predict zinc reserves, and the very poor performance of the geological models in predicting copper reserves. Taking into account the foregoing general conclusions, and considering that for the purposes of mineral exploration a unique figure for each area is required for each base metal, the need of establishing a global way of analyzing the efficiency arises, in order to select the best procedure to follow in the estimation of those potential reserves. The selection of the best procedure to use, should be based on two measures of the efficiency of each model: (1) The efficiency as defined by the index of forecasting, which .14 relates the estimates to actual production figures, and (2) the performance of the model as defined by its index of discriminant efficiency, which reflects the ability of the variables on which the estimates are based, to differenciate among the cells those with mineral potential. Therefore, the need for a final index of total efficiency. is obvious, a measure that would translate into a unique figure both independent measures of efficiency. In this case, the final index was obtained by weighting the index of discrimination by the index of forecasting, for all the cells and for those with positive forecasts. By this means, the following values were obtained for the performance of the models in separating barren from potentially mineralized cells: 2 8'1 Model Index of total efficiency. Lead - Combined 31.2% - Geochemical 13.8 - Geological 10.3 Zinc - Combined 53.0 - Geochemical 40.0 - Geological 55.2 Copper - Combined 66.0 - Geochemical 66.1 - Geological 42.0 Similarly, indexes of total efficiency may be calculated to analyze the performance of each model in relation to its ability to discriminate between areas with low and high potential: Model Index of total efficiency Lead - Combined 34.5% - Geochemical 15.9 - Geological 10.5 Zinc - Combined 26.1 - Geochemical 30.4 - Geological 51.8 Copper - Combined 36.0 - Geochemical 51.0 - Geological 30.0 From these total efficiencies, a procedure may be selected to forecast the mineral potential of the area subdivided into its component base metals. 0 2S The best procedure that can be envisaged is a two-stages one, in which in the first stage the cells with mineral potential are separated from the cells forecasted as barren, and in the second stage the mineral potential of the former cells is predicted on the basis of the model that gives the highest resolution in separating high from low-mineralized areas. In this context, for each of the three output categories distinguished, the following forecasting procedure can be envisaged as the best: Tyke of Reserves Stage 1 Stage 2 Lead Combined Model Combined Model supported by Geochemical Model Zinc Geological Model Geological Model supported by Geochemical Model Copper Geochemical Model Geochemical Model . supported by Combined Model This two-step procedure is applied in the next chapter, for the selection of areas in Northern England favourable for the presence of base metal Mineralization. • 2S CHAPTER 9 FINAL ESTIMATES AND PRELIMINARY GEOCHEMICAL INVESTIGATIONS IN SELECTED AREAS According to the procedure indicated in the previous chapter, in the following paragraphs the base metal mineral potential of all the cells within the studied area is given, together with confidence limits that may be computed for such potential. The results are indicated in thousands of sterling pounds, the reader being referred to Chapter 7 for the general method of computation and essential economic parameters that enable these final estimates. In addition, a brief account of preliminary geochemical investigations performed by the author in several areas is indicated. The selection of these areas was done on the basis of criteria -indicated in each individual case, the investigations comprising confirmation of anomalies detected during the regional reconnaissance, stream sediment sampling at selected locations of the drainage system, and soil sampling along traverses to detect possible mineralized structures related to the most obvious geological targets in each area. 9.1 FINAL ESTIMATES Following the conclusions reached in Section 8.4, different forecasting models should be used to assess the base metal mineral potential of the area, in terms of the metals that compose that potential (lead, zinc, and copper). As indicated, the best procedure to follow in this respect is a two-stage one, in which in the first stage the barren cells are eliminated, and in the second stage the cells with potential are discriminated according to the value of the forecasted reserves. It must be considered that many of the cells that are forecasted as "favourable" have had base metal production, and thus the present value of the latter should be discounted from the forecast to obtain final present potential values of the reserves still lying in each cell. In addition, it may be seen that the best model that can be applied in the • 2 first stage is different for each base metal, but those models are the same as should be used in each case in the second stage. Therefore, in order to further reinforce the results obtained, with the best model in the second stage, it was considered that the best way to proceed was to compute the optimum estimates according to the best respective model, and to regard as most favourable those cells that render a similarly high forecast when the second best model is applied (e.g. in the case of lead reserves, the forecasts of the combined model are supported by those of the geochemical model). According to the indicated procedure, the following estimates and 95% confidence limits can be considered for each base metal in the studied area. 9.1,1 Lead Reserves The final estimate of the potential lead reserves present in the area must be made mainly on the basis of the combined forecasting model designed. As an initial stage, this model can be used to separate the cells with potential from those barren (Table 7.20). By this means, 31 of the original 106 cells may be selected for further analysis, 9 of which have not had lead production until now (Cells 16, 24, 50, 55, 64, 65, 70, 90 and 91). Using the same model, a second stage of selection to differentiate between cells with high and low lead potential may be performed. Initially, the actual production in each of the favourable cells must be discounted from the forecasts, in order to eliminate all those cells that have had larger production that their forecast. The results of this computation are indicated in Table 9.1, where it may be seen that cells 25, 26, 71 and 106 have produced more than is forecasted for them, and therefore should be eliminated from a mineral potential view point, only 27 cells remaining as favourable for undiscovered lead reserves. TABLE 9 I FINAL FORECASTS - LEAD RESERVES (IN POUNDS X 1000) CELL P20OUC7ION FORECAST POTENTIAL CONFIDENCE LIMITS 7 882 3851 2969 0 6015 15 2247 8929 6692 3036 9728 16 -0 3557 3557 211 6903 17 22 4273 4251 603 7297 24 -0 11113 11113 7467 14159 25 56332 39625 0 0 26 57837 33689 0 0 27 21613 21785 172 3218 23 729 1298 569 3615 32 1357 2557 1170 4216 36 5604 24231 18657 1501 21703 37 12486 15613 3127 6173 38 15250 16810 1560 4o06 39 4645 9750 5104 145 8150 48 209 7711 7502 385 10548 50 -0 1300 1300 4345 51 5 3673 3973 22 6919 53 660 10799 10139 649 13155 34 16321 23321 7000 335 10046 55 -0 26622 26622 2297 29668 59 39 3562 3523 b569 64 -0 15032 15032 1133 13078 65 -0 13430 13430 9734 16475 70 -0 8421 8421 4775 11467 71 12735 12073 0 0 2384 72 4096 5366 4270 624 7316 82 1366 9960 8892 5246 11938 83 1442 4013 2571 0 5617 90 -0 9005 5005 5359 12051 91 -0 6507 6507 2861 9553 106 - 4998 2553 - 0 0 606 TABLE 9.3 FINAL FORECASTS - ZINC RESERVES (14 POUNDS X 1000) CELL PRODUCTION FORECAST POTENTIAL CONFIDrAC. LIMITS 5 -0 4430 4431 77 8783 5 -0 8345 8345 3992 12696 14 -0 12793 12793 8440 17146 15 -0 6232 6232 1879 10585 24 -0 2311 - 2311 0 5564 23 11650 11524 0 0 4227 26 2717 2634 0 0 4270 27 -0 3326 3323 0 6181 39 -0 3289 3239 0 7642 41 397 1102 705 0 5058 42 2318 1415 0 0 3450 45 -0 1513 1513 0 5866 52 -0 22106 22106 17753 25459 57 -0 3549 3548 0 7901 59 -0 1234 1234 0 5587 60 -0 530 850 0 5233 63 -0 19200 19200 14347 23553 72 -0 2280 2280 - 0 6633 74 -0 39144 39144 34791 43497 100 -0 7153 7183 2530 11536 101 -0 3573 3573 0 7926 TABLE 95 FINAL FORECASTS - COPP5R RESERVES (IN POUNDS X 1000) CELL PRODUCTION FORTCAST POTENTIAL CONFIOrNCE LIMITS 32 182 161 0 0 440 36 107 111 4 0 465 41 22 34 12 0 473 44 -0 143 148 0 609 52 -0 620 520 159 /081 53 13 25 15 0 475 56 -C 1265 1265 804 1726 63 -0 296 296 0 757 64 36 51 15 0 476 65 -0 375 678 417 1339 65 -0 921 921 460 138? 10 -0 71 71 0 532 75 2133 2133 0 0 461 77 -0 3557 3557 3096 4018 73 -0 2717 2'17 2256 3178 79 -0 2565 2585 2124 3046 89 -0 142 142 0 603 55 -0 3097 3397 2636 3558 36 -0 275J 2/50 2289 3211 87 -0 2476 2476 2015 2937 83 -0 2133 2133 1672 2594 90 -0 80 80 0 541 91 -0 0 0 0 461 94 -0 2475 2478 2017 2939 93 -0 172 172 0 633 99 -0 110 110 0 571 109 -0 561 561 100 1022 194 -0 1025 1025 564 1456 106 12 14 2 0 463 TABLE 9.2 RESIDUAL ESTIMATES - LEAD RESERVES (VALUES IN POUNDS x 1000) Cell Expected Actual Potential Estimate Confidence Limits No.of No.of No.of New Deposits Deposits Deposits 7 2 1 1 1925 0 8617 15 9 5 4 3967 0 10659 16 7 0 7 3857 0 10549 17 7 2 5 3052 0 9744 24 5 0 5 11113 4421 17805 27 14 15 0 0 0 0 28 4 4 0 0 0 0 32 1 4 0 0 0 0 36 25 21 4 3881 0 10573 37 14 26 0 0 0 0 38 11 14 0 0 0 0 39 7 6 1 - 1392 0 8084 48 9 2 7 5997 0 12689 50 4 0 4 1300 0 7992 51 5 1 4 3102 0 9794 53 6 4 2 3599 0 10291 54 3 3 0 0 0 0 55 2 0 2 26622 19930 33314 58 7 2 5 2544 0 9236 64 1 0 1 15032 8340 21724 65 6 0 6 13430 6638 20122 70 4 0 4 8421 1729 15113 72 8 4 4 4183 0 10875 82 6 3 3 4980 0 11672 83 6 4 2 1337 0 8029 90 12 0 12 9005 2313 15697 91 10 0 10 6507 0 13199 4 2 S 4 e Furthermore, it must be considered that the forecasts are based on- the prediction of a certain number of deposits per cell. Thus, in order to get reliable estimates, it becomes necessary to subtract the number of deposits actually worked from the number forecasted, and recalculate the estimates on the basis of the resulting figure. The final estimates obtained by this means are indicated in Table 9.2. It may be seen in that table, that six cells (27, 28, 37, 38 and 54) may be eliminated, only 21 cells remaining with possibilities of containing lead reserves in one or more ore deposits. Therefore, it may be estimated that 93 undiscovered deposits with lead reserves valued at £130,246,000 still lie in the studies area, a figure that represents 39% of the value of the lead production that has been raised until now, and which gives a lead endowment of £62,021 per square kilometre in the favourable cells. In order to select the most favourable areas for further investigation, an initial criterion of'separation could be to consider, among the favourable cells, only those with a forecast greater than £2.5m and an average value of the reserves in any of their deposits of Elm. Following this criterion, eight cells can be selected for further analysis: cells 24, 53, 55, 64, 65, 70, 72 and 82. Taking into account that the second best model to discriminate potential lead mineralization is the geochemical one, this model can be used for further refinement of the selection. It may be seen in Table 7.20, that cells 24, 53, and 55 have negative forecasts when the geochemical model is applied, and therefore these cells could be regarded as less likely to contain lead reserves. Thus, only cells 64, 65, 70, 72 and 82 should be regarded as primary targets. It is noteworthy that all these cells have geochemical forecasts greater than £5m. Now, considering the geological characteristics of the favourable cells, it may be seen that cells 70, 72 and 82 include favourable 24 3 5 watershed areas, that cells 70 and 72 contain extensive areas where the Upper Limestone Group constitutes the subsurface or is covered by younger horizons, and that cell 72 presents a large number of fault intersections, a feature favourable for the emplacement of lead ore bodies. In addition, if the geochemical samples within each cell are analysed, it may be concluded that cell 70 contains probably anomalous sites in Pb and Ba, cell 72 contains probably anomalous sites in Ba, cell 82 probably anomalous sites in Zn, and cell 65 probably anomalous sites in Pb. Furthermore, the two component factors considered to represent lead mineralization in the area (Cd-Zn-Pb and Ba-Pb) have anomalous values in cells 72 and 82, and 72, respectively. Thus, the most favourable areas to explore for lead deposits are cells 72, 70, 82, 65 and 64, in decreasing order of importance. The second of these was selected by the author to perform preliminary follow-up investigations, which are described later on. 9.1.2 Zinc Reserves According to Section 8.4, the final estimates of the zinc reserves existing in the area should be made mainly on the basis of the geological forecasting model designed. Applying that model, 21 of the original 106 cells may be selected for further analysis (Table'7.20). In a second stage of selection, using the same model, the actual production raised at each cell should be discounted from the forecasts. This computation is shown in Table 9.3, where it may be seen that cells 25, 26 and 42 may be eliminated because their production exceeds the value of the forecasted reserves. Similarly, if the number of deposits worked at each cell is discounted from that predicted to obtain the final estimates, and the resulting figure is used to recalculate the predictions, the results of Table 9.4 are obtained, where it may be seen that cell 41 is unlikely to have zinc deposits and thus 0 TABLE 9.4 RESIDUAL ESTIMATES - ZINC RESERVES (IN POUNDS x 1000) Cell Expected Actual Potential Estimate Confidence Limits No. of No. of No.oc New Deposits Deposits Deposits 5 4 0 4 4430 77 8783 8 9 0 9 8345 3992 12698 14 12 0 12 12793 8440 17146 15 5 0 5 6232 1879 10585 24 2 "0 2 2311 0 6884 27 2 0 2 3828 0 8181 38 2 0 2 3289 0 7642 41 2 2 0 0 0 0 45 2 0 2 1513 0 5966 52' 22 0 2 22106 17753 28459 57 2 0 2 3548 0 7901 59 2 0 2 1234 0 5587 60 1 0 1 880 0 5233 63 18 0 18 19200 14847 23553 72 3 0 3 2280 0 6633 74 37 0 37 39144 34791 43497 100 5 0 5 7183 7830 11536 101 2 0 2 3573 0 7926 • 233 could be eliminated from a mineral exploration view point. Therefore, according to the best model that can be used for this purpose, it can be estimated that 130 zinc deposits are still lying in 17 cells of the area, with reserves that may be valued at £135,889,000, a figure that gives a zinc endowment of £79,934 for the favourable areas. In order to select the cells most favourable for further investigation, an initial criterion of selection which may be taken is to select as most favourable cells those with a forecast greater than E1.5m and an average value of the reserves in any of their deposits greater than E0.75m. By this means, cells 59 and 60 may be discarded, because they do not fulfill the selecting premises. Taking into account that the second best model to discriminate between the cells with high and low zinc potential is the geochemical model, its forecasts (Table 7.20) may be used for further selection of areas suitable for detailed investigation. Those forecasts indicate that, among the favourable cells, only cells 15, 24, 45 and 57 have a real zinc potential, and thus they may be considered as the areas most favourable for undiscovered zinc deposits. Now, considering the geology of those cells, it may be concluded that their favourability arises from the fact that they all include large areas covered either by rocks of the Upper Limestone Group, or by younger horizons under which that group may be expected to lie. In addition, cells 15 and 24 have faults of average length less than the regional average, and include a relatively large number of fault intersections. Finally, cell 24 includes outcrops of the Whin Sill, and within it lies one of the main watershed zones of the area. From the geochemical point of view, the most favourable of those areas are cells 15 and 24, which include probably anomalous sites in Pb and Fe, and Ba and Fe, respectively. • 237 Summing up, the areas most favourable to perform detailed investigation for zinc deposits are cells 15 and 24, areas of the Northern Pennine region lying west of the Burtreeford Disturbance. The first of these areas was selected by the author to assess the validity of these conclusions, the results of the preliminary geochemical investigations carried out being indicated later on in this chapter. 9.1.3 Copper Reserves Taking into account the conclusions attained in Section 8.4, the final estimates of copper reserves in the area must be based on the geochemical forecasting model designed. By means of that model, 49 of the original 106 cells may be selected as favourable towards containing this type of mineralization (Table 7.20). As it was done in the former two sections, an initial criterion of selection among those 49 cells is to subtract the production raised at each of them from its forecast. The results of this computation are shown in Table 9.5, where it may be seen that cell 75 has produced more than it forecasted for it, and thus could be eliminated from further analysis. A second criterion of selection is to discount from the estimated number of deposits for each cell, the number of deposits that have been worked, computation that shows that cells 41 and 106 are not likely to contain undiscovered copper deposits (Table 9.6). Therefore, on the basis of the geochemical model, it may be estimated that there are 149 undiscovered copper deposits in the area, with reserves that may be valued at £54,392,000. This figure gives a copper endowment for the' favourable areas of £11,824 per square kilometre. Considering for further refinement of the estimates a forecast greater than £1.5m and an average value of the reserves in any of the deposits greater than £0.75m, the following ten areas may be regarded as • TABLE 9.6 RESIDUAL ESTIMATES - COPPER RESERVES (IN POUNDS x 1000) Cell Expected Actual Potential Estimate Confidence No. of No.of No.of New Limits Deposits Deposits Deposits 1 1 0 1 104 0 1026 2 1 0 1 201 0 1123 3 1 0 1 523 0 1445 9 1 0 1 106 0 1028 10 1 0 1 106 0 1028 11 1 0 1 49 0 971 12 1 0 1 64 0 986 34 1 0 1 104 0 1026 41 1 1 0 0 0 0 43 1 1 1 65 0 987 44 1 0 1 333 0 1215 45 1 0 1 93 0 1015 46 1 0 1 3353 2431 4275 47 3 0 3 3980 3058 4902 52 12 0 12 1252 930 2174 56 3 0 3 219 0 1141 57 1 0 1 66 0 988 58 1 0 1 471 0 1393 62 1 0 1 25 0 947 63 15 0 15 1494 572 2416 65 4 0 4 4946 4094 5868 66 4 0 4 5019 4097 5941 67 3 0 3 1219 297 2141 68 4 0 4 191 0 1113 69 2 0 2 107 0 1029 73 1 0 1 156 0 1078 74 25 0 25 2479 1557 3401 76 1 0 1 902 20 1824 77 1 0 1 109 0 1031 78 1 0 1 123 0 1045 79 5 0 5 5821 4899 6742 80 2 0 2 6477 5555 7400 84 4 0 4 3643 2721 4565 85 1 0 1 1512 590 2434 86 1 0 1 106 0 1028 87 1 0 1 116 0 1038 88 1 0 1 96 0 1018 89 2 0 2 1140 208 2062 90 3 0 3 140 0 1062 91 3 0 3 138 0 1060 92 3 0 3 146 0 1068 94 5 0 5 5071 4149 5993 97 7 0 7 1070 138 1992 98 6 0 6 637 0 1559 99 6 0 6 238 0 1160 104 1 0 1 14 0 936 105 4 0 4 168 0 1090 106 1 1 0 0 0 0 N 3 3 favourable in this respect: Cells 46, 47, 65, 66, 74, 79, 80, 84, 85 and 94. The refinement of the selection is in this case a complex problem, because, as indicated, the results of the research suggest that it is probable that reserves much greater than the ones exploited until now may still lie undiscovered in the area. Taking this fact into account, it appears that a good procedure to follow is to examine the forecasts of the two remaining models (combined and geological), and to eliminate in an initial step those cells which have negative forecasts in both cases. By this mean, cells 46 and 47 may be discarded. Now, considering the geology of the favourable areas, it may be seen that minor acidic intrusive bodies are present in cells 65, 66 and 74; that cell 79 has a large number of fault intersections; and that the average length of the faults in cells 65, 66, 80. and 85 is less than the regional average. Therefore, of the eight remaining cells, six bear geological features favourable towards containing copper mineralization, and two areas (cells 84 and 94) have no such features and thus could be discarded. On the other hand, if the geochemistry of individual samples is examined, it may be seen that cell 65 contains probably anomalous sites in Mo and high values of the factor Mo-Cu-As; cell 79 has anomalous values in Cu; and cell 85 has anomalous values in Mo at several sites. Therefore, the cells that may be considered as most favourable for containing copper mineralization are the following (in descending order of importance): Cells 65, 85, 79, 66, 74 and 80. The third of these was selected by the author to perform preliminary geochemical investigations, the results of which are indicated later on. 9.2 PRELIMINARY SURVEY IN CELL 15 9.2.1 General Considerations According to the procedure indicated in the previous section, 0 239 this cell was selected to perform preliminary geochemical investigations to assess the validity of the forecasting technique devised to predict zinc reserves in Northern England. The forecasting model chosen indicates the probable existence of 5 zinc-bearing deposits in this cell, with a total value of their reserves of £12,793,000, with 95% confidence limits set up at £8,440,000 and £17,146,000; in addition, lead reserves that may be valued at £6,682,000 may also be expected to be present in 4 deposits of the area. The geological features of this cell responsible for such high estimates are the large area covered by rocks of the Upper Limestone Group, and the short average length of its regional faults. 9.2.1.1 Location and general geography The area lies in the counties of Northumberland and Cumberland, its boundaries being the National Grid Reference System coordinates 550,000N; 560,000N; 370,000E; and 380,000E. It is a rural region, crossed by the A686 road joining Alston with Haydon Bridge, towns lying 3 miles to the south and 6 miles to the north-east respectively. The average altitude is 1200 ft., constituting essentially a region of moors drained by north-east flowing streams which are part of the basin of the West Allen River, tributary of the South Tyne. The westernmost part of the cell is drained by westerly flowing streams, members of the basin of the River Eden. 9.2.1.2 Geology The area consists of a sedimentary pile of Carboniferous age, which forms a sub-horizontal succession about 1100 ft. thick (Figure 9.1). The oldest levels are shales and sandstones with a limestone horizon inter- bedded, a sequence assignable to the Middle Limestone Group, which outcrops along the West Allen valley in the south-eastern part of the area. • CELL15-geological map 3 7 0 0 0 0 E 1 550,000N 1 2 3 4 KM FT9 COAL MEASURES 1 MILLSTONE GRIT UPPER LIMESTONE EZ3 GREAT LIMESTONE OEM MIDDLE LIMESTONE 4PAULT .•• (;) BACKGROUND STREAM SEDIMENT SAMPLE • ANOMALOUS STREAM SEDIMENT SAMPLE 4.4%...rSOIL TRAVERSE FIG.9.1 • 2 9 0 Over the former unit lies a pile of shales, sandstones and limestones, assignable to the Upper Limestone Group, a unit that forms most of the region at altitudes below 1300 ft. The succession is topped by a sequence of grits with a coal layer interbedded, representing the Millstone Grit Series and forming most of the Whitfield Mbor. Due to tectonic effects related to the regional Stublick Fault System, sandstones, mudstones and coal layers of the Coal Measures outcrop in restricted places of the north-western corner of the area. The structure of the region is fairly simple, the beds being mostly sub-horizontal, with a minor tilt towards the west. Normal faulting is the rule in the area, most of the faults trending between N15E and N15W; a second set of lesser important faults trends NE, and members of the Stublick system trend east-west.' No intrusive rocks are present in this cell, the closest outcrops lying some 4 kilometres to the north, where quartz-dolerites of the Whin Sill complex form an extensive dyke related to an east-west regional fault. 9.2.1.3 Mineralization Several mineralized structures are known in the -area, the most important being concentrated in the lower slopes of the West Allen valley south of Ninebanks. The best known of these structures are the veins at Ouston, Mohopehead, Keirsleywell Row, Longcleugh and Stag Rake. According to Dunham (1948), these structures trend N65-70E, throwing less than 45 feet to the NW or SE. They bear galena, barite and witherite, in horizons belonging to the Great Limestone. Numerous trials are recorded in these veins, rendering a total production of 8,081 tons of lead concentrate and 15,154 oz. of silver. In addition to the former, a minor vein trending N2OE is known in the north-central part of the area, at Church Burn. No information regarding this structure is available, except that 80 tons of lead 2 9 1 concentrate were recovered from some trials done in it. No zinc output is recorded in the area. 9.2.1.4 Soils According to observations performed in this research, the soils of the area are water-logged, with a peaty cover 5 to 8 inches thick, which overlies greyish-brown gleyey horizons. These soils are poorly , drained and developed, showing strongly meteorized remains of the bedrock (C horizon) at depths not greater than 2 feet. 9.2.2 Geochemical Investigations The geochemical data assessed during these investigations were the multi-element analysis of the stream-sediments collected during the regional survey that constituted the raw-data for this research, and analysis of detailed stream-sediment and soil surveys carried out by the author in several places. The analytical methods employed and sampling procedures, were indicated in Chapter 5. 9.2.2.1 Regional reconnaissance survey During this survey, 38 stream-sediment samples were collected in the area (Figure 9.1). The results of their analysis indicate that they tend to have trace-elements contents lower than the regional average, with the exception of Pb, Co, Ni and Li elements that on average are slightly higher than the regional mean (Table 9.7). Taking into account the average value of the elements in the cell, eight samples can be considered to be anomalous in one or more elements. Two of those samples are possibly anomalous in Mn or As, elements that bear no relation to zinc mineralization, and therefore they can be eliminated from a mineral exploration point of view. Similarly, two other samples with possibly anomalous values in barium may be eliminated because this element is present in rather low values in the area, rendering a fairly low mean as compared to the regional one. TABLE 9.7 MAIN STATISTICS OF SAMPLES OF REGIONAL SURVEY - CELL 15 ELEMENT MEAN VARIANCE ST. DEVIATION Fe 3.183% 3.168 1.780 Ga 5.989ppm 12.770 3.573 Cu 11.474 106.310 10.311 Pb 127.174 143856.351 379.294 V 19.316 160.222 12.608 Ba 200.808 14243.631 119.347 Co 30.039 1744.693 41.770 Ni 36.789 6690.279 81.794 Mn 2569.500 9038750.851 3006.452 Li 77.658 408.069 27.403 Mo 0.782 0.319 0.565 As 10.737 28.632 5.351 Zu 119.211 6079.070 77.869 Cd 0.237 0.348 0.590 292 Therefore, only 4 or the 38 initial samples can be considered interesting for the purposes of this research: (a) sample at Keenleyside Hill (No. 4016, coordinates 3793E, 5547N), which bears high values in Fe (12.4%), Cu (66ppm), Co (263ppm), Ni (524ppm) and Mn (more than 1%); (b)sample at Green Sike (No. 4149, coordinates 3736E, 5586N), which bears high levels in Pb (more than 1500ppm); (c) sample gathered at Church Burn (No. 7456, coordinates 3746E, 5585N), having high contents in. Ga (17ppm), Co (76ppm) Mn (more than 1%) and Li (154ppm); (d) sample collected at stream south of Green Sike (No. 4213, coordinates 3736E, 5588N), which gave high levels in Pb (307ppm) and Li (128ppm). Considering those results, preliminary investigations were planned to be carried out in two areas of the cell: (1) Church Burn-Greensike and (2) Keenleyfell West-Middle Edge. The results of the detailed investigations follow. 9.2.2.2 Preliminary Geochemical Investigations During these surveys 26 stream-sediment and 75 soil samples were collected in the two areas, with a twofold purpose: (a) confirming the anomalies obtained during the regional survey, and (b) establishing the origin of those anomalies, and the possible presence of mineralized structures undiscovered until now. The results attained were the following (in all cases, the discussion is centered in those elements that, according to the geochemical model designed, could be the best indicators for zinc mineralization). (A) Church Burn-Greensike Anomalies The anomalous sites existing in this area were investigated by means of detailed stream-sediment sampling, with samples collected at the most important sites of the drainage system.. Besides, two soil 293 traverses were sampled in order to assess the mineral potential of faults known in the area, and to examine the possible continuity of the vein known at Church Burn. Stream-sediments survey The results of this survey are shown in Figure 9.2. It may be seen that all the regional anomalies except one (sample at site 2) were confirmed. Most of the anomalous sites lie at Church Burn, bearing anomalous contents in Li, Pb, Co and Mn. Taking into account possible contamination arising from some of the trials done in that area, and that sediments deriving from the Millstone Grit bear high contents in Li and Co, it becomes difficult to assess the value of the anomalous samples as indicators of undiscovered mineralization. Therefore, the necessity of assessing the values of this survey together with the results of the soil traverses arises. Regarding the anomalous samples at the Greensike, it may be seen that they mostly bear Li contents, coupled with important concentrations in Ba, Co and Fe, a group of elements that are mostly concentrated in sediments derived from the Millstone Grit, a unit that outcrops nearby. Therefore, it is considered that these samples very probably represent lithological effects, and not mineralization.. Soil Survey Two soil traverses were performed in the area: the first one (A-C, Figure 9.2) was done to investigate the continuity of the vein worked at Church Burn, and to investigate the mineral potential of two NE trending faults known in that zone. The second traverse (B-D, Figure 9.5) was done to investigate the origin of the stream-sediment anomalies detected at Greensike, and to assess the mineral potential of a regional fault running south of that stream. In both cases the.best elements that could be used in the CHURCH BURN-GREEN SIKE AREA-stream sediment sampling 73 74 75 ~~-+'------l-----1I---.,.------i 59 74 75 77 SCALE o Stream sediment sample -Detailed surveyX a id -Regional survey x mmB COAL MEASURES ~ample (0 Soil 1 Co 'V Old pit 2 Li § MILLSTONE GRIT II Indicates anomalous sample 3 Zn Pb 4 Pb-Mn c=J UPPER LIMESTONE (~Anomalous stream 5 Co Fe 6 Fe-Be ~f.'V.-- 7 60 Cd -~~ Soils anomaly / :AULT 8 Co Li 9 Li VEIN 10 Mn Li /0' 11 Li 12 Li 13 Li 14- Mn-Ca-Li 15 Li Pb 16 Pb-Mn-Co 17 Pb 18 Ph FIG.9.2 • Church Burn-Green Sike Area -soil traverses. 800 00 ppm ppm Pb-Bo Li-Zn 600 300 40 200 200 100 ilgt"Aro. N`"4444.0,401 411 111-■-\ 0 81fre 1150ft- S'—'1 in I200-ft Wolf hills Bum Millstone Green Sike 1050 1100 Grit Upper Felltop limestone 1000 B C B D Traverse A—C Traverse B—D 0 05 1.0 1.5Km FIG 9.3 2 0 4 interpretation of the results were Pb, Zn, Ba and Li because of the good contrast that they give in these soils. In places, increases in the Co, Ga, V and Cd contents were noticed, and they are indicated whenever it is pertinent. Traverse A-C The most important feature of this traverse (Figure 9.3) is a very strong anomaly detected where the projection of the vein worked at Church Burn is intersected. In that area, the soils bear contents of 75Oppm Pb, 300ppm Zn, 2O6ppm Li and 239ppm Ba, values that suggest that the anomaly is related to a mineralised body lying underneath. These high values are coupled with strongly anomalous contents in Ga, Co, Cd and V (29ppm, 61ppm, 2.8ppm respectively), and by a very marked peak in the Ni content of the soils (lO8ppm). The anomaly was detected over a width of 300m showing a double peak for Li and Ba. It cannot be ascertained if this fact reflects a differential mobility of these elements, or if it is an indication of the presence of two bodies or of the repetition by faulting of a single ore body. It is worth noting that if this anomaly were representative of that vein, it would indicate a minimum length of 625m for the structure, rendering it into an interesting proposition to investigate in further detail. A second anomalous feature was detected in the western part of the traverse, near Wolf Hill Burn. This anomaly bears 427ppm Pb, with complementing high Ba values downdrainage (187ppm). It is considered that this feature is not caused by mineralization, but is the result of an outcrop of the Upper Felitop Limestone in the vicinities of the sampled site. No relation was found between anomalous trace-element concentrations in soils, and the faults intersected in the traverse. The only noticeable 2 9 5 effect of the faults is an enhancement in the Li and Ba contents of the soils, an effect that takes place downdrainage of those structures, but which is not matched by similar enhancements in other elements. Traverse B-D Two main features of this traverse are worth noting: firstly, an increase in the Li and Ba content of the soils, where the traverse intersects the fault running south of the Greensike. As indicated, this is a normal feature of the faults of the area, and is not related to mineralized structures, at least not directly. A second feature worth noticing is a minor lead anomaly (169ppm) at the stream which coincides with an increase in the zinc, cobalt and gallium concentrations.. It cannot be ascertained if this feature is related to the stream-sediment anomaly detected nearby and to mineralization, or if it is the result of the outcrop of the Upper Felltop Limestone lying immediately to the north of the stream. The latter hypothesis is strongly supported by high Li and Ba contents in the soils immediately to the north of this anomaly. (B) Keenleyfell West-Middle Edge Anomaly The anomaly detected in this area during the regional survey was investigated by means of stream-sediment and soil sampling. The main. purposes of the soil traverses performed (Figure 9.4) was to investigate the origin of the stream-sediment anomaly detected, and to assess the mineral potential of the southern part of a fault of regional importance known in that area. ' Stream-sediments survey The streams of the area are very ill defined, and therefore it becomes difficult to obtain adequate samples for geochemical purposes. Of the few samples that were collected (Figure 9.4) only the one gathered to confirm the anomaly detected during the regional survey gave • • • KEENLEYFELL WEST-MIDDLE EDGE AREA-stream sediment and soil sampling KEENLEYFELL • WEST • MIDDLE Pb-Re li-Zn PP. PP. 100 200 100 0 0.5 10Km 0 Stream sediment sample -Detailed surveyx Cool layer id -Regional survey x Lower Fel ItopLimestone 1300ft • Soil sample ool Io er x 'Indicates anomalous sample I UPPER LIMESTONE GREAT LIMESTONE TRAVERSE F-G TRAVERSE H I MIDDLE LIMESTONE 9 0 05 1.0 Km 0 0.5 Km __or-- FAULT rte- IMMO= ANOMALOUS STREAM OSOIL ANOMALY Sample Possibly Anomalous Probooly Anomalous . Elements Element 4016 Mn Fe-Co-Zn-Cd Fe-Co -Ba-Mn 2961 anomalous values with contents in Fe, Co, Mn and Ba well above the regional background (13.7%, 454ppm, more that 1%, and 1173ppm respectively). The remaining samples gave trace-elements contents below the regional average. Considering those results, the interpretation of the anomaly detected must be done exclusively on the basis of the soil traverses performed. Soil Surveys Two traverses were sampled during the detailed investigation of this anomaly. As may be seen in Figure 9.4 these traverses are orthogonal and their main purpose is to assess the possibility of relating the "- anomaly detected to the regional fault known in the area, or to mineralized structures that could exist at the Middle Edge ridge and which could be manifested through seepages detectable in the middle of the slope. Traverse F-G Several anomalous features were detected in this traverse (Figure 9.4). Firstly, where the regional fault is intersected for the first time a strong Pb anomaly is present (316ppm). This ,feature was confirmed by repeated analysis of the sample, but it was found that it is not complemented by similarly high values of other elements. Therefore, even though this could be a significant feature representing mineralization, it is more probably the result of other causes, as contamination in situ. Secondly, anomalous values in Li and Ba were found to the south of the previous site. These values are not considered to be related to mineralization, but to be the result of an outcrop of the Lower Felltop Limestone in the vicinities. Thirdly, south of the place where the fault is intersected for the second time, anomalous values of the main elements were found at two sites 297 200m apart. These sites bear more than 150ppm Pb, 5% Fe, 170ppm Li, 5Oppm Zn and 380ppm Ba. If it is considered that the samples are also anomalous in V, Ga and Co, and that they bear low Mn values (suggesting that this is not a secondary environment effect), it may be concluded that these anomalies probably reflect the presence of mineralization in this area. Traverse H-I The results of this traverse show two main features which are fairly similar: in two sites a peak of Pb is complemented by a peak in Li and Ba at the adjacent sampling site, in both cases the latter peaks being downstream of the former peak. These features are considered to arise from two separated structures, which are manifested by a couple of pd'aks due to the differential mobility presented by the elements in this calcareous environment. The sources of the anomalies cannot be ascertained. The possibility that they could represent mineralization must be strongly considered, especially if the most important of them is related to the anomaly detected in the traverse F-G giving a general N2OE direction for the anomalous area, which explains why the anomalous stream did not- give anomalous values at the site sampled upstream of that hypothetical line. If this interpretation is correct, this feature could be related to mineralization emplaced along tensional fractures generated in connection with the main fault at directions diverging about 40°. The importance of the minor peak detected in this traverse is difficult to assess. On one hand, if this site is linked to the western peak of traverse F-G, it could indicate the presence of minor` mineralization in tensional fractures conjugate to the previous fracture. On the other hand, it could represent the same mineralization as the previous anomaly, which is detected downdrainage because of the numerous springs existing in that area. No evidence to support these hypothesis is available. • 298 Finally, two facts relating the peaks detected in this traverse are worth mentioning: firstly, these samples bear very low Fe and Mn contents (less than 0.1%) and therefore no secondary environmental effects could be brought forward to explain the anomaly. Secondly, it could be argued that the peaks detected are caused by the coal layer that outcrops in the vicinities of the traverse; although this hypothesis cannot be dismissed on the basis of the available data, it is a highly improbable situation, because the samples are characteristically low in several elements that are normally present in high concentrations in coals (e.g. Ni, Zn and Cd). 9.2.3 Summary and Conclusions On the basis of the geochemical data gathered, the mineral potential of the area may be considered to be concentrated in the north- central and east-central regions, where stream-sediment anomalies were detected during the regional survey and confirmed during the detailed investigations performed. These anomalies lie in terrains underlain by rocks of the Upper Limestone Group, in zones where the Great Limestone is covered by younger horizons, and where faults that could be "leaders" for mineralized fractures are known to occur. The soil investigations performed revealed that the regional faults are manifested by enhancements in the Li and Ba contents of the soils, rendering peaks of those elements downdrainage. The probably mineralized fractures are manifested by peaks in Pb, Zn, Ga, Co and V which are associated to peaks in Li and Ba found either at the same Site or downdrainage. In addition, enhanceMents in the Li and Ba contents of soils were noticed where horizons belonging to the Upper or Lower Felltop limestones occur in the subsurface. Two anomalies trending NNE were found during this survey. The first of these coincides with the northwards continuation of the vein • 299 4 worked at the Church Burn, giving a minimum length of 625m for that mineralized structure. The second anomaly was located at the Middle Edge ridge, in the West Allen-East Allen watershed, and could probably represent mineralization in a branch of a main fault existing in that area. In conclusion, it may be stated that Cell 15 has a definite mineral potential, which needs to ne evaluated by means of detailed surveys. Such surveys could consider in the initial stages the performance of geochemical soil traverses spaced every 30 o5 50 metres, coupled with self-potential or electromagnetic geophysical surveys run parallel to the soil traverses' but at a greater spacing. Due to the superficial character of the bedrock, trenching at the most interesting anomalies detected would allow an easy and speedy assessment of the favourable areas that may be found. 9.3 PRELIMINARY INVESTIGATIONS IN CELL 70 9.3.1 Generalities The selection of this cell to perform preliminary investigations to assess the validity of the forecasts for lead potential in Northern England was done according to the conclusions attained in Section 9.1, and taking into account its accessibility, a factor that needed to be taken into account in the present case, considering the relatively short time available. The combined forecasting model predicts the presence of 4 lead- bearing deposits in this area, with an estimated value of their reserves of £8,421,000. In addition, one deposit may be expected to contain copper reserves valued at £71,000. The geological features of this cell that are responsible for the high forecast are the relatively high number of fault intersections present (31 as compared with a regional mean of 22) and the large area underlain by rocks of the Upper Limestone Group, which constitute almost half of the cell. • 3 0 0 9.3.1.1 Location and general geography The area is located in the counties of Westmorland and Yorkshire, in the southern part of the Northern Pennines, its boundaries being the National Grid Reference System coordinates 500,000N; 510,000N; 380,000E; and 390,000E. It is an essentially rural area, crossed by secondary roads that join the Swale valley with Edenside. The only populated centre is the village of Keld, lying in the south-eastern corner. The average altitude is 1500 to 1600 ft., the topography being one of moors dissected by north-south and east-west flowing streams, which are part of the Swale basin. The northern and north-western regions are drained by northwards and westwards flowing streams, part of the Eden basin. 9.3.1.2 Geology The area is formed by a sedimentary pile of Late Carboniferous age (Figure 9.5), which lies sub-horizontal, except where due to faulting the beds acquire inclinations ranging from 20° to 40°. The total thickness of the sequence may be estimated in 700 ft. An account of the features of individual beds may be found in Dakyns and co-workers (1891). The oldest levels present are flaggy sandstones, shales and limestones belonging to the Middle Limestone Group, which outcrop sub- horizontally in the bottom of the valleys of the River Swale and Thwaite Beck, in the south-eastern part of the area near Keld. Coal and chert beds are present in places, interbedded among clastic and calcareous horizons. Over the former unit lies a sequence of limestones, shales and siliceous sandstones belonging to the Upper Limestone, which forms most of the terrain at altitudes below 1700 ft. This unit rarely departs from a horizontal attitude, except near regional faults where it is tilted in different directions. A coal layer is present in places, as well as cherty beds. 0 MILLSTONE GRIT UPPER LIMESTONE MIDDLE LIMESTONE o 3 0 1 The upper part of the sequence is formed by grits, shales, sandstones and calcareous sandstones which belong to the Millstone Grit Series, a unit that forms most of the moors of the region. A coal layer which has been worked in places, normally lies at its base or in its vicinity. The structure of the area is simple, the beds lying mostly sub-horizontal. Normal faulting is a rule in the cell, with numerous regional faults striking east-west and north-west. These faults normally bring into contact high levels of the Millstone Grit, with various horizons of the Upper Limestone Group. No intrusive rocks are known in the area. 9.3.1.3 Mineralization Several mineralized structures are known in the area, in the lower slopes of the Swale valley near Keld. However, little information regarding these veins is available, and no production is recorded from them, except for 27 tons of lead concentrate which were dubiously raised at Lane End. The mineralized structures are emplaced in conjugate systems of faults trending north-east and north-west, the former being the most important of both. The veins bear galena and calcite as their main constituents and the presence of sphalerite and minor amounts of-Gq1amine have been noticed. In addition, the presence of a copper bearing vein is recorded at Sledale, the ore present in this structure being formed by chalcopyrite and covellite?; no production has been obtained from this vein, and its position is not indicated in the available 1"/1 mile maps. 9.3.1.4 Soils The soils fo the area are typically poorly drained with a peaty highly organic cover 5 to 8 inches thick, overlying a reddish-grey poorly developed soil, very argillaceous, which in the higher regions forms gley • 302 horizons. In general the profile is not well defined, with an abrupt transition - at depths of 1 to 2 feet - to highly meteorized bedrock OZ horizon). Streaks and spots of iron oxides are common, as well as pebbles in the lower parts of the area, where mixture with glacial drift occurs. 9.3.2 Geochemical Investigations The geochemical data assessed for this area were the multi- element analysis of the stream sediment regional reconnaissance survey basis of this research, and analysis of detailed stream sediment and soil surveys performed by the author in several parts of the cell. The analytical techniques and sampling methods employed were described in Chapter 5. 9.3.2.1 Regional Stream Sediment Survey During this survey 43 stream sediment samples were collected in the area (Figure 9.6). Their analysis indicate that they bear trace-elements contents that in general are lower than the average for Northern England (Table 9.8). Of especial importance in this respect are the very low average concentrations in Pb, Ba, Mn, Zn and Cd. On the other hand, high average contents in Fe, Ga and Li are recorded, showing the strong influence that the Millstone Grit and calcareous units of the Carboniferous Limestone have on the composition of the sediments. Taking into account the geochemical models designed for the forecast of lead reserves, it may be concluded that the best elements to use as indicators of such mineralization are Pb, Ba, Zn, Cd, Mo and Ga. Considering the area means, 11 samples may be selected as representative of anomalous features, 5 of which may be excluded from a mineral exploration point of view, because they contain anomalous concentrations only in elements other than those indicated. The remaining 6 samples that merit further investigation are the following: STREAM SEDIMENT RECONNAISSANCE—CELL 70 5652 Ton Hill 0 I0 20 30miles 0 Background samples A Anomalous samples FIG.9.6 S TABLE 9.8 MAIN STATISTICS OF SAMPLES OF REGIONAL SURVEY - CELL 70 ELEMENT MEAN VARIANCE ST. DEVIATION Fe 4.407% 2.765 1.663 Ga 14.114ppm 30.186 5.494 Cu 19.545 83.091 9.115 Pb 50.023 2088.441 45.699 V 53.955 524.277 22.897 Ba- 251.523 87352.999 295.555 Co 32.636 494.400 22.235 Ni 39.341 247.207 15.723 Mn 1086.727 3711603.645 1928.552 Li 91.409 1237.550 35.179 Mo 0.966 0.565 0.752 As 18.364 198.934 14.104 Zu 118.045 8048.789 89.715 Cd 0.477 0.581 0.762 3,0 3 (1)sample in the upper part of Thwaite Beck (No. 2700, coordinates 3896, 5006), bearing high levels in Pb; (2)sample at the West Stonesdale near its confluence with the River Swale (No. 2722, coordinates 3887, 5017) which has anomalous levels in Zn and Cd; (3) sample at stream near the High Brow Hill (No. 5650, coordinates 3889, 5054) which has high concentrations in Mo; (4) sample at Drover Hole Sike in upper West Stonesdale (No. 5652, coordinates 3892, 5068) bearing high levels in Mo; (5) sample at Great Sledale Beck (No. 2704, coordinates 3855, 5008) bearing high levels in Pb and Ba; (6) sample at Great Ash Gill (No. 3869, 5013) bearing high concentrations. of Ba. Taking those results into account and the fact that the known veins in the area could be present beyond their known westwards extension, in areas where the Main Limestone is covered by younger horizons, detailed stream sediment and soil surveys were planned in the northern flank of the Birkdale Beck and in the southern flank of the Great Sledale Beck. In addition, similar surveys were planned for the upper West Stonesdale area, in order to investigate the anomalies detected and to assess the possibility of detecting ore bodies that could exist in the Tan Hill- Polly Moss area. 9.3.2.2 Detailed Geochemical Investigations As indicated, these surveys considered detailed stream sediment sampling in streams draining selected areas, and soil sampling along traverses chosen to intersect known faults and veins, and to detect structures lying at depth, but which could be manifested in the surface through some of the many springs and seepages existing in the area. In general terms, the different sites sampled may be grouped into two areas: 30'4 Birkdale Beck-Great Sledale Beck and Tan Hill-Keld areas. The results attained with the sampling in both areas follow. (A) Birkdale Beck-Great Sledale Beck Area This area lies in the south-central part of cell 70 bearing anomalous streams in Pb and Ba. Taking into account the position of the known veins it was decided that the best approach that could be taken to study the mineral potential of the area by geochemical means, was to perform detailed stream 'Sediment and soil sampling in the northern slopes of the Birkdale Beck between Uldale Beck and Hill Top, and to carry out a preliminary stream-sediments survey in the southern tributaries of the Great Sledale Beck. By that means it was intended to detect mineralized structures at depth through some of the numerous springs existing in that area, and to investigate the possible northwards and westwards continuation of veins known in the eastern part of the area. Stream-Sediments Survey During this survey 32 samples were collected (Figure 9.7). Most samples bear high contents in Li, Mo and Ga, showing the strong influence that the oxidate sedimentary rocks of the Millstone Grit and the calcareous parts of the Carboniferous Limestone have in the composition of the sediments. Therefore, most of the 21 samples found with anomalous contents in one or more elements may be discarded from a mineral exploration view point. Of the total anomalous samples only 7 have anomalous concentrations in elements other than those mentioned in the foregoing paragraph (sample sites 1, 4, 6, 8, 19, 20 and 21) and thus could be considered to represent possible mineralization. Of these samples, two others may be discarded (sites 1 and 8) because their trace-element contents may be considered due to secondary environmental phenomena, manifested in their very • Birkdale Beck-SledaleArea - stream sediment sampling ASHGILL SIDE 10 § Millstone Grit Anomalous Elements sites 1 Li-Cd-Ga-Mn o Upper limestone .. Cd-Mo-Ga 6 Zn-Pb-Cd-Mo ~ Fault 8 Cd-Mo-Mn-Fe ,.... 19 Cd-Ga ..... Vein 20 Li-Cd-Ba .0 Stream sediment sample-regional surveyX 21 Pb o id -detailed surveyX SOil sample •x Indicates anomalous site FIG.9.7 • 3O 5 high Mn or Fe concentrations '(greater than 2500ppm or 5%, respectively). Therefore, five sites can be considered of interest for the purposes of the survey: sites 4 and 6 lying in a northern tributary of the Birkdale Beck draining the southern part of the White Mossy Hill, and sites 19, 20 and 21 located in southern tributaries of the River Swale and Great Sledale Beck, draining the Ashgill Side of the Angram Common. It cannot be ascertained if the anomaly detected at Birkdale Beck represents mineralization, or if it is a localized effect that enhances the features of sediments derived from Millstone Grit rocks; however, if it would represent mineralization, very probably it would reflect an ore body lying at depth or an outcropping ore body trending between N20oE and E-W, fact that can be ascertained because of the negative results attained in samples of the adjacent streams. The anomalies at Ashgill Side undoubtedly represent mineralization, part of which is already known in the lower slopes of the ridge, but part of which may lie at depth in the vicinities of site 21. Therefore, this area merits further investigation. Soil Survey As indicated, a soil traverse was sampled in the northern flank of the Birkdale Beck*at intervals varying between 125 and 200m. The main purpose of the traverse was to detect seepages indicative of mineralization in calcareous horizons at depth, and to assess the possibility of a northwards continuation of the veins known at Stone House and Firs. The results of the traverse are graphically shown in Figure 9.8. Firstly, it appears worth while to analyze the influence of the lithology in the trace-element content of the soils. It may be seen in that figure, that the presence of calcareous beds within the sequence 3 0 3 produces an increase in the Li and Ba contents in the soils, rendering peaks A, B, C and F which are produced by suboutcrops of the Great, Little and Crown Limestones. At the same time, the more clastic units (e.g. Grindstone and 10 Fathom Grit) produce a decrease in the concentrations of those elements, a feature especially evident in the lows separating the peaks B and C, and D and E. A similar though less marked behaviour may be noticed in the contents of Pb, Zn, Ga and Mo of the soils. Likewise, the faults of the area produce a similar behaviour of the elements in the soils, rendering the peaks E and G, which are principally marked by sharp rises in the Li concentrations. The three remaining peaks (D, H and I) cannot be explained on the"basis of lithological or structural effects. Peak D, the most important of the traverse, is marked by contents of 416ppm Pb, 2.7ppm Mo and 7.0% Fe. Low Mn, Co, Ga, Li and Zn contents indicate that this feature is not related to secondary environmental factors. Therefore, the possibility that this anomaly could represent mineralization in calcareous units such as the Upper Felltop Limestone, in the vicinity of Birkdale Cross, must be carefully considered. The two remaining peaks may be related to the northwards projection of NW-trending veins known at Stone House and Firs, which intersect the traverse north of Birkdale. If this interpretation is correct, those - structures would have a minimum length of about lkm, and therefore they would merit further investigation. (B) Tan Hill-Keld Area This area lies in the eastern part of cell 70, where stream- sediments with anomalous contents in Zn, Cd, and Mo were found during the regional survey. Considering that several veins are known in the area, as well as faults that could be "leaders" for mineralized 307 fractures, a detailed stream sediment survey was carried out at Stonesdale Beck north of Lad Gill, at a western tributary of that stream opposite to Lad Gill, and at a stream tributary of Thwaite Beck at Thorns. Besides, some stream sediment samples were collected at tributaries of the Swale near Keld and at tributaries of Easy Gill at Polly Moss. In addition, a soil traverse between Molds Hill and Hoods Edge was sampled at 200m intervals. The main purposes of these surveys was to detect possible ore bodies lying at depth in the north-eatern corner of the cell, which could be evidenced at the surface through some of the numerous seepages and streams existing in that area. As well, the possibility of detecting mineralization at the Black Hill of the Angram Common, and in the -westwards continuation of the Blackenthwaite Fault was investigated. Stream-sediments survey A total of 31 samples were collected in the area (Figure 9.9). The anomalous sites 2722 and 2700 were not resampled, because the first of them lies in the West Stonesdale in a site that should have contamination from mines and quarries lying to the north, and in the case of site 2700 because the anomaly is due to contamination (litter. dumping) from Keld. No anomalies were detected in the samples collected south of Keld or opposite to Lad Gill. The samples collected at Stonesdale rendered anomalous values in Ga, Cd, Li and Mo,which are considered to have been produced by calcareous horizons of the Upper Limestone Group present at the bottom of the stream of High Brown Hill. Therefore, no interesting zones were detected in the eastern part of the cell during this preliminary survey. • Tan Hill-l a MiistoneGrit o Upper Limestone _ Middlelimestone ~ Fault ...... Vein o Sedimenf sa_mple reglOna surveys o id-det~i led surveyx • Soilsample x Indicatesanomabus site Site Element 1 Mo 2 Ga 3 Ga 4 Ga 5 Ga-Cd 6 Ga 7 Ga-Fe 8 Ga 9 Ga-Li 10 Ga 11 Ga BLACK HILL 10 r FIG.9.9 3 0 S Soil Survey As indicated a soil traverse was sampled with the purpose of determining the possible presence of mineralization at depth in the areas of Tan Hill, Taylor Rigg and Polly Moss where the numerous seepages and springs present could give indications of the presence of buried ore bodies. The results of this traverse are graphically indicated in Figure 9.10. It may be seen that the Li, Ba and Ga contents of the soils are strongly influenced by the lithology of the sampling sites, the peaks A, B and D being related to suboutcrops of the Middle and Upper Felltop limestones. The only feature that could be of importance from the mineral exploration point of view is peak C which bears 651ppm Pm, 97ppm Zn, and 4.2ppm Mo. It cannot be ascertained if this anomaly is related to mineralization existing in the Tan Hill Moss or if it is due to the high organic content of the soils in that area, which is related to the presence of important coal layers nearby. It may also be seen that the anomaly dips towards the south having a complementary Ba peak downdrainage of the main peak. It is considered that if this anomaly were representative of mineralization, it would very probably reflect the presence of ore bodies at depth, beneath the Millstone Grit horizons, and not ore bodies that constitute suboutcrops in the vicinity. 9.3.3 Summary and Conclusions On the basis of the geochemical and geological information available it may be concluded that the area has a lead potential that may be considered to the concentrated in the lower and middle slopes surrounding the main moors of the region. Those terrains are constituted by horizons of the Upper Limestone Group, the Great or Main Limestone • Tan Hill-Keld Area -soil sampling Millstone Grit 1700_ • — ft ft Fells• limest _1600 1500_ 1400 F1G.9.10 w 3 1, 9 being covered by younger beds. Several faults are known in the area, possibly being "leaders" for mineralized fractures, obscured by the peaty and glacial cover that overlies most of the region. The stream sediment anomalies detected at Birkdale and Sledale becks during the regional reconnaissance were confirmed in the present survey as possibly related to mineralization. Those at West Stonesdale could not be confirmed, and are possibly due to lithological or contamination effects, the latter factor being responsible' for the anomaly at Thwaite Beck. Detailed stream-sediment sampling revealed the presence of four anomalous streams in he southern part of the area. These anomalies lie to the south-west of Cogill Knott and in the northern slopes of the Ashgill Side of the Angram Common. They are considered to represent mineralization lying in calcareous horizons belonging to the Upper Limestone Group. Other anomalies detected correspond to enhancements in the contents of Ga, Mo and Cd of the sediments, features that are considered to represent lithological effects that reveal the strong influence that the Millstone Grit and the calcareous horizons of the Carboniferous Limestone hate on the composition of the stream-sediments. The soil investigations performed revealed increases in the Li, Ba, Zn and Ga contents of the soils in areas where different limestones outcrop. Similar enhancements can also be observed in connection to the regional faults of the area. Four soil anomalies independent of lithological or structural factors were detected. Two of these lie to the north of Birkdale, and represent the northwards continuation of lead-bearing veins known at Stone House and Firs, in the lower slopes of the Swale valley. If this interpretation is correct, a minimum length of lkm could be considered for those veins, and thus they would merit further investigation. t 3 1. A third anomaly was detected near Birkdale Cross, at the Upper Birkdale Beck. This feature is interpreted as the probable result of base metal mineralization in calcareous horizons of the Upper Limestone Group; a connection between this feature and a regional fault known 250m to the east of the anomaly is probable. From the available data is cannot be ascertained if this feature indicates an ore deposit lying in the subsurface, or if it reflects mineralization lying at depth and which is manifested through springs. A last anomaly was detected in the vicintiy of Tan Hill. This feature may either reflect mineralization or may be the result of a high organic content in the soils, due to the presence of important coal layers in the vicinity. If this anomaly was representative of mineralization it is considered that very probably it would reflect a buried feature and not outcropping ore bodies. In conclusion, it may be stated that the preliminary survey of cell 70 tends to confirm its lead potential, at least in the southern part, where horizons of the Carboniferous Limestone underlie sequences of the Millstone Grit. Further detailed investigations are highly recommended to perform in this cell. These investigations should consider in their initial stages detailed stream-sediment sampling of the upper Swale Basin, coupled with soil traverses at widely spaced intervals in selected areas. In addition, detailed soil investigations by closely spaced north- south grids should be carried out at the Stonesdale and Ravenseat moors, in order to assess the possible presence of mineralization related to the western most extension of the Blackenthwaite Fault. These investigations could be coupled with self-potential or electromagnetic geophysical investigations, run in similarly orientated traverses but at a larger spacing that the soil ones. 3 1. 1 Finally, preliminary stream-sediment surveys could be performed in the rather inaccessible north-western part of the cell at Winton Fell, where faulted horizons belonging to the Great Limestone are known to exist. 9.4 PRELIMINARY INVESTIGATIONS IN CELL 79 9.4.1 General Considerations As indicated in Section 9.1, this is one of the most favourable cells of the area to explore for copper deposits. The geochemical model, the best expression found to define the presence of potential copper reserves, indicates the possible presence in this cell of one orebody, with reserves that may be estimated at £2,585,000. No lead or zinc reserves are forecasted in this area by the respective models. 9.4.1.1 Location and general geography The area lies in the counties of Westmorland and Yorkshire, in a region that is intermediate between the Lake District and the Northern Pennine chain. Its boundaries are the National Grid Reference System coordinates 360,000E; 370,000E; 490,000N; and 500,000N. It is an esentially rural area with Sedbergh as the only populated centre, lying in the southern part near the River Rawthey. The valley of the River Lune which flows southwards in the eastern part of the cell, separates the area into two morphological regions: to the west lie rolling hills of an average altitude of 900 ft., which constitute the easternmost ridges of the Lake District dome. East of that valley the terrain is very rugged and abrupt, with an average altitude of 1500 ft., forming the group of ridges of the Howgill and Yorkshire fessl, separated by the River Rawthey. The drainage of the western part takes place through poorly defined streams part of the Lune Basin, and the southernmost part is drained by short northwest-flowing streams, tributaries of the Rivers 31 2 Dee and Rawthey. The main part of the cell presents a well defined radial drainage, centered at the main peaks of the Howgill Fells, its streams being tributaries of the Rivers Lune and Rawthey. 9.4.1.2 geo.c2y. The area is constituted by a sedimentary sequence of Paleozoic age, pierced by dykes and minor intrusive bodies of predominantly basic composition (Figure 9.11). The oldest levels present lie in the easternmost part, where shales and limestones of the Ordovician Coniston Limestone Series constitute several isolated patches west of the Dent Fault; felsites and volcanic ashes are known within this sequence. Overlying the former unit in the same group of outcrops lies a series of shales, mudstones, and thin limestones which represent the basal Silurian. Over these, there is a sequence of massive flags (Coniston Flags) that form .a narrow belt along the western side of the Dent Fault, representing the Middle Silurain. Those rocks are overlain by mudstones, gritstones, slates and flagstones which represent the Upper Silurain (Ludlow Series). The youngest horizons present outcrop along the valley of the River Rawthey, east of Sedbergh. These rocks are reddish conglomerates and sandstones marking the base of the Carboniferous Limestone.: The outcrops of this unit are related to a complex system if faults part of the Dent system. The intrusive rocks of the area outcrop in the eastern part, where sills and dykes of micaceous (minette) and felsite (microgranitic) composition intrude levels of the Coniston Limestone Series and Coniston Flags. In addition, a small dolerite body occurs in the same area, piercing-levels of the Lower Silurian. Other minor bodies of micaceous composition are found near Sedbergh and Lowgill, in general associated with minor faults that cross the Silurian sequence. Cell 79-geological map 2 3miles Carboniferous Limestone lilt Basal Conglomerates Coniston Limestone Stockdale Shales Wenlock Series I I Ludlow Series Fault ‘s‘sZ:N Dyke CI Background stream sediment sample ■ Anomalous id FIG.9.II -3 t The structure of the area is rather complex. The most conspicuous features are vertical faults trending north-northeast, which cross the Siluro-Ordovician sequence in several places. These faults were produced by Caledonian movements, which in addition determined the formation of a strong cleavage of similar trend. During the Hercyian, the area attained its main structural characteristics, when the dome- like Howgill Fells Anticline was formed. This structure is bounded to the north and south by Carboniferous rocks, and to the east is separated from rather unfolded rocks by the complex Dent Fault Line. In addition during this period some-north-east trending faults were formed, bringing into contact horizons of the Basal Carboniferous Conglomerates with Silurian rocks. No mineralized structures are known in the area. The closest ore bodies lie to the east of the Dent Fault, in the upper Ure valley, where minor NE trending copper-bearing veins are known to occur. 9.4.1.3 Soils The soils of the area are of two types. Along the valleys and lower to middle slopes the predominant soils are of the acid brown type, non-calcareous soils often shallow and stony, with only the few top inches freely drained. On the higher terrains the soils are gleyey, with strong surface compaction, which causes their drainage to be very poor or impeded; stony and peaty soils with much bare rock and scree are also present in those areas. 9.4.2 Geochemical Investigations The geochemical data assessed for this area were the multi- element analysis of stream-sediments collected during the regional reconnaissance of Northern England, and the analysis of detailed stream- sediment and soil surveys performed by the author in selected areas. The sampling procedures and analytical techniques employed, were those 31 4 indicated in Chapter 5. 9.4.2.1 Regional Geochemical Reconnaissance During this survey 48 stream-sediment samples were gathered in the area (Figure 9.11). With the exception of Cu and Ni, the analysis of those samples shows that their trace-elements content lower than the average for Northern England (Table 9.9), of special importance in this context being the very low average contents in Pb and Ba (3Oppm and 235 ppm respectively). The geochemical models designed for the forecast of copper reserves indicate that the best elements that can be used to analyse the copper potential of the area are Cu, Mo, Fe, V, As, and Zn. In addition, anomalous contents in Pb and Ba should also be considered since they might indicate base metal mineralization in an area like this, where they are present in very low concentrations. Bearing those elements in mind, the following six samples may be considered worth following up: (1) samples 601 and 2402 at Capplethwaite (coordinates 3613E, 4925N; and 3619E, 4918N respectively), bearing anomalous concentrations of Pb (96ppm) and Zn (340ppm); (2) sample 2412 at Bottom Holmes (coordinates 3967E, 4932N), bearing high contents in Mo (3.5ppm); (3)sample 2413 at Hobdale Beck (coordinates 3984E, 4938N), bearing anomalous contents in Cu (92ppm); (4) sample 7387 at Cautley Holme Beck (coordinates 3993E, 4968N), bearing high levels in Zn (400ppm) and Fe (7.5%); (5) sample 2471 at Dillicar (coordinates 3908E, 4983N), with high contents in V (118ppm); According to these results it was decided to perform detailed sampling stream-sediment/along the different anomalous streams, as well as along TABLE 9.9 MAIN STATISTICS OF SAMPLES OF REGIONAL SURVEY - CELL 79 ELEMENT MEAN VARIANCE ST. DEVIATION Fe 3.608 0.481 0.693 Ga 9.679 8.492 2.914 Cu 27.735 .346.622 18.618 Pb 30.938 186.953 13.673 V 58.250 446.872 21.139 Ba 235.812 4496.879 67.059 Co 20.811 59.756 7.730 Ni 51.521 274.936 16.581 Mn 1954.729 7294861.053 2700.900 Li 47.042 2838.126 53.274 Mo 0.502 0.216 0.465 As 15.500 161.234 12.698 Zu 138.583 7094.078 84.226 Cd 0.625 0.963 0.981 3A. % the eastern trubutaries of the River Rawthey north cf Cross Hall, in order to investigate streams arising from the Coniston Limestone and the effect of doleritic bodies existing in the vicinity. In addition, a detailed soil survey was planned to be carried out in the northern flank of the Rawthey valley east of Sedbergh, with the purpose of assessing the mineral potential of the swarm of Hercynian faults existing in that area. The results fo those detailed investigations follow. 9.4.2.2 Detailed Geochemical Investigations As indicated these investigations consisted in stream-sediment and soil sampling in three areas : Dillicar, Capplethwaite Beck and Sedbergh. The results attained in each area were the following: (A) Area of Dillicar The analysis of the stream-sediments gathered in this area (Figure 9.12) confirmed the V anomaly detected during the regional survey, rendering values greater than 130 ppm. However, since this anomaly is not complemented by high values in other trace-elements, it is considered that this feature reflects local characteristics of the Silurian rocks, and thus it is not worth pursuing further. (B) Area of Capplethwaite Beck (Firbank) The detailed sampling of the stream-sediments in this area (Figure 9.13) confirmed the Pb and Zn anomalies detected during the regional survey. However, no systematic trends were detected, existing erratic highs in Zn, Cu, Pb and As. Since those high contents are not consistent-and correspond to isolated samples, it is considered that they probably arise from contaimnation (litter dumpling, ploughing, etc.) and hence do not reflect the presence of mineralization. (C) Area•of Sedbergh As indicated, several detailed investigations were preformed in this area, including detailed sampling of stream-sediments in several • Dillicar area-stream sediment sampling - 0,1 A 5, • PilliCar, --- 0 • . Y --\___...---' _ 0 EMI WI. S. Antonaleus Son SO" Mammas VienkKi Sena V-0Ao 1%. Mtn,* 2 mo Snamn an:Canal soup fl Ma ..grout surveym v-Ato 0 id•slotmled snow' S V-Ato x Indicate anomalous sample, 6 v-me FIG.9.12 Firbankarea-stream sediment sampling „.... _, F i r b a— k .:. Iv • 1 --.43--- • 0 _ -•,- +-- o - „.,_ ` tc..! \ 24,-= ‘ --71 , _ _ ,,i f;0 t -1– 1------..-- oi \ wy ,T.-- 15---- , — ---_=-_:-7_-. ______y7J ------_ _. _ _ c,..,. ..,...____.3k. F"-77-- -1 Ludlow 50505 -.., Anomalous saes Sat Elenants Wenloci Senn I So L—_] .,,,. 2 1n-Mn , _ «,,, Almelo 3 Sn-Ma L.. — A 2.4e-mu 0 SII•om onlan•nt maple reg.onol Ervore 5 V-Me 0 td.d•im:ed su,ty. FIG 9.13 • X Indnonn onnenolout •ample -3 t_ q becks, and a soil traverse run in the northern flank of the valley of the River Rawthey. The results of the stream-sediments surveys were the following (Figure 9.14a): (a) samples from Settlebeck Gill and stream to the east of Bottom Holmes showed average contents in trace-elements, no anomalies being detected; (b) the samples at Bottom Holmes showed that the lower part of the stream is anomalous in Cu (71ppm), V (155ppm), Mo (2.5ppm) Pb (185ppm) and Ba (3O9ppm). The anomaly extends for about 250m from the mouth of the beck, the samples gathered further upstream showing that it is discontinued. A possible explanation for this feature is that it is related to some of the ENE faults present in that area, and thus it would merit further investigations; (c) the detailed sampling of the Hobdale Beck did not confirm the anomaly detected during the regional survey, most of the samples bearing average contents in trace-elements. However, it must be mentioned that sediments from streams draining the RowantreeGrainsbear high Pb, Ba and Cd contents (up to 130ppm, 412ppm and 6.8ppm respectively). No satisfactory explanation can be put forward to explain these localized anomalies; (d)detailed sampling of the Cautley Holme Beck confirmed the high copper levels found during the regional survey in that stream. This anomaly is related to a stream that drains the Great Dummacks area at Coonthard Brow, bearing anomalous levels in Cu (67ppm), Fe (5.9%), V (171ppm), Pb (149ppm) and Mo (2.1ppm). A second anomalous stream, which influences the upper part of the beck, rises from Cautley Crag; in this case, the anomalous elements are Pb (150-3Olppm) and V(120-130ppm). The first of these anomalies lies in terrains of the Coniston Limestone Series, in an area where it is affected by faulting with associated lamprophyric dykes. The second anomaly lies in Silurian rocks, which upstream of the anomaly are faulted and pierced by similar dykes. . Sedbergh Area':'streamsediment sampling o_____-=====- -=====:::i2 km § 80$01Conglomerates [IJJJ Conislon LimestoneSeries Anamalous sites Sites Elements . Ni-Pb Stockdale Shales §B3 Ni-Ba-Cd 3 Ni ConislonGrit and flags D ~ Cu- V-Ma-Pb-8o 5 Cu-V-Ma . + Diabase [2j 6 Pb-V 7 Pb-V Minnetle 0 I Cu-fe-V-Pb-Ma 0 Stream sediment sample r~ional survey' 0 id-detailed survey Jl • Sail sample X Indicates anomalous sa~1a Fig.9.14a Sedbergh Area-soil sampling , , PP ppm ppm Cu Ba Pb-Zn 60 300 _150 200 100 _50 Hob dale 600—, Ye n? ft 500.. arboniferous 400-, Conglomerates 0 2km F1G.914b 3 17 It cannot be ascertained if these anomalies are related to the dykes and faults, or if they reflect mineralized structures. Therefore, those areas would merit further investigation; (e) stream sediment samples from the eastern tributaties of the River Rawthey showed average trace-element contents, with the exception of As, an element that is present in contents ranging from 75 to 2Slppm. Therefore, these streams lack interest from a mineral exploration point of view. The results of the soil traverse performed are indicated in Figure 9.14b, where the contents in Cu, Zn, Ba and Pb of the soils are indicated. These elements are the ones which give the best contrast and hence facilitate the interpretation of the results. Three main features are worth mentioning regarding the results obtained: firstly, the general low trace-elements content of the soils in areas underlain by Basal Carboniferous Conglomerates. Secondly, the enhancements in those contents occuring when the traverse reaches Silurian basements, a fact that is especially evident in the westernmost part of it, in an area underlain by rocks of the Coniston Grit. Thirdly, a main anomaly is observed in the central part of the traverse, rea g the trace-element concentrations values of 66ppm Cu, 178ppm V, 141ppm Pb, 292ppm Zn and 336ppm Ba. These values, obviously, are not related to effects of the underlying conglomerates and sandstones. A possible relation could exist between this anomaly and NE-trending faults present in the Bottom Holmes area, which in turn could produce the stream- sediment anomaly in that area. Therefore, it is possible that copper mineralization could be emplaced in these faults, and hence detailed investigation of the area appears worthwhile. 9.4.3 Summary and Conclusions During the detailed investigations performed in this celly most of the stream-sediment anomalies detected during the regiOnal survey were • 3 confirmed. The anomalies at Dillicar and Capplethwaite are not consistent enough as to indicate mineralized structures, and thus are considered to represent lithological effects and contamination, respectively. The anomaly at Hobdale Beck was not confirmed, though high Pb, Ba and Cd levels were detected in streams draining the Rowantree Grains, for which no satisfactory explanation was found. The anomaly at Cautley Holme Beck arises from a stream draining the Great Dummacks area, with another anomaly detected at a stream draining Cautley Crag. It cannot be ascertained if these features represent possible mineralized structures, or if they are related to mica traps (minettes) emplaced in minor faults in that area. A main stream sediment and soil anomaly was found at the Bottom HolMes area, a feature that is possibly related to NE-trending Hercynian faults that are known to the east of the anomalous sites. The anomaly dips towards the east, extending along a width of 250m, and presents eastwards- shifting of the Cu and V peaks, with respect to the Pb, Ba and Zn peaks. It is possible that this shifting could be due to differential mobility of the different elements in this rather calcareous environment, a case in which the most probable locus for the source of the anomaly would lie under the Pb, Ba and Zn peaks. Further detailed investigations are therefore recommended at Bottom Holmes and in the Cautley Holme Beck, in order to assess the possible presence of copper bearing ore bodies in those areas. These detailed investigations could consider closely spaced soil sampling grids orientated in a north-south direction, planned so as to intersect the swarm of NE-trending faults present and their projection towards the west. In addition, short soil traverses to intersect some of the known faulted mica traps should be considered, in order to assess their possible importance as sources of barren anomalies. CHAPTER 10 SUMMARY AND CONCLUSIONS 10.1 Regional Geochemical Reconnaissance Survey The main aim in interpreting the results of this survey was to determine the existence in Northern England of regional geochemical patterns related to bedrock geology and mineralization. The geochemical variations detected were the basis for the interpretation of the signifi- cance and usefulness of the geochemical forecasting models designed to predict base metal reserves in the area. 10.1.1 Sampling and analytical techniques (i) The survey was based on stream sediment sampling at an average density of one sample per 2.8 square kilometres. The sampling coverage of the different stratigraphic and lithological units present in the area was found to be adequate for the purposes of the research. A high degree of agreement exists between the actual number of samples collected over each geological unit, and the theoretical optimum calculated according to the total area covered by each unit; exceptions to this are the Silurian and post-Carboniferous terrains, the former having almost 20% more samples and the latter almost 25% less than the optimum, a fact that is,,mainly due to the glacial cover, drainage, and topography of those terrains. Therefore, the data used in the present research may be considered as a good cross- section of the geological population of the area. (ii) The -80 mesh fraction of the sediments was analyzed for more than 20 elements by means of a low-precision direct reading spectrometer (Quantometer); 10 of these elements (3a, Co, Cu, Fe, Ga, Li, Mn, Ni, Pb, V) were selected in this research. In addition, the samples were analyzed by atomic absorption and colorimetric methods for As, Cd, Movand 1") Precision and accuracy were, to a certain extent, compromised for high analytical productivity; however, since it has been previously demonstrated that even at precisions lower than 20% the sampling error greatly exceeds the analytical error, it is considered that the results obtained are adequate for the purposes aimed at, and thus the samples are representative of the geochemistry of individual sampling sites. 10.1.2 Data Handling (i) The handling of the results was done entirely by computerized methods, the data being stored in magnetic tapes. A preliminary selection of the results was done by analyzing the frequency distribution of the selected trace-elements, as displayed by the division of their range into 18 equal classes. This analysis showed that most elements had strong bimodality and positive skewness, features indicating'the presence in the set of a certain proportion of high values, part of which might have been the results of contamination. To overcome this problem, the value of each element at each site was checked, and if any content was higher than the detection limit, the sample was set aside for further examination. If that sample was gathered at less than lkm downstream of an orebody that had been mined, it was considered to be a possibly contaminated sample, and rejected. In this way, 5.1% of the original samples were rejected, the final set on which the research was based being thus reduced to 3806 samples, totalling 53,284 bits of information that needed to be interpreted. (ii) The analysis of the regional patterns displayed by each element was done using a grey-scale computer program, which plotted the data using deciles of the frequency distribution as class limits, and smoothed the results at each site by moving average. This type of mapping was found to be extremely useful, its main advantage being that it expresses very clearly all the trends existing in the sub-anomalous region, a very important feature when dealing with elements that have strongly skewed distributions._ 321 10.1.3 General distribution of selected trace-elements (i) The analysis of the frequency distribution of the 14 trace-elements selected showed that Fe, Ga, and Ni follow a gaussian curve; Li and V are quasi-normal having only a slight departure from that curve; Ba, Cu, and Pb are clearly log 10-normally distributed; and As, Cd, Co, Mn, Mo, and Zn display complex distributions (usually bimodal) that cannot be ascribed to a normal or log-normal curve. (ii) Most trace-elements are present in rather high concentrations in the Lake District, and within that area in terrains underlain by pelitic rocks. The Pennines region has average concentrations of the elements, though differences may be noticed between the concentrations in the rigid faulted block of the Northern Pennines, and the levels present in similar rocks lying outside that block, which bear lower concentrations in most elements probably due to their more calcareous and less detrital nature. The low- lands formed by post-Carboniferous terrains bear low contents in most elements. Within the Northern Pennine Block itself, it may be noticed that the northern part (Alston Block) has higher concentrations in most elements than the southern part (Askrigg Block), a feature possibly related to different tectonic settings already developed in the Early Carboniferous; the influence of contrasting magmatic activities and differences in the basement of both sub-regions cannot be disregarded in this respect. 10.1.4 Regional geochemical patterns related to bedrock geology. (1.) The clayey argillaceous rocks of the area render sediments that show lower trace-elements contents than similar rocks throughout the world, with the exception of their concentrations in Cu and Mo which are rather high, possibly due to the effect of contamination or secondary environmental effects, respectively. (ii) The stream-sediments arising from slates and greywackes formed in shallow marine environments (Skiddaw Slates), resemble a mixture of hydro- • 3 2 2 lizate and oxidate sediments, with high contents in Fe, Mn, Al, As, Co, Ni, Pb, V, and Zn, and very high concentrations in Li and Cu. Similar rocks but deposited during the Silurian in deeper environments resemble hydro- lizate materials, with high contents in Co, Cu, Cd, Ga, Mo, V, Zn, and As, and very high concentrations of Ni. (iii) The friable Permo-Triassic sandstones constitute resistates whose stream-sediments have lower trace-element contents than the regional average. Exceptions to this are localized enhancements in Ba and Mo, due to the presence of detrital barite in sediments from streams arising from mineral- ized terrains or to secondary environmental effects, respectively. (iv) The sediments arising from massive Carboniferous limestones normally present strong influences of the higher neighbouring terrains. Where free from that influence, they show low to average contents in most trace-elements, and relatively high contents in Cu and Zn, probably reflecting primary high concentrations in those metals. (v) The Carboniferous Limestone - series formed by mudstones, shales, hard sandstone, and massive limestones - renders sediments characterized by relatively high concentrations in Ba and Li, and very high levels in Pb and Zn. Most of these contents appear to be due to magmatic and mineral- izing effects, and hence they do not reflect the primary geochemistry of those rocks, mainly representing superimposed patterns. Within this series, an increase in the contents in Fe, Co, Li, and Mn of the sediments, and a decrease in the contents in Mo and V, may be noticed from the base to the top of the succession, indicating that the sequence was deposited in always more oxidizing environments. (vi) The sediments arising from the mudstones, shales, and hard sandstones that form the Millstone Grit and Coal Measures are characterized by lower trace-element contents than the regional average, a feature especially evident for As, Cd, and Zn. The comparative geochemistry of both series a 3 3 indicat$ that they were deposited in environments every time shallower and more oxidizing, a feature suggested by an increase from base to top in As, Ba, Fe, Mn, and V, and a decrease in the same stratigraphic order in Co, Cd, Ga, Mo, Ni, and Zn. (vii) The sediments derived from the Borrowdale Volcanics present low Ba contents, low to average concentrations of Co, Cu, Fer Ga, Mo, Nil Pb, and V, and high levels in As, Cd, Li, Mn, and Zn. The latter concen- trations may probably be related to ferromagnesian minerals (Li, Mn, Cd, Zn), to ferric iron oxides (Zn, Cd), or to iron sulphides (As), the high arsenic concentrations probably indicating late volcanic fluids or emanations. (viii) Sediments derived from the acidic intrusive bosses present in the area, bear lower contents in Co, Cu, Fe, and Ni than the regional average, and in most cases well below the average content in igneous rocks. The elements that tend to be concentrated in late fractionates or pegmatites (As, Li, Mo, Ga) are normally present in high concentrations in these sediments. The influence of the basic intrusive bodies of the area cannot be assessed from the regional survey, because they have very restricted outcrops, therefore it is practically impossible to separate that influence from the one of their country rocks. 10.1.5 Regional geochemical patterns in relation to mineralization (i) The Lake District orefield is evidenced by high Cu, Mo, and Pb con- centrations in the sediments, by minor enhancements in the levels of Ga„ Li and V, and by enrichments in Mn where psilomelane disseminations occur in the veins. The lead-zinc mining districts of that field are related to enhancements in Pb, and the copper-bearing districts to enhancements in the Mo content of the sediments. (ii) The mineralization known in the Alston Block of the Pennines is evidenced in the sediments by high contents in Ba, Cd, Li, Pb, and Zn, as • 3 2 4 well as by restricted high levels in Co and Mo. The lateral mineral zoning of that area is roughly evidenced in the trace-elements present in the sedi- ments: High Cd, Li, and Zn values are normally found in the fluorite zone, high Pb and Ba levels characterize the barite zone peripheral to the former, and high Mo concentrations are found in connection with the copper-bearing districts. (iii) The mineralization in the Askrigg Block of the Pennines is charact- erized by high concentrations in Cd, Li, Mo, Pb, and Zn. The fluorite- bearing districts are typified by high concentrations of Cd, Li, and Zn, the main Pb values being found in the periphery of those zones. High Mo values characterize the copper-bearing districts. (iv) The ore deposits in the Haydon Bridge area do not give broad regional patterns due to their reduced extension. However, their presence is mani- fested by minor highs noticeable in the Ba, Cd, Pb, and Zn contents of the sediments. (v) The spatial distribution of major elements in the area revealed the presence of three patterns probably related to hydrothermal alteration produced by the mineralizing fluids in rocks of the main mineralized areas of the Pennines. These patterns indicate an enrichment in potassium, and in minor proportion in iron, over the fluorite-bearing zones, as well as as a depletion in silicon in those areas, though the latter component is normally present in high concentrations in the central parts of those zones (where quartz is the main gangue of the ore deposits). These patterns agree with conclusions previously attained on the basis of geological evid- ence, about the nature of the brines that originated the deposits. 10.1.6 Regional distribution of selected trace-elements interpreted by R-mode factor analysis (i) An R-mode components solution was applied to the data of the regional reconnaissance, in order to try to express the relationship existing between • 3;5 the trace-elements in as few significant and interpretable parameters as possible. Direct and derived (orthogonally and obliquely rotated) solutions were computed for the whole set of results. The solution chosen as the most meaningful for the purposes aimed at, contained six orthogonally rotated factors which accounted for 72.4% of the variance of the original data set. The number of optimum factors to extract was estimated from a screegraph, the significance of the factor loadings being determined by considering them as correlation coefficients to which the Burt-Banks formula was applied. Factor scores were computed for each factor in each sample, and these scores were plotted as grey-level maps similar to the raw-data. (ii) Three factors of the chosen solution were interpreted as represent- ative of lithological assemblages: Fe-Mn-Li-Co-Ga, which represents the slate-greywacke association that forms the Skiddaw Slates; V-Ga, represent- ing the pelitic components of the rocks that form the Lake District; and Ni, unique factor representing the hydrolizate sediments forming the Silurian terrain. The lithological assemblages of the Pennines are represented by a mixture of these factors, due to their heterogeneity. Massive limestones and post-Carboniferous terrains of the lowlands are not evidenced by the model, mainly because of the fairly uniform low content in trace-elements that the sediments arising from those terrains have. (iii) Two of the chosen factors were considered7to be representative of mineralization: Ba-Pb, a factor representing the "Northern Pennine" type of lead-zinc deposit(vein or flat constituted mainly by galena, sphalerite, and barite), and Cd-Zn-Pb, an association clearly related to the ore deposits in the Askrigg Block of the Pennines, but which is obscured elsewhere by components of the "slate-greywacke"factor which creep into the factor scores during their computation. (iv) The last factor of the model (Mo-Cu-As) is a mixed one, partly 313R representing the hydrolizate sediments of the Silurian terrain, partly the acidic bosses of the Lake District, and partly the copper mineralization scattered in the two orefields lying within the studied area. 10.2 Forecast of Base Metal Mineralization in Northern England by Multiple Linear Regression For the purpose of forecasting the base metal mineral potential, the area was subdivided into 100 square kilometre cells. In each cell three types of parameter were computed (geological, geochemical, and production indexes), their relationship being established by multiple linear regression, a technique that was employed to design three groups of models (geochemical, geological, and combined geochemical-geological) for each base metal that thas been produced in the area (lead, zinc, and copper). 10.2.1 Compilation of the data (i) The geological indexes computed were eighteen stratigraphic parameters and four parameters related to faulting, all of which were measured from 1"/1 mile geological maps. The former were computed as percentage of area covered by each main stratigraphic unit recognizable in the area, and the • latter were computed as absolute values or length in miles. Prior to the statistical analysis, the stratigraphic indexes and the length of faults were multiplied times 10, the remaining indexes being introduced into the models as measured. (ii) The geochemical indexes were computed as average per cell of each metal as expressed by standard scores. Four types of score were computed for each cell: A and B were obtained from statistics of the whole data set; C and D were calculated from statistics of subsets of.the population representing different site-geology; A and C, depending on the frequency distribution of each element, were calculated using the arithmetic or geo- metric mean and the standard deviation or its logarithmic expression; and 3 2 7 B and D were computed from arithmetic mean and standard deviation values. In order to avoid negative numbers, all the scores were multiplied times 10 and a constant (50) was added to the resulting figure. (iii) Three types of production index were computed for each cell: Total production, average output per deposit, and number of deposits mined. The last index was expressed as an absolute figure, and the first two were expressed in terms of present expected value, which was obtained by adding the production and reserves (if any) of each base metal in each cell, and weighting the'resulting figures by the average settlement price attained by each metal during 1971 at the London Metal Exchange. The use of this type of weighting was considered justified, because the output in the different mining districts was raised over a long period, and because the use of a gross value term as a means of expressing mineral wealth is most meaningful if expressed in current figures, since it illustrates the importance of the output in the face of present costs and prices. 10.2.2 Multiple linear regression techniques employed (i) A variation of the classical stepwise regression procedure was select- ed in the present research to analyze the relationship existing between the various production parameters computed, and the geochemical and geolog- ical indexes. (ii) ,Considering the widely contrasting outputs obtained in the region for the different base metals, it was regarded that a simple model for the forecast of total base metal reserves would be very unlikely to be success- ful. Therefore, it was decided to design models for each individual base metal and later try to combine the forecasts obtained, in order to attain a more realistic prediction of the reserves. To assess this assumption, combined total and lead-zinc models were computed at the same time, and their results were compared with those obtained by indirect means. (iii) In order to include in the forecasting models the maximum possible • 3 ! 8 amount of "local" weight, which would render more meaningful estimates than regionalized models, it was considered that the optimum way of forecasting was to follow a convergent path. This convergent regression considered the design for each metal of models for the forecast of the number of deposits per cell, and the independent design of models for the prediction of the average value of the reserves contained in those deposits. At the end, both predictions were combined, rendering models for the prediction of the potential reserves existing in the area. To test the validity of this convergent forecasting method, straightforward models were calculated, where the total reserves were predicted, and their results were compared with those attained by convergent means. 10.2.3 Preliminary forecasting models (i) With the purpose of assessing the influence that the geology of the sampling site could have in the results, the four types of geochemical scores computed were regressed against the selected output indexes. It was concluded that the best scores to use were scores type A, which ignore the local geology but take into account the frequency distribution of each element. This is probably due to the fact that the scores represent averages over 100 square kilometres (i.e. about 35 samples), and thus the influence of the site-geology is strongly diminished, especially when several geological units are present within a single cell. In addition, it must be considered that transformations that render gaussian the frequency distribution of individual parameters should give better results than the use of untransformed values, since multiple regression operates at its best when dealing with multinormal sets of data. (iii) The coefficients of correlation between the parameters show a strong antipathetic relationship between copper and lead, and an always negative relationship between production and barium. The lead-copper antipathy is 3 2 9 a reflection of the fact that the lead-zinc districts of the area bear little or no copper ores, if any, and vice versa. The negative correlation between barium and output indicates that few important deposits are to be found where barite is the main constituent of the deposits. The good correlation found between the lead production and lithium is noteworthy, and suggests that this element could be a good pathfinder for that type of mineralization in marine environments similar to that of the Northern Pennines. (iv) The use of regression models that do not include a constant term was investigated by designing several preliminary models. It was concluded that most of the models without intercept have higher standard error of their estimates and lower multiple correlation coefficients than the corres- ponding models including a constant term. Besides, a great proportion of the models investigated were not significant at the 0.05 level; therefore, after these preliminary investigations, it was concluded that the use of regression models without intercept was not justified in the present case. (v) The possibility of transforming the variables in order to obtain more meaningful results, was investigated in several ways. The following transfortations were applied to the geochemical models: Reciprocal, square root, logarithmic, exponential, multiplicative, and polynomial; it was concluded that although in some cases the use of transformed variables could improve the results, in most cases nothing could be gained by effect- ing such manipulations. The transformations tested with the geological models were the following: Exponential,logarithmic, addition in several ways of parameters representing the Carboniferous Limestone, and expression of faulting parameters as ratios. As with the geochemical models, it was concluded that the transformation of the variables in designing geological models was not justified in the present case, because the results were worsened when such manipulations were performed. 3 3 0 (vi) The possible influence of the geological environment as a whole in the results, was investigated by the use of two scaled (dummy) variables which would take into account that three different environments lie in the area (Alston and Askrigg blocks in the Pennines, and Lake District). When those dummies were used, it was found that the production indexes were not correlated with them, and that only the variables most obviously dependent on the environment or characterizing it, were significantly correlated with such variables. The models obtained were in all cases similar to those attained without the use of these variables, and thus their use does not appear to be justified in the present case. This fact suggests that the particular combination of variables that constitute each model, would on its own be a clear reflection of the geochemical and geological environments present in the area. (vii) Another problem investigated by means of dummy variables was the possible influence in the geochemical models of the number of samples that each score represents. It was concluded that only Mn was significantly correlated with that dummy, probably because of the tendency of this element to render high values with the analytical method employed; however, the coefficient of correlation obtained is not high enough to consider, the use of that element as unjustified or biased. The output indexes were not correlated with the dummy, and thus the- models attained were similar to those obtained without the use of it. 10.2.4 Forecasts based on conver•ent multi le linear regression of production indexes (i) The best way of forecasting the base metal reserves present in the area was considered to be the design of three models for the estimation of the number of deposits that could be expected in each cell, and to combine the results of these models with those of three other models designed to predict the average value of the reserves contained in those deposits. Thus, • 3,3 I the convergent regression used to predict base metal reserves in the area considered the design of six models for each metal: Two of these were based on geochemical parameters, two on geological indexes, and two on a combin- ation of both. (ii) Investigations were performed in order to analyze the best way of combining the models indicated in the foregoing paragraph. It was concluded that the best results were obtained when the estimates were combined in an equation obtained by multiple regression, which would give differential weights to each of the output indexes predicted. Those weights are a direct consequence of the varying influence that those indexes have on the output of each metal, and are also a result of the way in which the mining of each base metal was organized in the past. (iii) The final model designed for the prediction of lead reserves explained 80.35% of the variance of the actual lead output, its estimates being very conservative since an average productive cell would render fore- casts 41% below the mean lead production. The differential loadings of the production indexes in that model agree with the fact that lead product- ion took place in the area in a large number of small to medium sized mines, and not in only a few big operations. The results of the convergent models are systematically better than those obtained by direct regression. The geochemical models perform better than the geological ones, explaining a higher proportion of the variance of the response with a lower standard error of the estimate; moreover, it may be concluded that the combination of geochemical and geological information renders the best results, more ••■ than doubling the amount of variance explained and halving the quadratic deviation. (iv) The final predictions for zinc reserves were obtained with a model explaining 97.84% of the actual zinc production, its estimates being also conservative since an average productive cell would render forecasts 45% • 3 3 2 lower than the mean zinc production. The differential loading of the indexes in the equation suggest that the zinc output was raised in the area mainly at numerous small to medium sized mines, and that only few mines raised large amounts of this kind of ore. The results obtained by converg- ent and direct regressions are comparably efficient, showing only marginal differences; however, the use of convergent regression appears desirable on the face of the high dependency of the output on the number of deposits worked at each cell, a feature that can only be assessed by indirect methods of forecasting. (v) The final model for the prediction of copper reserves explains 99.97% of the variance of the actual copper output, its estimates being fairly similar to the production figures, with a mean deviation of less than 4%. The loadings that the individual indexes have on the model indicate that the output was in this case dominated by a reduced number of mines which produced important amounts of ore (in terms of the total production). The convergent models explain similar amounts of the variance of the response as the direct models, but in the latter case the standard error of the estimates are usually higher. Furthermore, considering the erratic nature of the copper output that has been obtained in the area, it appears that the use of convergent regression is extremely desirable and even necessary, if meaningful localized forecasts are desired. Most modelS' render estimates much higher than the actual output, thus indicating the possible presence in the area of reserves much larger than the production that has been obtained till now. (vi) Generalizing the results obtained, it may be concluded that convergent regression is a perfectly valid method for the forecast of base metal reserves, its results being in most cases statistically better and more significant than those attained by simple or direct regression, with the advantage of introducing in the forecasts a greater local weight, a feature • 333 that is especially important in the case of mineral exploration problems. 10.2.5 Forecasts of combined reserves (i) The models designed by regressing geological and/or geochemical parameters against the total combined reserves of the area, show a strong similarity with the models built-up for the prediction of lead reserves, confirming the predominance of this type of ore in the total output which has been raised. The similarity is especially evident with the model to forecast the number of lead deposits present in each cell, pointing out the importance of this factor in the control of the total output. (ii) A forecasting model built up by multiple regression of production - indexes of the component base metals, showed that the indexes of copper production have little influence on the value of the total output raised, and that the silver production indexes are independent of it. According to this model, which explains 94.43% of the variance of the total combined production, an average productive cell of the area would render an estimate very similar to the actual output, its estimates being on average only 2% over the mean total production. The results obtained with this model are much better than those obtained by direct regression of total output, indicating that if total combined reserves are desired for an area, the best way to obtain them would be to design models for production indexes of the component metals, and to combined these estimates in a final model obtained by multiple regression. (iii) The results of the forecast of combined reserves are not as conser- vative as those for individual base metals, and therefore they must be interpreted cautiously, and checked against those obtained for individual elements. The latter forecasts are in the opinion of the author more reliable than those for combined reserves, since they are not so affected by extraneous factors, and thus most of the remaining conclusions refer to predictions obtained for individual base metals. 3 1 1 10.3 Other methods of forecasting base metal reserves 10.3.1 Qualitative estimates based on conventional geological data (i) The most favourable areas for mineralization in the Pennines region lie in the watershed areas, where the Great Limestone and other calcareous horizons are covered by younger beds, and where it may be expected that some of the lengthy mineralized structures known in that area may be inter- sected. Minor speculative targets can also be considered in relation to the outcrops of the Whin Sill, especially where they are related to faults with a larger throw than normal in the mineralized fractures of that area. (ii) No clear exploration targets may be indicated for the Lake District orefield, because of the little knowledge available with respect to the factdrs controlling the emplacement of the mineralization. However, according to the shape of the deposits and to the amount of work that has been carried out in them, undiscovered lead-zinc deposits may be expected around Keswick and Borrowdale, and copper deposits around Coniston. (iii) Several other areas may be suggested as containing base metal deposits, on the basis of indicators found to be related to mineralization while the geological models were built-up: Areas of Alston, Borrowdale, and Shap, all of which bear a high number of fault intersections; and several areas in the Lake District which have numerous acidic dykes, features apparently favourable for zinc and copper mineralization in that region. (ivy) Ore bodies lying within the known mining districts at depths beyond those reached by the mine workings may possibly exist in several areas, but their presence cannot be ascertained from the regional geological information available. 10.3.2 Qualitative estimates based on regional geochemical data (i) The most favourable areas for the presence of lead-zinc mineralization S 335 are those that contain anomalous samples in Pb, Zn, Cd, Ba, Li, and Fe, as well as anomalous values of the two component factors found to be related to this mineralization in the area (Ba-Pb and Cd-Zn-Pb). (ii) The favourable areas for copper mineralization are evidenced by anomalous contents in Cu and Mo, as well as by high values of the component factor Mo-Cu-As, which has been interpreted as partly representing the copper mineralization scattered throughout the region. (iii) Combining the results of these estimates with those obtained from geological information, it may be concluded that the most favourable areas for lead-zinc mineralization are the regions of Alston, Milburn Forest- Burnhope Seat, and Arkengarthdale (cells 25,36, and 72), and that the region of Coniston is the most promising for the presence of copper deposits. 10.3.3 Forecasts based on the frequency distribution of production indexes (i) The output parameters computed in this research were found to be log 10-normally distributed in the area, a fit that was measured by means of the non-parametric Kolmogorov-Smirnov test, applied at the 0.05 probability level. (ii) Taking into account the frequency distributions found, and the geo- logical and geochemical characteristics of the area, it may be postulated that 399 lead deposits would exist in 61 favourable cells, their reserves being valued at £394m; in those same cells, 154 zinc-bearing deposits with reserves valued at E82m may also be expected to exist. In addition, 68 deposits with copper reserves valued at £8m may be expected to,exist in 42 of the original 106 cells. (iii) Considering the deposits that have been.mined until now, 147 lead deposits with reserves estimated at E108m may still be expected to lie in the area, as well as 119 zinc deposits and 47 copper deposits, with reserves estimated at £63m and £5.6m, respectively. Those reserves would lie in 31 cells having all three kinds of ore, 30 cells bearing only lead and zinc 336 ores, and 12 cells containing only copper reserves. (iv) The average value of the reserves which may be expected in the zinc and copper deposits, is similar to the value of the ore in the deposits mined until now. On the contrary, the lead deposits would on average be smaller than those worked up to the present, with reserves 27% less than the average value of the lead output per deposit. (v) The mineral endowment of the favourable areas is £24,281 per square kilometre, a value composed of £14,784 of lead reserves, £8,630 of zinc reserves, and £767 of copper reserves. The rate of expectation for the 31 most favourable cells is one deposit per 16.6 square kilometres; that for the 30 cells containing only lead and zinc deposits is one deposit per 22.7 square kilometres; and that for the cells containing only copper deposits is one deposit per 62.5 square kilometres. 10.3.4 Quantitative forecasts based on a combination of factor and multiple regression analysis (i) Orthogonally rotated factor scores for the solution indicated in Section 10.1 were computed for all the samples collected in the area, and averaged for each cell. When these averages were regressed against the output indexes selected, it was found that only a few significant equations could be designed, and that these were much worse than the ones built up with the raw-data. (ii) A second approach employed considered the factorization of the geo- chemical scores using models containing 2 to 6 factors, and the regression of the resulting scores against the output indexes. In this case it was also found that nothing could be gained by this means, since only a few of the models designed were significant at the desired level, and these were worse than those designed with the raw-data. In addition, it was found that this approach would not reduce the number of variables, one of the objectives of performing the analysis, because it was seen that the larger •- 3 1 7 the number of factors in the equation, the greater were the chances of obtaining significant values. (iii) Orthogonally rotated principal component solutions containing 3 to 15 factors were computed for the geological variables, and the resulting factor scores were regressed against the output indexes. It was found by this means that when 15 factors were used, significant equations were attain- ed in all cases, these equations being poorer than those built-up with the raw-data in the cases of lead and zinc reserves, but were slightly better for the case of copper' reserves. Careful weighting of these results against the difficulties in interpretation posed by the factorized models, led to the consideration that factor analysis is not a very adequate tool to use in the present case prior to multiple regression analysis; this fact is especially evident if it is considered that no reduction in the number of independent variables can be achieved by this means. (iv) The possible causes for the failure of factor analysis in the present case, are complex. Probably, the most important of them is that although the factors are meaningful while visualized from a regional point of view, their meaningfulness ceases to exist when they are applied to localized geological features as mineralization, possibly as a result of the lack of connection between the factors. This hypothesis. would indicate that the use of independent pieces of information of the geological system, which are necessary components of it but which do not define it, is not likely to reveal at its best the minor components of the environment. Other hypothesis that could be brought forward in this connection, are related to the nature of the technique itself, in the sense that the factors being highly dependent on the number of samples included in the analysis, would lose consistency when averaged or partitioned into sub-sets, as required for the design of forecasting models. In this respect, the effect of the constant sum problem, and of the distortion produced by background • :3 '3 8 noise when the scores are computed, must also be considered as possible causes for the poor results attained. 10.4 Evaluation of Regional Stream Sediment Geochemistry in the Fore- casting of mineral potential Several methods were used in the present research to evaluate the efficiency of the forecasting models designed on the basis of the regional geochemical data. Taking into account that the geological information available for the area is excellent, and that the geochemical survey was not done for. exclusive purposes of mineral exploration, it is considered that if the efficiency of the geochemical models approactes that of the geological models, and if the addition of geochemical to geological information improves the forecasts, the use of regional geochemical infor- mation should be considered adequate for the purposes of forecasting the mineral potential of broad regions. 10.4.1 Qualitative-quantitative evaluation of the geochemical models The evaluation of the geochemical models taking as a basis the forecasts obtained by means of conventional analysis of geological, geo- chemical, and production information (sections 10.3.1, 10.3.2, and 10.3.3), gave the following results: (i) Regarding the identification of favourable cells for base Metal mineralization, the geochemical models are the most efficient of the models designed, with rates of 80% and 64% for the identification of potential lead-zinc and copper reserves, respectively. In both cases, the addition of geochemical information to geological data improves the estimates. (ii) Considering the forecasts of the number of deposits of each base metal that may be expected to exist in the area, the geochemical models perform better than the geological ones for the prediction of lead and copper deposits, but worse for the prediction of zinc deposits. It cannot S 3 1 9 be ascertained if this is a defect of the geochemical model, or it it is a result of defects on the statistics of production available, which would indicate less zinc deposits than really exists. (iii) With respect to the prediction of the average value of the reserves per deposit, the geochemical models do reasonably well in the case of the lead and zinc reserves, but give rather high estimates for copper reserves. Apparently, this is not a defect of the geochemical model, but it is a feature shared by all the models, suggesting that the production of copper ores in the area has been much less than could be expected from the geolog- ical or geochemical characteristics of the area. . 10.4.2 Statistical evaluation of the geochemical models The consideration of statistics intrinsic to the models, suggests the following features regarding the value of the geochemical models as forecasting tools: (i) The geochemical models perfori better than the geological ones, if the forecast of the total value and number of lead and zinc deposits are considered; for copper reserves the geological models perform better than the geochemical models, as a result of the very high estimates rendered by the latter. In most cases the combination of both types of information renders the best results. (ii) All the models are similarly efficient to predict the average value of the copper reserves per deposit, the geochemical models being more efficient than the geological ones when predicting zinc reserves, and less efficient when estimating lead reserves. In all these cases the forecasts are improved by the combination of geochemical and geological data. (ii) Considering the final results of the research, which were obtained by convergent regression of production indexes, it may be concluded that the geochemical models are equally efficient as the geological models, and that the combined models rendered better results than the individual parameters. 340 10.4.3 Discriminant analysis as a means of evaluating the efficiency of the geochemical forecasts Discriminant analysis was used in the present case to examine the behaviour of individual forecasts, as opposed to the behaviour of the model as a whole which was analyzed in the foregoing paragraphs. With that purpose, three sets of discriminant functions were computed for each base metal, on the basis of the variables included in the design of the different° forecasting models. Each set was formed by two functions, each of them computed on the basis of the productive cells of the area, divided into high and low-productive. Subsequently, discriminant scores were computed for all the cells, and the probabilities of their belonging to either group were calculated, the observations being assigned to the group with a prob- ability greater than 0.7; if both probabilities computed were lower than 0.7, the cell was assigned to a barren category. Tabulation of the class- ified cells against the output category corresponding to them on the basis of the forecasts obtained with the different models, brought the following conclusion about the behaviour of individual predictions: (i) The overall rate of successful forecasting of the geochemical models is similar to the rate of the geological models; an important increase in the rate of success may be achieved by combining both types of information. (ii) The geochemical models perform well when lead or copper reserves are to be predicted, but their performance is less than average when pre- dicting zinc reserves. The geological models are most efficient when forecasting lead and zinc reserves,but are very poorly efficient when estimating copper reserves. The combined models are the best to forecast copper and zinc reserves, but their performance in predicting lead reserves is rather poor as compared to the other models. (iii) Considering that the barren cells are much more than the mineralized cells, a second approach was taken, by classifying only the cells with a 3 4 1 positive forecasts into high and low-productive cells. The set of contingency tables computed as before, indicates that the overall success of the geochemical models to predict favourable cells is greater than the success of the geological models, the combination of both types of information rendering the best resutls. The performance of individual models for the forecast of the different base metals is similar in this case to the one observed when all the cells are considered. (iv) In general terms, the efficiency of the models for the forecast of zinc and copper reserves diminishes when only the cells with positive fore- casts are considered, the reverse being valid for the case of lead reserves. This feature indicates that the models for the prediction of lead reserves have a better resolution than the models for the estimation of the two other metals, in the sense that they are better for distinguishing between high and low-mineralized areas. However,, the models for the forecast of lead reserves are worse than the others, if the separation of all the cells into barren and undifferentiated mineralized cells is intended. Probably, these differences in partial efficiency are a result of the different numher of mineralized cells available for the definition of the production groups in each case. (v) Considering that for mineral exploration purposes it is not only important to assess the rate of success, but that the nature of the failures is also important, a system of scores was devised, in which the forecasts were assigned points according to their coincidence or non-coincidence with the discriminant classification. The failure scores were computed as representing major or minor possible losses in opportunity or capital, and were considered as penalties to be discounted from the scores of success, the resultant figure being expressed as percentage of the optimum. By this means it was concluded that the overall success-failure rate of the geochemical models is similar to the one of the geological models, the e" 3 4 2 combined information rendering the best results to separate within a broad region the areas likely to contain base metal mineralization. The behaviour of individual models for the forecast of the different base metals considered, is in agreement with the conclusions attained earlier on. (vi) If global estimates for the base metal mineral potential of an area were desired, it appears that the best way to proceed is to use combined geochemical-geological data to separate barren from mineralized areas, and to use geochemical models to separate - within the latter - those that have high potential from the ones with low potential. 10.5 Final Estimates (i) The conclusions attained from the evaluation of the forecasts, indicate that the efficiency of the different models is not consistent for the different types of reserve to estimate, but varies within fairly broad limits. Considering this fact, and taking into account the need for a single figure for each area, the need for establishing a global method of analyzing the efficiency arises, in order to select the best procedure to follow in the estimation of the potential reserves for the different base metals involved. It is considered that the'best procedure to use for the evaluation of the forecasts should combine the index of forecasting efficiency, which relates the predictions to actual.production figures, with the index of discriminant efficiency, which reflects the ability of the models to differentiate among the cells those with mineral potential. (ii) Considering the index of total efficiency as defined by the method indicated in the foregoing paragraph, the geochemical models are highly efficient for distinguishing cells with copper potential, moderately efficient in separating areas with zinc potential, and poorly efficient for distinguishing areas favourable for lead mineralization. (iii) On that same basis, it may be concluded that the geological models are very efficient for separating barren areas from those with zinc potential, 3 I 3 moderately efficient in distinguishing favourable cells for containing copper reserves, and are very poor in the prediction of lead reserves. (iv) The combined models are moderate to highly efficient for distinguish- ing all three types of potentially favourable areas. (v) The best procedure to follow to forecast base metal reserves is a two- stages one, in which in the first stage the cells are divided into barren and possibly mineralized cells, and in the second stage the latter are discriminated according to the value of their forecasts. Taking into account that the best model that can be applied in the second stage is in this case the same as in the first stage, it is considered that, in order to reinforce the predictions, the most favourable cells should be selected from the two best models which may be applied to differentiate between cells with high and low potential. (vi) On the basis of the indicated procedure, it may be estimated that 93 undiscovered lead deposits still lie in 21 cells of the area, with reserves that may be valued at £130,246,000, a figure that gives a lead endowment for the favourable areas of £62,021 per square kilometre. Consider- ing as an initial criterion of separation for the most favourable cells a forecast greater than £2.5m for the combined model, and an average value of the reserves per deposit greater than Elm, eight cells may be selected as the most favourable for the presence of undiscovered lead reserves (cells 24, 53, 55, 64, 65, 70, 72, and 82). Taking the forecasts of the geochem- ical model, second best in this respect, cells 24, 53, and 55 may be elim- inated because they have negative forecasts; thus, only five cells remain as more favourable: Cells 72, 70, 82, 65, and 64, in descending order of importance according to their geological and geochemical characteristics. (vii) Similarly, it may be estimated that 130 undiscovered zinc deposits still lie in the area, with reserves valued at £135,889,000, a figure that gives a zinc endowment for the favourable areas of £79,934 per square • 314 kilometre. Taking as initial criterion for the selection of the most favourable cells a forecast (geological) greater than £1.5m, and an average value of the reserves per deposit greater than £0.75m, fifteen cells may be considered as the most favourable for containing zinc deposits (cells 5, 8, 14, 15, 24, 27, 38, 45, 52, 57, 63, 72, 74, 100 and 101). Considering the geochemical forecasts, second best in this respect, it may be concluded that the cells with real potential are 24, 15, 45, and 57, in descending order of. importance according to their geological and geochemical characteristics. copper (viii) The presence of 149 undiscovered/deposits may be predicted in 46 cells of the area, with reserves valued at £54,392,000, a figure that gives a copper endowment for those areas of E11,824 per square kilometre. Taking criteria of selection similar to the case of the zinc deposits, it may be considered that ten cells are the most favourable for the presence of this type of mineralization (cells 46, 47, 65, 66, 74, 79, 80, 84, 85, 85, and 94). The refinement of the selection is in this case fairly complicated, because it appears that the reserves still lying in the area are much greater than the value of the production raised until now; therefore, the forecasts of the two remaining models must be examined to.select the most favourable areas, which according to these models would be cells 65, 85, 79, 66, 74, and 80, in descending order of importance according to their geological and geochemical characteristics. 10.7 Preliminary geochemical investigations in selected areas Taking into account the selection of areas according to the procedure indicated in the previous section, three areas were selected to carry out preliminary geochemical investigations, in order to assess their possible mineral potential as predicted by the models designed. The preliminary surveys included confirmation of anomalies detected during the regional survey, detailed stream sediment sampling at selected sites of the drainage system, and soil sampling along traverses to detect possible 3 mineralized structures related to the most obvious geological targets that can be observed in the chosen areas. 10.7.1 Cell 15 (i) The geological model indicates the possible presence of five zinc- bearing deposits in this area, with total reserves that may be valued at £12,793,000; in addition, lead reserves that may be valued at £6,682,000 may also be expected in four deposits in the area. (ii) On the basis of the geochemical information gathered, the mineral potential of this area appears to be concentrated in the north-central and east-central regions, where several confirmed stream sediment anomalies were detected. These anomalies lie in terrains underlain by the Upper Limestone Group, in zones where the Great Limestone and other underlying calcareous horizons are covered by younger beds, and where faults, that could be "leaders" for mineralized fractures are known to occur. (iii) Two anomalies probably related to mineralization were detected during the soil surveys. They are manifested by peaks in the Pb, Zn, Ga, Co, and V contents of the soils, which are associated to peaks in Li and Ba, found either at the same site or downdrainage of the main anomaly. One of these anomalies coincides with the northwards continuation of a vein worked at Church Burn, and the other was found in the West Allen-East Allen watershed, probably representing mineralization in a branch'of a regional fault existing in that area. (iv) The soils of the area present enhancements in Li and Ba where horizons belonging to the Upper or Lower Felltop limestones occur in the subsurface. Similar enhancements were found downdrainage of regional faults. These anomalies differ from those arising from possible mineral- ized structures in their contents of Pb, Zn, Ga, Co, and V, which are low to average. 0 31 1 10.7.2 Cell 70 (i) The combined model indicates the presence in the area of 4 undiscovered lead-bearing deposits, with reserves that may be estimated at £8,421,000. The geological components that produce the high estimates for this cell rare: a large number of fault intersections, and the large proportion of area covered by rocks of the Upper Limestone Group,which constitute almost half of the cell. (ii) According to the geochemical information gathered, the area has a clear lead potential which appears to be concentrated in the lower and middle slopes of the main moors of the region. In those areas the Great Limestone and other calcareous horizons are covered by younger beds, and the presence of several regional faults that could be "leaders" for mineralized fractures is known. (iii) Stream sediment anomalies detected during the regional survey at Birkdale Beck and Sledale, were confirmed as possibly related to mineral- ization; other similar anomalies were detected during the preliminary investigations at Cogill Knot and Ashgill Side. The anomalies detected during the regional survey at West Stonesdale and Thwaite Beck are consider- ed to be due to lithological effects produced by the Millstone Grit and calcareous horizons in the Upper Limestone, or by contamination related to litter dumping. (iv) Four soil anomalies independent of lithological, contamination, or secondary environmental factors were detected. Two of these lie north of Birkdale, in the northwards continuation of lead-bearing veins known at Stone House and Firs (Swaledale). Another anomaly was detected near Birkdale Cross, which was interpreted as representing mineralization in calcareous horizons of the Upper Limestone Group; a relationship between this feature and a regional fault existing nearby is possible. A last anomaly was detected near Tan Hill; it was not possible to ascertain if it 3 1 7 represents either mineralization at depth or if it is a consequence of high organic content of the soils in that area, due to the presence of coal layers in the vicinities. 10.7.3 Cell 79 (i) The geochemical model indicates the possible presence of one copper- bearing ore body in this area, with reserves valued at £2,585,000. The geological features of the area which render the preliminary investigations worthwhile are: the presence of numerous intersecting faults, the existence of patches of rocks of the Coniston Limestone Series, the presence of several acidic dykes (felsites), and the existence of a swarm of Hercynian faults - that could be "leaders" for mineralized fractures, as they are to the east of the Dent Fault. (ii) Several stream sediment anomalies were detected in this area during the regional survey and confirmed during the preliminary investigations. High Pb, Ba, and Cd levels were detected in streams draining the Rowantree Grains, for which no satisfactory explanation could be found. Similar anomalies were detected at Cautley Holme Beck; it was not possible to ascertain if they represent mineralized structures or if they, are related to mica traps emplaced in minor faults in that area. (iii) A main stream sediment and soil anomaly was found at Bottom Holmes. 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APPENDIX I GEOLOGICAL PARAMETERS NUMPFRS CORRESPOND TO FOLLOWING VARIABLES (1) LIASSIC,(2)KEUPFt< MARL.(3)9UNTER SANDSTON::,(4)PaRMIAN,(5)CUAL MEASURES,(6)MILLSTOE GRIT (7)LOWER LIMESIONE,(5)MIDOLE LIMESTONE.(9)UPFER 1.,IMESION't:,(11)6ASAL CONGLOMERATES.(11)SILURIAN (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) I. 94.0 23.5 76.5 -0.0 *0,0 -0.0 *0.0 -0.0 -0.0 -0.0 *0, 0 2 -0.0 17.8 68.9 3.2 -0.0 -0.0 -0.0 *0.0 -0.0 10.1 -0.0 3 *0.0 *0.0 35.3 2.2 *060 *0.0 7. 5 10.2 0.6 44.1 *0. 0 4 *Do 0 .4.0 -0.0 -.0.0 5,2 1.6 11. 0 21.0 34.4 2 5./ *0.0 5 -0.0 -0.0 *0.0 -0.0 1.8 5.6 9.4 22.4 52.9 1.8 -0.0 6 .4. 0 *0.0 *0.0 -6.0 46, a 23.0 *0, 0 31.1 37.3 -0.0 *0. 0 7 -0.0 -0.0 -0.0 *0.0 1.6 31.1 -0.0 2.1 64.7 -0.0 -0.3 3 -0.0 -0.0 *0.0 -0.0 19.7 29, 6 *0.0 *0.0 50.6 -0.0 -0.0 9 -U. 0 100. 0 -0.0 *Do 0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 10 12.3 87.7 *0.0 *0,0 -0,0 *0.0 -0.0 -0,0 -0.0 -0.0 -0.0 11 2845 58.2 13.1 -0.0 -0,0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 12 -0.0 8,4 80.7 104 5 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 13 -0.0 *0.0 45.7 1. 6 *0.0 ...0. 0 2.8 32.0 16.5 0.8 *0.0 14 -0.0 -0.0 -0.0 -0.0 9.5 1.4 -0.0 11.6 76.7 -0.0 -0.0 15 -0.0 -0.0 -0.0 -0.0 1,1 16.4 -0.0 4.8 77.7 -0.0 -0.0 16 -0.0 -0.0 *0.0 *6.0 -0.0 49.2 -0.0 0.4 50. 4 -0.0 -0,0 17 *0.0 -0.0 *0.0 *0.0 6.6 56. 4 -0s0 *0.0 37.0' -0.0 -0.0 18 *0. 0 *0, 0 -0.0 *0.0 48.3 41.6 *0.0 -0.0 10.1 -0.0 *0. 0 19 *0.0 30.9 46.6 1.7 18.3 2.5 -0.0 *0.0 -0.0 -0.0 -0.0 20 -0.0 24.0 31.3 3. 0 16.0 1 3. 3 -0.0 9.3 2.6 -0.0 -0.0 21 -0.0 0.. 27.7 12.1 36.5 15.4 -0.0 6.7 1.2 -0.0 -0.0 22 -0.0 -0.0 6,2 52.1 -0.0 36.4 -0. 0 -0.0 4.3 -0.0 *0.0 23 -0.0 -0.0 42.3 46.7 -0.0 -0.0 0.2 8.9 1.0 -0.0 -0.0 24 *04 0 -0.0 -0.0 7. 8 -0.0 *0.0 0.4 44.5 46.3 -0.0 0.1 25 -0.0 -0.0 .4,0 -0.0 -0.0 -0.0 -0.0 52.7 47.3 -0.0 -0.0 26 -0.0 -0,0 -0.0 -0.0 *0.0 6.5 -0.0 14.3 79,1 -0.0 -0.0 27 *0.0 *0.0 -0.0 -0.0 -0.0 15.4 -0.0 3.6 81.6 -0.0 -0.0 28 -0.0 -0.0 -0.0 -0.0 25.0 63.4 *0.0 *0440 11.6 -0.0 -0.0 29 -0,0 -0.0 25.3 -0.0 56.8 7.4 1.7 2.3 3.2 -0.0 -0.0 30 *0.0 *0,0 -0.0 *0.0 4.2 3.8 34 1 32.2 2.3 0.7 *0.0 31 -0.0 *0.0 -0.0 *0.0 *0.0 0.6 24 1 22.5 1.4 2.5 .4.0 32 -0.0 -0.0 -0.0 -0.0 -0.0 6.2 2.1 37.9 1.1 -0.0 -0.0 33 -0.0 -0.0 -0.0 8.4 -0.0 6.6 -0.0 48.6 34.4 -0.0 -0.0 34 *0.0 -0.0 23.1 76.4 -0.0 -0.0 *0.0 -0.0 0.5 -0.0 -0.0 35 *04,0 *O. 0 33.0 0. 6 -0.0 0. 4 8.0 38.7 5.9 0.4 0.1 36 *04 0 *0. 0 -0.0 *0.0 -0.0 *0.0 1. 0 74.1 21.4 -0.0 *Os 0 37 *Os 0 -0.0 *0.0 *0,0 *0,0 0.4 24 7 56.4 35.6 -0.0 -0.0 38 *06 0 -0.0 -0.0 *0.0 ...0, 0 8. 5 .4.0 28.7 61.7 -0.0 *0. 0 39 -0.0 *0.0 .4.0 -0.0 0.3 51.1 -0.0 5.7 40.6 -0.0 -0.0 40 *4.0 -0.0 *0.0 0.6 73.3 2.4 5.8 6.0 4.8 -0.0 -0.0 41 *Ilt 0 -0.0 -0.0 *O. 0 *0. 0 *0.0 0. 4 *0.0 *0.0 -0.0 -0.0 42 -0,0 -0.0 -0.0 *0.3 *0.0 -0.0 *0.0 -0.0 -0.0 -0.0 -0.0 43 -0.0 -0.0 -0.0 *Do 0 *0.0 *0.3 0.1 0.4 -0.0 2.1 *0. 0 44 -040 -0.0 -0.0 -0.0 -0,0 -0.0 6.3 27.9 044 28.9 -0.0 45 *Os 0 -0.0 -0.0 40.3 -0.0 1.2 3.4 16,7 27,1 -0.0 -0.0 45 ...0, 0 -0.0 19.4 58.3 -0.0 9.6 0. 4 1.1 6.6 ...0.0 0.5 47 -0.0 -0.0 5.0 5.7 -0.0 -0.0 5.3 68.0 0.4 2.5 1.2 48 -0.0 -0.0 -0.0 *0• 0 *0.0 0.2 4.0 77.1 3. 6 1.0 *0.0 49 -0.0 -0.0 -0.0 *0.0 1.7 21.4 -0.0 40.1 32.7 -0.0 -0.0 50 -0.0 *0.0 -0.0 -0.0 49.5 33.5 -0.0 042 16,0 -0.0 -0.0 51 *0.0 -0.0 4.0 667 20.4 1.9 7. 0 0.9 0,8 1.2 *0. 0 52 *0.0 -0.0 -0.0 -0.0 *0.0 -0.0 -0.0 -0.0 *0.0 -0.0 -0.0 53 *0.0 -0.0 -0.0 *0.0 *0.0 *0.0 *04 0 -0.0 *0.0 *0,0 *0.0 54 *0.0 *0.0 -0.0 *0.0 -0.0 -0.0 -0.0 *0.0 -0.0 -0.0 *0.0 55 .44 0 *0.0 *0.0 *0.0 *04 0 -0.0 *0,0 -0.0 *0.0 -0.0 *0.0 56 -0.0 *0.0 -0.0 -0.0 -0.0 -0.0 16.0 24.0 9.3 2.7 -0.0 57 *0.0 -0.0 -0.0 9. 3 ...0, 0 1. 1 O. 2 41. 4 48.0 -0.0 -0.0 58 ...04 0 *0.0 6.8 55.6 *0.0 *0.0 7.7 10.5 16.5 O. 3 0,1 59 *0.0 .4.0 1.3 0.1 0. 4 2 1,1 0. 5 41,7 34.9 -0.0 *0.0 60 -04 0 -0.0 *0.0 -0.0 -0.0 30.5 -0.0 • 6.7 62.8 -0.0 -0.0 61 -6.0 -0.0 *0.0 *0.0 *O. 0 33.0 *0. 0 42.3 24,7 -0.0 -0.0 62 .4.0 -0.0 72.3 0.6 *0.0 -0.0 -0.0 *0.0 -0.0 -0.0 -3.0 63 -0.0 *0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 *0.0 -0.0 64 -0.0 *0.0 -0.0 -0.0 *0.0 -0.0 -0.0 -0.0 -0,0 -0.0 -0.0 65 -0.0 -0.0 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LI -0.0 -0.0 -3.0 . -0.0 -0.0 ..0. 0 34 22 52.5 51 APPENDIX IIA ALLOCATED OUTPUT PER CELL APPENDIX IIB NUMBER OF DEPOSITS PER CET,T, APPENDIX IIC AVERAGE OUTPUT PER DEPOSIT ALLOCATO OUTPUT PER CELL CLLL TOTAL LEA 0.-ZINC C ZINC OPPER 6 1.32E1 11961 12092 1169 0 7 905 882 632 0 0 8 r; 4 4 0 0 15 2314 2247 2247 0 0 17 23 22 22 0 0 25 70060 67962 70060 11656 1 26 62307 60554 57837 2717 0 27 22490 21613 21613 0 0 28 802 729 729 0 0 30 1 1 1 0 0 31 4 3 3 o 2 32 /477 1776 89 182 35 1'74:9 29 29 0 0 36 6003 5605 6003 1 107 37 12537 12537 52 ,0 38 15'13 15250 MN 0 0, 39 4751 4646 4646 0 0 41 458 434 37 397 22 424469 4340 4489 2313 2 43 1 / 1 0 0 47 2383 2293 2293 0 0 43 214 209 209 0 0 49 12512 12551 12812 317 0 51 5 5 5 0 0 702 660 660 1 13 N 17589 16321 16321 0 1 59 41 39 0 0 60 26 la 25 0 0 64 36 0 0 0 36 71 13034 12735 13034 1 0 72 4209 4095 4239 0 0 75 2134 1 1 0 2133 81 12 12 o 0 82 1099 1068 1068 0 0 83 1457 1457 9 0 92 96 93 13 C 3 99 L30 420 420 0 0 100 536 526 526 0 0 106 5160 ' 4998 4998 1 .12 TOTAL NUMBELg-MIRUCTIVEF APOSITinpER CELL CELL COPPFR 6 5 6 6 2 0 7 1 1 1 0 0 1 1 1 o ig 5 5 5 0 0 17 2 2 2 0 0 25 52 50 52 14 1 26 15 15 15 1 - 0 27 15 15 15 C 0 28 4 4 4 0 0 30 1 1 1 0 0 31 1 1 1 0 32 5 4 5 3 3 35 1 1 1 0 0 36 23 21 23 1 3 37 26 26 26 2 0 38 12 14 14 0 0 39 6 6 6 o 41 1 1 1 2 1 42 3 3 3 3 1 43 1 1 1 0 0 47 3 3 3 0 0 48 2 2 2 c 0 49 9 9 9 1 o 51 1 I. 1 o 0 53 5 4 4 1 2 54 3 3 3 0 1 59 2 2 2 0 0 60 1 1 1 0 0 64 2 0 0 0 2 71 9 9 9 1 0 72 4 4 4 0 0 75 2 2 2 6 ' 2 81 2 2 2 0 0 82 3 3 3 0 83 4 4 4 1 0 92 3 3 3 0 0 99 5 5 5 0 o 100 4 4 4 0 0 106 13 12 12 1 1 tVERAGE PRODUCTION P".:R DEPOSIT PER CELL CELL TOTAL LEAD-ZINC LcA0 ZINC COPPER 6 1656 1983 201 584 0 7 905 852 512 o 8 5 4 4 0 0 15 432 449 449 0 0. 17 11 11 11 0 0 25 1347 1353 134 532 1 26 4153 4036 3855 2717 0 27 1499 1440 1440 0 6 28 230 182 1 e o 30 1 81 o o 31 4 3 3 a 2 32 355 369 35 29 60 35 29 29 29 0 0 3t. 261 266 26 1 35 37 193 482 49 26 0 38 13C9 1059 1039 0 o 39 791 774 774 0 0 41 L.178 434 37 198 22 42 1469 1446 148 772 2 43 1 1 1 0 0 47 794 764 764 0 0 48 1)7 104 104 0 o 49 1L23 1394 142 317 0 51 5 5 5 3 0 53 110 165 1:55 1 6 54 ''E3 5440 3.4 0 1 59 20 19 19 0 U 60 2C 25 25 C 0 b4 lii 0 0 0 15 71 144E 1415 1.4 1 a 72 1['r2 1024 125 0 0 75 1067 1067 0 0 1056 81 6 6 6 o 0 52 156 356 356 0 0 83 371 365 37 1 o 92 31 31 0 0 99 F56 84 84 0 0 106 134 131 131 0 0 126 396 416 41 9 12 APPENDIX III GEOCHEMICAL SCORES TYPES A C AND D 929'947 *LT "M T59'5* 0S 9.2+7 +72'•19 959'547 2+72'29 002°T5 22'1'947 0 171'2* 90T 629 ° Th 091'9* 6T5•4"47 529'247 92£'05 524"9* 99£•55 992•TS 6 4,9 .9* 4719''347 gOT 291 'T* 0*2"547 962'947 522.°947 929'1£ 2T0 .6* 915°9* 201°647 16 47"2+7 301 '4* -'101 ET9 •947 *25 °6* 9+72 °5+7 152'647 909 .147 26'1'05 656 .9+7 05 4 •04 196"447 96T'9' 20T Z69 .15 261 .61 T51 .847 TOTS 2£1'647 9T2 •2 47 6T1 6 £+, 222'25 222"15 1;0'647 20T 002 12+7 5T2•947 19T•05 226°647 57J2 °OS 69£•99 +722'2* 511'475 OTT '6* 10**6* TOT 92 0 '9* 569°05 O*0 *29 905'09 4+x0'147 02 T '147 9 22 •T5 990'647 99T'05 919 °L5 OOT 1***64, 20 47•E5 20 47 1'9+7 T92•9* 122°25 696°247 499°L5 209 .05 916'9* T22 *cc 66 29 0 '2* 96+7 '647 +79L •94; 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