Geological and structural investigation based on regional gravity and vertical electrical sounding data of the East Nile Rift Basin – Sudan
Item Type Theses and Dissertations
Authors OSMAN ADAM ALI, ABDU ELAZEEM
Download date 10/10/2021 09:15:17
Item License http://creativecommons.org/licenses/by-nc/3.0/
Link to Item http://hdl.handle.net/1834/5080
Geological and structural investigation based on regional gravity and vertical electrical sounding data of the East Nile Rift Basin – Sudan
By ABDU ELAZEEM OSMAN ADAM ALI B.Sc.(Hons.) Geophysics Red Sea University
Thesis submitted to the Graduate College (U. of K.) in fulfillment of the requirements of the M.Sc. degree in Geology (Geophysics)
Supervised by Dr. ABDALLA GUMAA FARWA
Department of Geology - University of Khartoum Khartoum - October 2011
Chapter One
Introduction
Chapter Two
Regional Geology and Tectonic Setting
Chapter Three
Gravity method
Chapter Four
Resistivity Method
Chapter Five
Results and Discussion
Appendices
Dedication
To my parents, brothers and sisters.
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Acknowledgements
I would like to thank everyone who helped and contributed to me to fulfill the requiements of this thesis to this form. In particular, I would like to thank Dr. Abdalla Gumaa Farwa for his contribution with data and for his fruitful and accurate supervision during the whole stages of the study. I would like to thank Dr. Ahmed Suleiman Dawoud, Dr. Abdalla El Hag Ibrahim, Dr. Ibrahim Abdo, Mr. Abboud Suleiman Ahmed and Mr. Mohammed El Amin Abd El Hameed for their scientific and academic contributions. Also, I would like to thank Mr. Migdad El Kheir and Mr. Mutaz for their help in the field work. Finally, I would like to thank GRAS staff for their permit to use their library and computer programs.
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Abstract
The analysis of geology and structure of the study area (East Nile - North Khartoum) is attempted by utilizing regional gravity and vertical electrical sounding (VES) data to investigate the source of the high gravity encountered over the basin features in this area as well as to reveal the structures, sedimentary sequences and groundwater condition in the area.
The regional gravity measurements are achieved along two profiles in the area using Scintrex CG-3 gravimeter.
All corrections common in gravity method are applied to the field data to produce Bouguer anomalies. The Bouguer anomalies are combined together with those produced by Sun Oil Company in 1984 and the residual anomaly separation is made using the least-squares method. The residual anomalies are interpreted using a 2D gravmodeller program (computer program) with the aid of geologic information in the area to produce geologic sections of subsurface of the area.
As a result, the most convenient explanation of the high anomalies is the presence of granulites with density of 3.1 g/cm 3. They are suggested to be uplifted during the period of the Pan-African movement to a depth of less than 3000 m below gneissic rocks with a density of 2.7 g/cm 3 beneath the Nubian Sandstone with a density of 2.3 g/cm 3, and its tip is thrusted to the surface at Sabaloka. Additional results are obtained from the interpretation of the gravity data. Several sedimentary basins, which were previously discovered, are delineated here again. The most important one is Atbara Basin in which the total thickness of sediments is about 3000 m. A depth map of the Basement surface of the study area is prepared. A dextral strike slip fault parallel to that appears at Sabaloka area is discovered in the area extending beyond River Atbara.
The vertical electrical sounding (VES) measurements are conducted in the area using SAS 1000 meter to reveal the sedimentary sequence and further to iv iv
investigate the groundwater condition in the area. The measurements are concentrated at Musawarat, El Awatib, Es Salama and Wad Musa areas. The present resistivity data are combined together with the old available data for more details.
The VES data are interpreted using IPI2win software. A number of 8 geoelectric/geologic cross sections are prepared.
As a result, the subsurface of the area consists of six geologic layers:
- The first layer is the surface layer consists of undifferentiated sedimentary facies (gravels, sands, clayey sands, sandy clays and clay).
- The second layer consists sandy-clay, clayey sands and sands.
- The third layer is saturated sandstones.
- The fourth layer is silicified sandstones/claystones (aquifuge).
- The fifth layer is saturated sandstones.
- The sixth layer is Basement Complex.
The third layer and the fifth one are upper free aquifer and lower confined aquifer, respectively. The lower aquifer is thicker than the upper one. So, its water is the most abundant and convenient for drinking and irrigation purposes. Five subsurface geologic maps are prepared. Two of them are depth maps of the top surface of the upper and lower aquifers. The other two are thickness map of the upper and lower aquifers. The last one is a depth map of the Basement surface.
Keywords: Gravity modeling, vertical electrical sounding, subsurface structure, groundwater.
v v
ا
ان ا ا و ا ا را ( ق ا - ل ا ط م ) ﺗ و ام ت ا ذ ا و ا ا ا ا ر ا ات ا ا ا ﺗ دف ق ا اض ا ا ا ﺗ ا ا وا ا وا ا و ا . .
إ ن ت ا ذ ا ا ط ل و ا ام ز س ا ذ ا ا ة Scintrex CG-3 . .
ﺗ ا اء ا ت ا ز ت ا ذ ا ل ات . ﺗ د ھ ه ا ات ﺗ ﺗ ا ل ا او ( Sun Oil Company ) م 1984 م و ﺗ ا ات ا ام ط ا ت ا ى و ﺗ ﺗ ھ ه ا ات ا ة ا ت ا ل ط ا . .
، ﺗ ا ا أ ن ا ا ات ا ﺗ ھ ر ا ا ذات ا ا ( 3.1 \ 3 ) ا ﺗ أ ر ا و ر ا ا ا ذوي ا ت ا ( 2.7 \ 3 ) و ( 2.3 \ 3 ) ا ا ، إ ر أ ﺗ ر إ ا إ ا 3000 م ل ة م ا ( Pan-African Movement ) أ دت إ ظ ر ھ ه ا ات ا ﺗ ق ا . . ذ ﺗ ا ف د ا اض ا و ا ﺗ ً و ض ه، و إ ن ا ا ى ت ا 3110م . إﺗ اد ا ر ا س و ﺗ ا ف ع إ ٍ از ا ھ ا و ا وراء ة . .
إﺗ ام ط ا و ا ا – ﺗ ا ا أ ( VES ) ام ز SAS 1000 ط ا ت ق ا رات، ا وﺗ ، ا و ود
vi vi
ا ا ا رو . ﺗ ا ت ا ا ت ا ً . .
ﺗ ﺗ ت ھ ه ا ام ا ا IPI2win و ﺗ ا اد 8 8 ط / . .
، ﺗ ا ج أ ّ ن ا ط ت ھ ا : :
- ا ا و ھ ط ﺗ ت ر ( ت، ر ل، ر ل ط ، اط ن ر واط ن .) .)
- ا ا ﺗ ر ل، ر ل ط و اط ن ر . .
- ا ا ھ ط ر ء . .
- ا ا ا ھ ط ط ر / ط . .
- ا ا ھ ط ر ء . .
- ا ا د ﺗ ر ا س . .
إن ا ت ا وا ﺗ ن ان ي و ان ر، ا ا . ا ان ا ا ر ا ً ا ان ا ي ا ا ا و ءاً و ا ء ً اض ا ب و ا ي . إﺗ اد ا ﺗ أ ق و ت ا ا ت ا و أ ق ر ا س . .
ت : ا ا ، ا ا ا أ ، ا ت ا ، ا رو . .
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Contents
Dedication…………………………………………………………………………ii
Acknowledgements……………………………………………………………….iii
English abstract……………………………….…………………………….……iv
Arabic abstract……………………………………………………………..…….vi
Contents…………………………………………………………………………viii
List of Tables………………………………………………………….…………xv
List of Figures……………………………………………………….…………..xvi
Chapter One
Introduction ………………………………………………………………………1
1.1 Introduction ……………………………………………..……………1
1.2 Location and access.………………………………..………………...1
1.3 Climate and vegetation ………………………..……………………..3
1.4 Physiography and drainage system... .…………………..……..…….3
1.5 Previous work ………………….….……………..………………….5
1.6 Present work ………….….…………………..………………………7
1.6.1 Objectives of the study ………………...…………………….8
1.6.2 Methods of the study ……………….………………………8
1.6.2.1 Data acquisition .………………………...………8
1.6.2.2 Data processing ………..………………………..8
1.6.2.3 Data analysis and interpretation ……...…………9
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Chapter Two
Regional Geology and Tectonic Setting ………………………………………..10
2.1 Introduction …………………………………………………………10
2.2 Regional geology ……………...……………………………………10
2.2.1 Precambrian (Lower Proterozoic) rocks ……………………11
2.2.2 Precambrian igneous rocks ……...………………………….11
2.2.3 Paleozoic (Ordovicion) igneous Rocks …………..…….…..11
2.2.4 Paleozoic (Devonian) igneous rocks …………………..…...14
2.2.5 Mesozoic (Jurassic) igneous rocks …………...…………….14
2.2.6 Mesozoic (Cretaceous) sedimentary rocks ……….……..….14
2.2.7 Mesozoic (Cretaceous) volcanic rocks ……………..….…...15
2.2.8 Cenozoic Hudi Chert ……………..………………………...15
2.2.9 Quaternary deposits ………………..…………………….…15
2.3 Dykes ………………..…………………………….………………..16
2.4 Tectonic setting ……………………………………………………..16
Chapter Three
Gravity method ………………………………………………………………….18
3.1 Introduction …………………………………………………………18
3.2 Theoretical backgrounds of gravity method ..…...………………….18
3.2.1 Newton’s Law of gravitation ……………………..………..18
3.2.2 Acceleration of gravity ……………………………….…....18
3.2.3 Gravitational potential .…………….………………………19
3.2.4 Potential field equations ..………………….………………21
ix ix
3.2.5 Derivatives of the Gravity Field ….………….…………….21
3.2.6 Absolute and relative gravity ..…………..…………………22
3.2.7 Variation of gravity .……………………………..…………23
3.2.8 The International Gravity Formula ………………..……….24
3.2.9 Gravity measurements .……………………………………24
3.2.9.1 Gravity instruments ………………...…………..24
3.2.9.2 Instrumental drift .…………..………………….26
3.2.9.3 Gravity Surveying ……………...………………27
3.2.9.4 Gravity data corrections ..…………..………….28
3.2.9.4.1 Free-air correction .…………….....28
3.2.9.4.2 Bouguer (Slab Plate) correction. ....29
3.2.9.4.3 Terrain corrections .…………..…...29
3.2.9.4.4 Latitude correction .…………….....30
3.2.9.4.5 Tidal correction ……………..……31
3.2.10 Free-air and Bouguer anomalies .………………..……….31
3.2.11 Accuracy of Bouguer anomaly .…………..………………31
3.2.12 Rock densities. …………………..………………………..32
3.2.13 Regional and residual anomaly separation.. …………...….36
3.2.13.1 Graphical methods of estimating the regional Effects…………………………..……………36
3.2.13.2 Grid or numerical methods ..…………… …...37
3.2.13.2.1 Empirical gridding residual Methods………………………...37 3.2.13.2.2 Analytical methods …………….38
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3.2.13.2.2.1 Second vertical derivative methods.. ………....38
3.2.13.2.2.2 Least-squares residual methods …...…..….39
3.2.13.2.2.3 Downward continuation41
3.2.14 Gravity interpretation ……….……..………………………42
3.2.14.1 Gravity effect of a sphere .……………...……..43
3.2.14.2 Gravity effect of a horizontal rod (line element) ….44
3.2.14.3 Gravity effect of a horizontal slab ...……….....44
3.2.14.4 Gravity effect of a complex shape and iterative modeling ...... 45
3.3 Gravity analysis of the study area ..………….……………………...48
3.3.1 Qualitative interpretation of gravity data of the study area....48
3.3.2 Anomaly separation of gravity field of the study area …..…55
3.3.2.1 Graphical separation of gravity field of the study Area……………………………………………..55
3.3.2.2 Anomaly separation of gravity field of the study area using Least-squares method …………...…61
3.3.3 Quantitative interpretation of gravity data of the study area …...67
3.3.3.1 Introduction …………………..………………..67
3.3.3.2 Depth-density models and geologic models long selected Profiles in the study area……...………67
3.3.3.3 Depth map of the basement surface of the study
area ………………………………………….....76
3.3.4 Conclusions…….…………..………….…………………..78
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Chapter Four
Resistivity Method ………………………………………………………………79
4.1 Introduction …………………………………………………………79
4.2 Theoretical background. ………………………………..…………..79
4.2.1 Electrode configurations .………………………..…………81
4.2.2 Rock resistivities .……………..……………………………81
4.2.3 Field work procedures .…………………….………………83
4.2.3.1 Field equipment...……………………………….83
4.2.3.2 Survey types .……………………………..….…84
4.2.4 Geo-electric Parameters …………………………..………..85
4.2.5 Types of electrical sounding curves over horizontally stratified media ………..………………………..……....…87
4.2.5.1 Homogeneous and isotropic media.... ……….....87
4.2.5.2 Two-layer media... ………………..……….…...87
4.2.5.3 Three-layer media... ………………..……….….87
4.2.5.4 Multi-layer media... …………………………….88
4.2.6 Analysis of electrical sounding curves ...………….……….88
4.2.6.1 Qualitative interpretation ……………..….…….89
4.2.6.2 Quantitative interpretation ………………...…...90
4.2.6.2.1 Introduction …………….………...90
4.2.6.2.2 Quantitative interpretation of two horizontal beds ...... ……90
4.2.6.2.3 Quantitative interpretation of multiple
horizontal beds…………………….93
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4.2.6.2.3.1 Partial curve matching…..93
4.2.6.2.3.2 Complete curve matching.94
4.2.7 Ambiguity in sounding interpretation...... ……………..96
4.2.7.1 Extraneous effects on resistivity measurements..96
4.2.7.2 Distortion of sounding curves ..………………...96
4.2.7.2.1 Formation of cusps ..…………..….96
4.2.7.2.2 Sharp maximum ..……………..…..97
4.2.7.2.3 Curve discontinuities …………...... 97
4.2.7.3 Principle of equivalence ..………………………98
4.2.7.4 Principle of Suppression …………….…………98
4.2.7.5 Principle of Anisotropy …………….…………..99
4.3 Resistivity analysis of the study area ..…………………..……….…99
4.3.1 General description ..……………………………..………..99
4.3.2 Qualitative interpretation of resistivity data of the study area ...100
4.3.2.1 Type-map of the study area ..……………...…..100
4.3.2.2 Apparent resistivity maps of the study area ...... 102
4.3.2.3 Pseudo-sections of the study area .…………....111
4.3.2.4 Total longitudinal conductance map(S-map) of the study area ……………………………………….107
4.3.3 Quantitative interpretation of resistivity data of the study area …...119
4.3.3.1 Introduction …………………………..……….119
4.3.3.2 Geo-electric sections along selected profiles in the
study area ………………………………………120
4.3.3.3 Geologic sections along selected profiles in the study
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area ……...... 123
4.3.3.4 Subsurface geologic maps of the study area...... 132
4.3.4 Conclusions………………………………………………134
Chapter Five
Results and Discussion…………………………………………………………140
Conclusions and Recommendations…………………………………………..143
References………………………………………………………………………147
Appendix (A)…….……………………………………………………………...158
Appendix (B)…….……………………………………………………………...172
Appendix (C)…….……………………………………………………………...179
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List of Tables
Tab. (3.1): Densities of rocks and minerals ..……………………………..…..34
Tab. (3.8): First order polynomial coefficients .…………………………..…..62
Tab. (3.9): Second-order polynomial coefficients ..…..…...………………….62
Tab. (3.10): Third-order polynomial coefficients ....……………………….…...62
Tab. (4.1): Resistivities of various rocks and sediments..…………………….83
Tab. (4.2): Variation of rock resistivity with water content…………………..83
Tab. (A.1): Gravity data of the study area (Bouguer, regional and residual
anomalies)……………………………………………………...... 148
Tab. (B.1): Graphical residual anomaly values of profile DD`………...... …..162
Tab. (B.2): Graphical residual anomaly of profile BB`…………………..…..163
Tab. (B.3): Graphical residual anomaly of profile AA`……………………...164
Tab. (B.4): Graphical residual anomaly of profile BC………………….……165
Tab. (B.5): Graphical residual anomaly of profile FF`..………………...…....166
Tab. (B.6): Graphical residual anomaly of profile EE`..…………....………..167
xv xv
List of Figures
Fig. 1.1: Location map of the study area………………..……………………..2
Fig. 1.2: Satellite image of the study area ……………..………………………4
Fig. 2.1: Geological map of the study area…………………..………………..12
Fig. 3.1: Principle of the unstable gravimeter……………..………………….25
Fig. 3.2: The gravimeter drift curve …………………….……………………26
Fig. 3.3: Terrain correction chart ………………….………………………….30
Fig. 3.4: Nettleton's method for estimating surface density….……..………...35
Fig. 3.5: P-wave velocity-density relationship for different lithologies …..… 35
Fig. 3.6: Schematic representation of application of Eq. (3.23)…..……….… 38
Fig. 3.7: Areas not used in regional calculation. (a) White points. (b) Circled area.………………………………………………………………….41
Fig. 3.8: Gravity effect of a sphere..…………………………………………..43
Fig. 3.9a: The Gravity anomaly across a vertical fault…………..…………….45
Fig. 3.9b: Structure of a fault with vertical displacement ( ) …...…….……….45
Fig. 3.9c Model of the anomalous body as a semi-infinite horizontal slab of height ……………………….…………………………………….. 45
Fig. 3.10: Polygon approximation of an irregular vertical section of a two- dimensional body .……………..……...…………………………….46
Fig. 3.11: An illustration of the parameters used in the computation of Line- integral at point 5.……..…………………………………………….47
Fig. 3.12: Base map showing profiles selected for interpretation..…………….50
Fig. 3.13: Bouguer anomaly map of the study area…………………………….51
Fig. 3.14: High anomaly zones, low anomaly zones and steep gradient zones on
xvi
Bouguer anomaly map of the study area…...…..……………….….52
Fig. 3.15: Bouguer and geologic map of the study area..……..……………….53
Fig. 3.16: Bouguer, regional and graphical residual anomaly curves of profile DD`………………………………………………………………….58
Fig. 3.17: Bouguer, regional and graphical residual anomaly curves of profile BB`…………………………………………………………………..58
Fig. 3.18: Bouguer, regional and graphical residual anomaly curves of profile AA`…………...……………………………………………………..59
Fig. 3.19: Bouguer, regional and graphical residual anomaly curves of profile BC……...……………………………………………………………59
Fig. 3.20: Bouguer, regional and graphical residual anomaly curves of profile FF`…………………………………………………………………...60
Fig. 3.21: Bouguer, regional and graphical residual anomaly curves of profile EE`…………………...……………………………………..….…....60
Fig. 3.22: Bouguer anomaly map showing gravity high zones (shaded Area)…63
Fig. 3.23: First order regional anomaly map of the study area……..……….…63
Fig. 3.24: Second Order Regional Anomaly Map of the Study Area………….64
Fig. 3.25: Third order regional anomaly map of the study area………..………64
Fig. 3.26: First order residual anomaly map of the study area…..……………..65
Fig. 3.27: Second order residual anomaly map of the study area……………...65
Fig. 3.28: Third order residual anomaly map of the study area………….…….66
Fig. 3.29a: Depth-density model along profile AA'……..……………..……..…70
Fig. 3.29b: Geologic model along profile AA'…..………………………..….….70
Fig. 3.30a: Depth-density model along profile BB'……...………….…..………71
Fig. 3.30b: Geologic model along profile BB'….…………………………....….71
xvii
Fig. 3.31a: Depth-density model along profile BC…..………………..…….…..72
Fig. 3.31b: Geologic model along profile BC…..……..…………………….…. 72
Fig. 3.32a: Depth-density model along profile DD'………….………………….73
Fig. 3.32b: Geologic model along profile DD'…..……………………..……...... 73
Fig. 3.33a: Depth-density model along profile EE'…...…………..………….….74
Fig. 3.33b: Geologic model along profile EE'..…………………….………..…..74
Fig. 3.34a: Depth-density model along profile FF'..…………………………….75
Fig. 3.34b: Geologic model along profile FF'..…………………………..……...75
Fig. 3.35: Structural contour map of Basement surface of the study area……..78
Fig. 4.1: Current distribution and equipotential surfaces in homogeneous and isotropic medium…….………..……………………………….……81
Fig. 4.2: Types of electrode configurations. (a) Wenner. (b) Schlumberger. (c) Pole-dipole. (d) Double-dipole..….……………………….……..82
Fig. 4.3: Columnar prism used in defining the geo-electric parameters of a section….…….………………..…………………………………….86
Fig. 4.4: Three layers curve type…..…………………….………………..…..88
Fig. 4.5: Two layers master curves of Wenner configuration………………...92
Fig. 4.6: Diagram showing the sequence of operation in the interpretation.…95
Fig. 4.7a: Distortion of sounding curves by cusps caused by lateral inhomogeneities……..……………………………………………....97
Fig. 4.7b: Discontinuities on Schlumberger curves caused by shallow dike-like structure ………………….……….……………………………..…. 98
Fig. 4.8: Base-map of resistivity and borehole data in the study area……….101
Fig. 4.9: Type-map of the study area…..………………………………….…103
xviii
Fig. 4.10: Apparent resistivity map of the study area for AB/2=4 m………...105
Fig. 4.11: Apparent resistivity map of the study area for AB/2=50 m……...... 106
Fig. 4.12: Apparent resistivity map of the study area for AB/2=100 m…..….107
Fig. 4.13: Apparent resistivity map of the study area for AB/2=200 m……....108
Fig. 4.14: Apparent resistivity map of the study area for AB/2=400 m………109
Fig. 4.15: Apparent resistivity map of the study area for AB/2=600 m……....110
Fig. 4.16: Pseudo-section along profile AA'….……………………………....112
Fig. 4.17: Pseudo-section along profile BB'……..…………………………....112
Fig. 4.18: Pseudo-section along profile CC'……………………………..…....113
Fig. 4.19: Pseudo-section along profile DD'…….………………………..…..113
Fig. 4.20: Pseudo-section along profile EE'…………………………..………114
Fig. 4.21: Pseudo-section along profile FF'….……………………………..…114
Fig. 4.22: Pseudo-section along profile GG'….……………….……………...115
Fig. 4.23: Pseudo-section along profile HH'…………………………….……115
Fig. 4.24: Total longitudinal conductance map (S-map) of the study area…...118
Fig. 4.25: Geo-electric /geologic section along profile AA'…...…………..….124
Fig. 4.26: Geo-electric /geologic section along profile BB'…...…………..….125
Fig. 4.27: Geo-electric /geologic section along profile CC'…...……………...126
Fig. 4.28: Geo-electric /geologic section along profile DD'……..……………127
Fig. 4.29: Geo-electric /geologic section along profile EE'…..………...….…128
Fig. 4.30: Geo-electric /geologic section along profile FF'..………………….129
Fig. 4.31: Geo-electric /geologic section along profile GG'…..…………..….130
Fig. 4.32: Geo-electric /geologic section along profile HH'…..……………....131
xix
Fig. 4.33: Depth map of the top surface of the upper aquifer……….……..…135
Fig. 4.34: Thickness map of the upper aquifer…………………………..……136
Fig. 4.35: Depth map of the top surface of the lower aquifer……....………...137
Fig. 4.36: Thickness map of the lower aquifer…………………………….….138
Fig. 4.37: Depth map of Basement surface…...………….……..…………….139
xx xx
Chapter One
Introduction
1.1 Introduction
High gravity anomalies are observed south of Jebel Umm Ali village in the East Nile (Nile State) area. It is known that this area is covered with thick sediments and such high anomalies cannot be interpreted as shallow Basement. A geophysical (gravity and resistivity methods) and geological investigations are carried out in the area using previous geological and borehole data to investigate the geology and structures of the area, to delineate the causative bodies of the high anomalies and to investigate the tectonic setting of the area.
1.2 Location and access
The study area is situated north of Khartoum bounded by latitudes 15⁰ 45` – 17⁰ 30`N and longitudes 32⁰ 30` – 34⁰ 30`E. It is bounded by River Nile from the west and by River Atbara from the north (Fig.1.1). It covers an area of about 24100 square kilometer.
The area can be reached using several routes. It can be accessed by railway or by asphalt road from Khartoum, Shendi, Ed Damer to Atbara. Numerous other tracks exist throughout the area, which are easily tractable by vehicles having four wheel drives.
1
Fig. 1.1: Location map of the study area.
2
1.3 Climate and vegetation
The climate of the area is desert to semi-desert. The winter period extends from November to March. In the summer months (May – September) temperatures can rise over 40⁰C. Rainfall is confined to the late summer months.
The area is sparsely vegetated except along the banks of the Nile and Atbara Rivers. Along the river banks various varieties of palm tree flourish and irrigation schemes allow intensive agriculture. Away from the permanent water courses, vegetation consists of scattered clumps of Acacia Species and ephemeral grasses during the rainy period.
1.4 Physiography and drainage systems
As it is observed from satellite images of the study area (Fig.1.2), the area is characterized by many distinctive physiographic features and drainage patterns.
Physiographically, the light-blue tone around Sabaloka and at the southern part of the area is attributed to Precambrian Basement.
A black ring around Sabaloka is attributed to the Sabaloka Ring Complex.
A circular shape in the northern part with a dark tone and a dark-brown to black tone adjacent to W. Awatib are attributed to Cretaceous Nubian Sandstone.
A dark-blue tone at the eastern part of the area is attributed to Cenozoic deposits.
A white tone at the eastern part is attributed to sand dunes.
Finally, a yellow tone within the whole area is attributed to superficial deposits.
3
Satellite image of the study area
4
The drainage in the study area is represented by the Nile River flowing northward then northeastward, and Atbara River in northeastern corner of the study area flowing northwestward. In addition, many seasonal wadis appear on the satellite image (Fig. 1.2). So, the area situated south of latitude 16⁰N and west of longitude 34⁰ is considered as a water divide where some wadis and khors flow outward in all directions. The wadis that flow northward are W. El Hawad, W. Jugjugi, W. Abu Talh, W. Garabana, W. Es Sawad, W. Gangy and K. Awatib. Others flow northeastward such as W. El kitir and W. Faragallah, and they pour in ephemeral lakes within Colluvium sand. The wadis that flow northwestward join directly the Nile. On the other hand, there are also small wadies flowing from the center of the circular shape outward in all directions. Some of these wadis flow eastward and southeastward to join the Nile.
1.5 Previous work
Ahmed (1968) studied the geology of J. Qeili and J. Sileitat Es Sufur igneous complexes. J. Sileitat Es Sufur complex is composed mainly of soda granite and syenite intrusions with minor rhyolite, pegmatite and diorites.
Sadig (1969) investigated Sabaloka area using gravity and magnetic methods. He suggested that the gravity lows over Jebalat El Humor and over the Basement Complex north of the plateau are attributed to the extension of the acid volcanic rocks in the northern part of the ring complex and deep granite, respectively. The gravity high north of J. Rawiyan was attributed to rising of the Basement Complex to the datum line.
Mohammed (1976) investigated Khartoum area between latitudes 15⁰ 15` – 16⁰ 00`N and longitudes 32⁰ 15` – 33⁰ 00`E to determine the depositional environment of the Nubian sandstone in the area. He concluded that the sedimentological parameters obtained for the Nubian in the area are of modern braided channel systems and the climate was tropical with alternating wet and dry seasons.
5
Ibrahim (1993) studied the Mesozoic-Cenozoic basins through the entire region of Sudan using aeromagnetic and gravity data. He discovered several sedimentary basins NW of the Central African Shear Zone (CASZ).
Farah (1994) studied the groundwater geology of the northern part of Khartoum Basin. He concluded that the subsurface of the area is an aquifer that consists of upper zone and lower zone. The groundwater of the lower zone is more fit for drinking, domestic and irrigation purposes than the upper zone. He recommended introducing simulation groundwater modeling.
El Dawi (1997) studied the area of Khartoum State east of the River Nile using gravity method and vertical electrical sounding techniques. She concluded that not all gravity low zones in the area are basinal features. Some of the depressions are step fault zones.
Mohammed (1997) investigated the paleoenvironment and evaluated the technical and engineering properties of mudstone of Shendi Formation at Jebel Umm Ali area. He concluded that the Shendi Formation can be subdivided into two members and three associations with lacustrine, transitional and fluvial environments.
Mekki (1999) investigated Lower Atbara area using hydrogeological and geophysical methods. He produced subsurface geological and hydrogeological map of the area.
Osman (2000) investigated the sedimentology and engineering properties of kaolinitic mudstone of Omdurman and Jebel Umm Ali areas. She concluded that the kaolinitic rich mudstone in these areas can be used as refractory brick. She recommended making more treatments to remove the impurities from the mudstone in order to suit other applications.
Salvatore (2000) investigated the area around Abu Deleig village (Khartoum State) between latitudes 15⁰ 00` – 16⁰ 15`N and longitudes 33⁰ 30` –34⁰ 30`E using
6 magnetic, gravity and resistivity methods. He concluded that the area is covered by thin thickness of sedimentary rocks and the gravity low over Wad Burwa and Qeili could be explained by emplacement of syenite bodies.
Ali (2001) studied the area of Khartoum and Shendi between latitudes 15⁰ 35` – 16⁰ 30`N and longitudes 32⁰ 30` – 33⁰ 50`E using remote sensing and gravity method to reveal the geology, structure and geometry of the Northeastern Khartoum basin and to resolve the groundwater problem in the area. She concluded that the dominant lineaments are strike-slip faults parallel to the Central African Shear Zone (CASZ) whereas the second set is normal faults parallel to the Khartoum and Blue Nile basins. She discovered several new sub-basins.
Badi (2001) investigated the situation of groundwater pollution and water quality in the southern part of the River Nile State. He concluded that the quality of the groundwater along the river Nile is of the fresh type, but far away from the river Nile it ranges from hard to very hard.
1.6 Present work
The regional gravity measurements of the East Nile - North Khartoum area show high Bouguer anomalies south of Umm Ali area. As the area is generally covered with thick sediments, the observed high gravity anomalies cannot be explained by shallow B.C. Such phenomenon is uncommon in the geology of Central Sudan and more work is needed to investigate the source of the high gravity encountered over the basin features in this area.
The area of the study is covered with Cretaceous Nubian Sandstone. It is bounded from the north by Abu Dom Complex and from the south by Sabaloka Igneous Complex. Abu Dom Complex comprises alkali granite and syenite with patches of preserved volcanics. Sabaloka Igneous Complex comprises a central subsided block of basement gneisses with preserved layers of basalts, trachyte and rhyolitic
7 lava flows surrounded by microgranitic dykes. Some Ignimbrite ash flows are known from amongst the rhyolitic volcanoes.
1.6.1 Objectives of the study
The main purposes of the study are to: Determine the nature and depth of the causative bodies of the high gravity anomalies. Determine boundaries of the body and its relation with the surrounding area. Determine the nature and the thickness of the sedimentary formation that overly the source body. Investigate the tectonic evolution of the sedimentary basins as determined by results of interpretation of geophysical data.
1.6.2 Methods of the study
In order to achieve the above mentioned objectives the following stages of work are adopted:
1.6.2.1 Data acquisition
This stage includes the following steps: Collecting gravity, resistivity and borehole data. Collecting geological and topographic maps. Study the Land sat images. Performing more gravity measurements at selected lines. Performing geo-electrical resistivity measurements.
1.6.2.2. Data processing
This stage requires using a computer and software of the gravity and resistivity techniques to: Correct the gravity data and produce Bouguer anomaly map. Process the resistivity data and produce geo-electrical sections.
8
1.6.2.3. Data analysis and interpretation
This stage requires geological, borehole and geophysical data to be analyzed with computer programs to: Determine anomalous gravity zones using relevant software. Calculate the thickness of the sedimentary layers from the geo-electrical sections and determine a type of each layer. Integrate and compare the results obtained from gravity and resistivity methods.
9
Chapter Two
Regional Geology and Tectonic Setting
2.1 Introduction
This chapter outlines the regional geology and tectonic setting of the study area. The regional geology is generally represented by rock units with different ages and geological structures over a wide region of the area. It is used as a supporting tool in interpreting the geophysical anomalies and reducing ambiguities associated with geophysical methods.
The regional geology of the study area is represented by different rock units ranging from Pre-Cambrian to Quaternary (Fig. 2.1). These units can be arranged from the oldest at the bottom to the youngest as follows: Quaternary Deposits (Superficial Deposits). Hudi Chert Formation (Thc). Nubian Sandstone Formation (Kst, Kf and Klac). Basement Complex. The Basement Complex includes all igneous and metamorphic rocks in the area ranging from pre-Cambrian to Devonian in age (Fig. 2.1) (GRAS and RRI Staff 1995).
The tectonic setting of the study area represents movements to which the area was exposed in the past. It is part of the Pan-African episode which controlled the formation of different rocks and structures.
2.2 Regional geology
The study area is surrounded by different rock types with different ages. It is bounded from the south-west by Sabaloka Igneous Complex, from the south by Khartoum Basin, from the east to south-east by Butana Plain and from the north to north-east by Shendi and Atbara Basins. These types are explained below in some details (GRAS and RRI Staff 1995).
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2.2.1 Precambrian (Lower Proterozoic) rocks
The following rock units have been observed in the study area (Fig. 2.1): Undifferentiated Precambrian rocks juxtapose on south and west of the area.
Gneisses are mainly quartzo-feldspathic with biotite and hornblende biotite varieties. Additionally, minor intercalations of muscovite kyanite schist, mica schist and graphite schist also occurs. This unit appears only as small outcrops, in the southwestern corner of the study area.
Locally developed granulite facies appears among the undifferentiated Precambrian rocks (GRAS and RRI Staff 1995).
2.2.2 Precambrian igneous rocks
Within the area affected by the middle-late Pan-African events, three varieties of plutonic granitoid intrusions have been distinguished. They are syntectonic granitoid intrusions, granites and gabbros. syntectonic granitoid intrusions range from alkali granite to granodiorite and have distinct internal fabrics and/or markedly concordant with the metamorphic banding in the country rocks. Highly diffuse patches could be areas of anatectic migmatites produced by more or less in situ melting of the country rocks. This unit appears in small areas south and south-west of Sabaloka area (Fig. 2.1).
Gabbros also appear at a small area adjacent to syntectonic granitoid intrusions (GRAS and RRI Staff 1995).
2.2.3 Paleozoic (Ordovicion) igneous rocks
Ordovicion igneous rocks in the study area crop at Wadi Abu Tuleih (16⁰24`N; 32⁰ 52`E) (Fig. 2.1). This complex was first mapped by Delany (1958), but Almond (1977) was first to carry out any detailed work. The complex is anorogenic and consists of syenitic and microgranitic varieties. The complex was probably emplaced about 463 Ma (Middle Ordovicion) (Harris et al. 1983; Klemenic 1984).
11
Geological map of the study area
12
LEGEND: Lithostratigraphic Units Recent Colluvium Sand Qal Qc Qs Alluvium dunes
Old alluvium Dunes and dunes field
Quaternary Old , often stabilized dunes
Umm Ruwaba Deposits CENOZOIC
Hudi chert Tertiary
Undifferentiated fluviatile sandstone, Basalts and Siltstone and minor conglomerates dolerites
Lakes within fluviatile environment of deposition of kst
Cretaceous Ferruginous horizons in the kst
MESOZOIC J Υ 4 Anorogenic
granitic rocks PHANEROZOIC
Jurassic (ring complex)
Acidic to Anorogenic DΥ4 intermediate granitic rocks volcanic rocks (ring complex)
Anorogenic
Devonian granitic rocks
(ring complex Anorogenic O Υ 4 granitic rocks PALEOZIOC
Anorogenic
Ordovician syenitic rocks
PЄ Υ 2 Syntectonic granitic intrusion and
anatectic migmatites 570? 570? Ma
– PЄ Υ Undifferentiated 900
Precambrian dioritic U. PROTEOZOIC U. and granodioritic rocks PЄp: Undifferentiated Proterozoic Metamorphic rocks Undifferentiated
PROTEOZOIC PЄpgns: gneissic areas Precambrian gabbroic
1600 1600 Ma
L. L.
– rocks
Granulite facies variants of PЄpgns
2500 2500
PROTEOZOIC
Miscellaneous Units: Ages Unknown: Field checked Dips/strikes: Dykes Measured dip: sedimentary bedding
Measured dip: metamorphic banding Geological Boundaries: Faults and shear zones: Geological boundary: observed or distinct on imagery strike slip fault Geological boundary: transitional 0r obscured Undifferentiated linear features: major Younger symbol: point to younger unit Undifferentiated linear features: minor
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2.2.4 Paleozoic (Devonian) igneous rocks
Devonian igneous rocks in the study area are represented by Sabaloka igneous complex which is divided into Devonian volcanic units and Devonian plutonic units (granitic and syenitic rocks). The Devonian volcanic units are acid or acid to intermediate volcanic rocks, pyroclastic debris and ash flow deposits (ignimbrite) associated with dated Devonian anorogenic ring complex (Almond 1971, 1977). The granitic rocks are associated with anorogenic ring complex, (Delany 1958; Almond 1971, 1977). The syenitic rocks of Devonian age are found in anorogenic ring complex in Ban Gedid (Ban Gedid complex) (Almond et al. 1969, 1977, 1984; Barth et al. 1983).
2.2.5 Mesozoic (Jurassic) igneous rocks
Jurassic igneous rocks are found in the study area as Jebel Sileitat Es Sufr complex (Fig. 2.1). The complex was first mapped by Delany (1955) and subsequently by Ahmed (1968, 1977). They found that the complex consists of a pluton of riebeckite granite, volcanic and sub-volcanic rocks, including rhyolite lavas and breccias, microdiorite, pegmatitic syenite and riebeckite quartz syenite. The complex is regarded as Middle Jurassic in age.
2.2.6 Mesozoic (Cretaceous) sedimentary rocks
Cretaceous sedimentary rocks have been mapped within the area, although none has been dated. The units cover most of the northern half of the study area (Fig.2.1). The units are undifferentiated Cretaceous sandstone, siltstones and mudstones; bioturbate lacustrine siltstones and mudstones; and ferruginous sandstones.
Undifferentiated Cretaceous sandstone, siltstones and mudstones have been studied by Omer (1983) south of Ed Damer, but are thought to be unfossiliferous. This unit was deposited by currents flowing generally in northerly direction.
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Bioturbate lacustrine siltstones and mudstones are certainly diachronous and represent the intermittent development of ephemeral lakes within the generally fluviatile environment of deposition of sandstone, siltstones and mudstones.
Ferruginous sandstones are of secondary origin and occur as hill capping nits or as bands within the ordinary sandstone sequence. These bands have no stratigraphic significance and cannot be used for correlation. They are generally no more than 1- 2 m thick. Whiteman (1971) states that north of Khartoum the ironstone cap of the „Nubian‟ sandstones may be older than the presumed early Tertiary Hudi Chert.
2.2.7 Mesozoic (Cretaceous) volcanic rocks
Cretaceous basalts including fine-grained dolerites are generally olivine-bearing alkali basalts. They appear only in a very small area, several kilometers south of Wadi Mukabrab.
2.2.8 Cenozoic Hudi Chert
The Hudi Chert outcrops usually in form of boulders in small patches over the area (Cox 1932, 1933; Andrew and Karkanis 1945; Whiteman 1971; Medani 1972). The cherts are yellow-brown, contains non marine gastropods may be of lower Tertiary age. This unit actually appears in four small areas in the northern part of the study area (Fig. 2.1).
2.2.9 Quaternary deposits
Within the area, the following Quaternary deposits have been mapped (Fig. 2.1):
Recent alluvium includes all active or recently active alluvial material, and part of the swamp deposits and also wadi deposits. It always concentrates along River Nile, River Atbara and all seasonal wadies and khors.
Old alluvium includes raised terraces, abandoned distributary channels that can be expected to have a less ephemeral vegetation cover than recent alluvium.
15
Sand dunes are shown as amalgamated dunes, and individual barchans in the eastern part of the study area.
Active or recently active sand occurs in the form of sheets or amalgamated dunes.
Colluviums are slope deposits of nearby origin. They form scree or talus plus finer equivalents.
2.3 Dykes
A large number of dykes have been observed in the area (east of Sabaloka area). The main dyke trend is roughly ENE-SWS, but the other set trends NW-SE. The dykes occur in form of acid and basic varieties. The acid types are probably related to the Paleozoic-Mesozoic acid ring complexes and the basic type seem related to the Cenozoic volcanic field (GRAS and RRI Staff 1995).
2.4 Tectonic setting
During the late Proterozoic the Central African Shear Zone (CASZ) was initiated. It can be traced from Cameroon trough of Central Africa, Chad to North Kordofan in Central Sudan, and probably further into the Red Sea in NE Sudan representing one of the major shear zones of lithosphere weakness in Africa (Schandelmeir et al., 1987). Therefore the Central Sudan lies in the eastern part of the Central African Rift System (CARS) which extends from Benue Trough in Nigeria to the Atbara Rift in Sudan (Browne and Fairhead 1983).
Along the Central African Shear Zone a series of NW-SE trending transitional basins developed in response to intermittently reactivated pre-Cambrian discontinuities (Schandelmeir et al. 1987; Jorgenson and Bosworth 1989).
On the basis of geological and geophysical investigations, Bussert et al. (1990) and Wycisk et al. (1990) confirmed the existence of several deep (>2km) graben and half-graben structures. These structures are located southeast the Central African Fault Zone (CAFZ) (Bussert et al. 1990, Schandelmeir and Pudlo 1990).
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Bussert et al. (1990) suggested that Shendi-Atbara sub-basin was formed as isolated half-graben structure during upper most Jurassic to lower most Cretaceous time. At the beginning it was formed during the north-eastern extension of the Central African Rift System. This was followed by a thermal-sag-phase and the basins expanded their areal extent beyond the limits of the graben structures. These outcropping sediments in the area represent the period of the basin evolution.
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Chapter Three
Gravity method
3.1 Introduction
Gravity prospecting involves the measurement of variation in the gravitational field of the earth caused by local variations in density of subsurface rocks. The measurements are normally made on the earth surface or on ship. Airborne measurements and underground surveys are also possible.
Gravity prospecting is used as a reconnaissance tool in oil exploration, as well as in mineral exploration.
This chapter includes a theoretical background of gravity method and gravity analysis of the study area.
3.2 Theoretical backgrounds of gravity method
3.2.1 Newton’s Law of gravitation
The expression for the force of gravitation is given by Newton‟s Law which is the basis for gravity work. This law states that the force (퐹) between two particles of mass (푚1) and (푚2) is directly proportional to the product of the masses and inversely proportional to the distance (푟) between their centers. The force is given by the equation,
푚 푚 퐹 = −훾 1 2 퐫 (3.1) 푟2
Where 퐫 is a unit vector directed outward from the center of 푚1, and 훾 is the Universal Gravitational Constant. It equals to 6.67 × 10−11푁. 푚2 푘𝑔2.
3.2.2 Acceleration of gravity
The acceleration of gravity is a vector quantity found by dividing the force 퐹 by the unit mass (푚2). If we substitute 푚1 and 푟 by the mass of the earth (푀푒 ) and its
18 radius (푅푒 ) respectively, the acceleration of the mass (푚2) at the surface of the earth is
퐹 푀푒 𝑔 = = −훾 2 퐫 (3.2) 푚2 푅푒
It is called the acceleration of earth gravity. It was first measured by Galileo and equals to 980 푐푚 푠2. In honours of Galileo, the unit of acceleration of gravity, 1푐푚 푠2, is called the gal.
3.2.3 Gravitational potential
The gravitational field, 푈(푟), is the work done in moving unit mass from a very distant point, mathematically from infinity, by any path at all to a point distant (푅) from the center of gravity of 푀푒 .
푅 푅 푑푟 푀 푈 푟 = 𝑔. 푑푟 = −훾푀 = 훾 푒 (3.3) ∞ 푒 ∞ 푟2 푅
It is often simpler to solve gravity problems by first calculating the scalar potential, U, then obtain 𝑔 by differentiating Eq. (3.3).
Considering three-dimensional mass of arbitrary shape, the potential and the acceleration of gravity at a point some distance away can be calculated by dividing the mass into small elements and integrating to get the total effect. The potential due to an element mass (푑푚) at a distance (푟) from P is
푑푚 푑푥푑푦푑푧 푑푈 = 훾 = 훾휍 푟 푟
Where 휍 is the density and 푟2 = 푥2 + 푦2 + 푧2. Then the potential of the total mass (m)
1 푈 = 훾휍 푑푥푑푦푑푧 (3.4a) 푥 푦 푧 푟
Sometimes it is convenient to use cylindrical coordinates. Since, 푑푥푑푦푑푧 =
푟0푑푟푑휙푑푧, the above expression becomes
푟 푈 = 훾휍 ( 0 )푑푟푑휙푑푧 푟 휙 푧 푟 (3.4b)
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In spherical coordinates, 푑푥푑푦푑푧 = 푟2푠푖푛휃푑푟푑휙푑휃; hence we have
(3.4c) 푈 = 훾휍 푟 휙 휃 푟푠푖푛휃푑푟푑휙푑휃
The acceleration in the direction of the z-axis is given by
휕푈 푧 𝑔 = = −훾휍 푑푥푑푦푑푧 (3.5a) 푧 휕푧 푥 푦 푧 푟3 or, in the other coordinate systems,
푧 𝑔 = −훾휍 푑푟푑휙푑푧 (Cylindrical) (3.5b) 푧 푟 휙 푧 푟2
푧 𝑔 = −훾휍 푠푖푛휃푑푟푑휙푑휃 = −훾휍 푠푖푛휃푐표푠휃푑푟푑휙푑휃(Spherical) (3.5c) 푧 푟 휙 휃 푟 푟 휙 휃
If the mass is very long in the y-direction, and have a uniform cross-section of arbitrary shape in the z-direction, the following two-dimensional expression is used to calculate the potential field
+∞ 푑푦 푈 = 훾휍 푑푥푑푧 푥 푧 −∞ 푟
In order to keep the integral finite, we replace the limits of ±∞ 푏푦 ± 퐿. Then let L approach infinity. The above equation becomes
1 푈 = 훾휍 – log 푥2 + 푧2 푑푥푑푧 = 훾휍 − log 푟2푑푥푑푧 = 2훾휍 log 푑푥푑푧 (3.6) 푥 푧 푥 푧 푥 푧 푟
Then the gravity effect of two-dimensional body is
휕푈 z 𝑔 = = −2훾휍 푑푥푑푧 (3.7) 푧 휕푧 푥 푧 r2
In Eqs. (3.4) to (3.7), we have assumed the density to be constant throughout the volume. This is not generally the situation in the field. If 휍 is a function of the coordinates, the potential can be calculated only for a few simple shapes.
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3.2.4 Potential field equations
The divergence theorem (Gauss theorem) states that the integral of a vector field over a region of space is equivalent to the integral of the outward normal component of the field over the surface enclosing the region. Mathematically we have
(3.8) 푣 ∇. 𝑔푑푣 = 푠 𝑔푛 푑푠 if there is no attracting matter contained within this volume, the integrals are zero, and
∇. 𝑔 = ∇. ∇푈 = ∇2푈 = 0 (3.9a) which satisfy Laplace equation in free space. In the respect coordinate systems Laplace equation is (Telford et al. 1990),
휕2푈 휕2푈 휕2푈 ∇2푈 = + + = 0 (3.9b) 휕푥 2 휕푦 2 휕푧 2
1 휕 푟휕푈 1 휕2푈 휕2푈 = + + = 0 (3.9c) 푟 휕푟 휕푟 푟 2 휕휙2 휕푧 2
1 휕 푟2휕푈 1 휕2 휕2푈 1 휕2푈 = + 푠푖푛휃 + = 0 (3.9d) 푟2 휕푟 휕푟 푟2푠푖푛휃 휕휃2 휕휃2 푟2푠푖푛 2휃 휕휙2
On the other hand, if the volume contains attracting matter, the above equation doesn‟t equal zero and thus satisfies Poisson‟s Equation
∇2푈 = 4휋훾푀 (3.10)
3.2.5 Derivatives of the Gravity Field
Quantities useful in gravity analysis may be obtained by differentiated the potential in various ways. We have already noted in Eq. (3.7) that vertical gravity is measured by gravimeters (Telford et al. 1990).The first vertical derivative of 𝑔 is
휕𝑔 휕2푈 1 3푧 2 = − = −푈 = 훾휌 − 푑푥푑푦푑푧 (3.11) 휕푧 휕푧 2 푧푧 푥 푦 푧 푟3 푟5
The second vertical derivative is
21
휕2𝑔 휕3푈 5푧 3 3푧 = − = −푈 = 3훾휌 − 푑푥푑푦푑푧 (3.12) 휕푧 2 휕푧 3 푧푧푧 푥 푦 푧 푟7 푟5
This derivative frequently is employed in gravity interpretation for isolating anomalies and for upward and downward continuation.
Derivatives tend to magnify near-surface features by increasing the power of the linear dimension in the denominator. That is, because the gravity effect varies inversely as the distance squared, the first and second derivatives vary as the inverse of the third and the fourth power, respectively, for the three-dimensional bodies.
By taking the derivative of 𝑔 in Eq. (3.5a) along the 푥 푎푛푑 푦 axes, we obtain the components of the horizontal gradient of gravity
휕𝑔 푥푧 푈 = − = 3훾휌 푑푥푑푦푑푧 (3.13) 푥푧 휕푥 푥 푦 푧 푟5 and similarly for the 푦 component 푈푦푧 . The horizontal gradient can be determined from gravity profiles or contour maps as the slope or rate of change in 𝑔 with horizontal displacement. The horizontal gradient is useful in defining the edges and depths of bodies (Stanley 1977).
3.2.6 Absolute and relative gravity
An absolute gravity is gravity acceleration at a point on the earth's surface. The measurement of an absolute value of gravity is difficult and requires complex apparatus and a lengthy period of observation. Such measurement can be made using large pendulums or falling body techniques with a precision of 0.01gu. Instruments for measuring absolute gravity in the field were originally bulky, expensive and slow to read. A new generation of absolute reading instrument (Browne et al. 1999) is now under development which does not suffer from these drawbacks and may well be in more general use in years to come.
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The relative gravity values are the differences in gravity acceleration between locations on the earth's surface. They can be measured by relative instruments. They can be converted to absolute values by reference to the International Gravity Standardization Network (IGSN) of 1971 (Morelli 1971) (a network of stations having absolute gravity values). By using a relative reading to determine the difference in gravity between an IGSN station and a field location the absolute value of gravity at that location can be determined.
3.2.7 Variation of gravity
The gravity acceleration varies in magnitude from point to another on the earth‟s surface. This variation comes from five factors. They are latitude, elevation, topography of the surrounding terrain, earth‟s tide, and density variations in the subsurface.
The variation of gravity with latitude is caused by difference in Earth‟s radius from the Equator to Poles that comes from Earth‟s rotation. It equals 5gal from Equator to Pole. The compensation to this variation is called latitude correction.
The variation of gravity from station to another with different elevation is caused by first, the difference in distance from the station to Earth‟s centre and second, the material that fill the spacing (difference in elevation) between the two stations. The compensation to this variation is called free air + bouguer slab correction.
The gravity value of the station is reduced by the surrounding topography which tends to attract the mass on the spring of the gravimeter. The compensation to this variation is called terrain correction.
The variation of gravity with the Earth‟s tide is caused by attraction of Sun and Moon. Thus, they tend to reduce the gravity value. The compensation to this variation is called tidal correction.
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Lastly, different rock types in the subsurface which have different densities give different gravity values.
3.2.8 The International Gravity Formula
The change in gravity with latitude comes from the fact that the equatorial radius is greater than the polar radius. This means that the variation depends on the earth‟s shape. The shape of the earth is found to be spheroidal and the earth‟s surface could be a spheroid which approximates the mean-sea level (with land masses above removed and ocean deep filled). Thus, in 1930, the International Gravity Formula
(IGF) was adopted to calculate the theoretical value of gravity (𝑔푡ℎ ) at any point on the reference spheroid. It was modified in 1967 by Geodetic Reference System (GRS67) as it is shown below
2 2 𝑔푡ℎ = 𝑔0(1 + 훼푠푖푛 휙 + 훽푠푖푛 휙) (3.14)
Where:
𝑔0: the gravity at equator = 978049 푚𝑔푎푙 for IGF30. = 978031.8 푚𝑔푎푙 for IGF67. 휙 : latitude. 훼 : constant = 0.0052884 for IGF30. = 0.0053024 for IGF67. β : constant = −0.0000059 for IGF30. = −0.0000058 for IGF67.
3.2.9 Gravity measurements
3.2.9.1 Gravity instruments
Previous generations of relative instruments were based on small pendulums or the oscillation of torsion fibers that took considerable time to read. Modern instruments capable of rapid gravity measurements are known as gravity meters or gravimeters.
24
Gravimeters are basically spring balances carrying a constant mass. Variations in the weight of the mass caused by variation in gravity cause the length of the spring to vary and give a measure of the change in gravity. In Fig. (3.1) a spring of initial length (푠) has been stretched by an amount ∆푠 as a result of an increase in gravity (∆𝑔) increasing the weight of the suspended mass (푚). The extension of the spring is proportional to the extending force (Hooke's Law), thus
푚 푚∆𝑔 = 푘∆푠 푎푛푑 ∆푠 = ∆𝑔 (3.15) 푘
Where 푘 is the elastic constant of the spring.
Fig. 3.1: Principle of the unstable gravimeter
∆푠 must be measured to a precision of 1:108 in instruments suitable for gravity surveying on land. Although a large mass and a weak spring would increase the 푚 ratio 푘 and, hence, the sensitivity of the instrument, in practice this would make the system liable to collapse. Consequently, some form of optical, mechanical or electronic amplification of the extension is required.
The necessity of the spring to serve dual functions, namely to support the mass and to acts as the measuring device, severely restricted the sensitivity of early gravimeters, known as stable or static gravimeters. This problem is overcome in modern meters (unstable or astatic) which employ an additional force that acts in the same sense as the extension of the spring and consequently amplifies the movement directly.
25
An example of an unstable instrument is the LaCoste and Romberg, and Worden gravimeters. Thermal effects on LaCoste and Romberg gravimeter are removed by a battery- powered thermostatting system, whereas in Worden gravimeter they are normally minimized by the use of quartz components and a bimetallic beam which compensates automatically for temperature changes. Consequently, no thermostatting is required and it is simply necessary to house the instrument in an evacuated flask. The reading range of LaCoste and Romberg gravimeter is 5000 mgal whereas for Worden gravimeter is 200 mgal.
3.2.9.2 Instrumental drift
A shortcoming of gravimeters is the phenomenon of drift. This refers to a gradual change in reading with time when the instrument is left at a fixed location. Drift results from the imperfect elasticity of the springs, which undergo an elastic creep with time. Drift can also result from temperature variations which, unless counteracted in some way, cause expansion or contraction of the measuring system and thus give variations in measurements.
The instrumental drift can be checked by repeating readings at a base station throughout the day. The meter reading is plotted against time (Fig. 3.2) and drift is assumed to be linear between consecutive base readings.
Drift curve
B.S.
g
n
i
d
a
e
r
r
e
t
e
m
i
v
a r
G B.S.
7:00 7:20 7:40 8:00 8:20 8:40 9:00 Tim e Fig. 3.2: A gravimeter drift curve constructed from repeated reading at a fixed location.
26
3.2.9.3 Gravity surveying
The station spacing used in a gravity survey may vary from a few meters in the case of detailed mineral or geotechnical surveys to several kilometers in regional reconnaissance surveys. The station density should be greatest where the gravity field is changing most rapidly. During a gravity survey the gravimeter is frequently read at a base station dependent on the drift characteristics of the instrument. At each survey station, location, time, elevation and gravimeter reading are recorded.
To correct the readings which were taken between two successive base station (B.S.) reading:
- The drift at one minute (Dmin) is computed
Dmin = (R2 – R1)/∆t
Where:
R1 is the B.S. reading at the first time
R2 is the B.S. reading at the second time ∆t is the total time
- Dmin is multiplied by the difference between the first B.S. time and the time of each station to obtain the drift correction at them. - The drift correction at each station is subtracted from the station reading to obtain readings corrected from the drift.
In order to obtain a reduced gravity value accurate to ±0.1 mgal, the reduction procedure described in the following section indicates that the gravimeter must be read to a precision of ±0.01 mgal, the latitude of the station must be known to ±10 m and the elevation of the station must be known to ±10 mm. The latitude of the station can consequently be determined from maps at scale of 1:10000 or smaller, or by the use of electronic position-fixing systems. Uncertainties in the elevation of stations probably account for the greatest error in reduced gravity values. The optimal equipment to determine coordinates and elevation at present is the global
27 positioning system (GPS), whose constellation of 24 satellites is now complete and an unadulterated signal is broadcast. Signal from these can be monitored by small, inexpensive receiver. Use of differential GPS, that is, the comparison between GPS signals between a base set at a known elevation and a mobile field set, can provide elevations to an accuracy of some 25mm (Keary et al. 2007).
3.2.9.4 Gravity data corrections
Gravity readings are generally influenced by five factors (Sec. 3.2.7), hence we must make corrections to reduce gravity readings to the values that they would be if they are measured at sea level surface or at a surface everywhere parallel to it.
3.2.9.4.1 Free air correction
Free air correction (∆𝑔퐹퐴퐶 ) is a correction made to compensate or reduce the measured gravity for the effect that is caused by the difference in elevation between the station and the reference level neglecting the effect of the material between them, which will be taken in the Bouguer plate correction. It can be obtained by differentiating Eq. (3.2) (dropping the minus sign)
∆𝑔퐹퐴 휕𝑔 휕 푀푒 푀푒 2𝑔 −1 = = 훾 2 = −2훾 3 = = 0.3086 푚𝑔푎푙 푚 ℎ 휕푅푒 휕푅푒 푅푒 푅푒 푅푒
∆𝑔퐹퐴퐶 = 0.3086ℎ 푚𝑔푎푙 (3.16)
It is added to the measured gravity if the gravity station is above the reference level and vice versa.
The free air correction is always of the opposite sense to the Bouguer plate correction. For convenience, the two are often combined in a single elevation −1 correction (∆𝑔푒 = 0.3086 − 0.419휌 ℎ), which amounts to about 0.2 푚𝑔푎푙 푚 . This must be added for the stations above the reference level and subtracted for that below it (Lowrie 1997).
28
3.2.9.4.2 Bouguer (Slab Plate) correction
After leveling the topography, there is now a fictive uniform layer of rock with density 휌 between the gravity station and reference level. The gravity acceleration of this rock-mass is called Bouguer plate correction (∆𝑔퐵푃). It is included in the measured gravity and must be removed (Lowrie 1997). This is modeled by a solid disk of density 휌 and infinite radius centered at the gravity station P. Let the angle 휙 in Eq.(3.18) increases to 2휋, the inner radius decrease to zero and the outer radius goes to infinite. The value of gradually become insignificant compared to
푟2, and the second term tend to zero. Thus, the Bouguer plate correction (∆𝑔퐵푃) is
−3 ∆𝑔퐵푃 = 2휋훾휌ℎ = 0.0419 × 10 휌ℎ 푚𝑔푎푙 (3.17) Where −3 휌 is in 푘𝑔. 푚 and is in meter.
The Bouguer plate correction (∆𝑔퐵푃) must be subtracted from the measured gravity, if the gravity station is above the reference level and vice versa.
In marine gravity survey all gravity stations are on sea-level. To compute (∆𝑔퐵푃) over an oceanic region we must in effect replace the sea-water with rock of density 휌. However, the measured gravity contains a component due to the attraction of the sea-water (density of 1030푘𝑔푚−3) in the ocean basin. The Bouguer plate correction is therefore made by replacing the density 휌 in Eq. (3.17) by (휌 − 1030) 푘𝑔푚−3, whereas, in the case of a large deep lake, the density is replaced by (휌 − 1000) 푘𝑔 푚−3.
3.2.9.4.3 Terrain corrections
The terrain correction allows for surface irregularities in the vicinity of the station. Hills above the elevation of the gravity station exert an upward pull on the gravimeter, whereas valleys (lack of material) below it fail to pull downward on it. Thus, both types of the topographic undulations affect gravity measurements in the
29 same sense and the terrain correction is added to the station reading (Telford et al. 1990). Practically, terrain corrections can be made using the terrain chart (Fig. 3.3) on which concentric circles and radial lines divided the area around the gravity station into sectors that have radial symmetry. The mean elevation of the sector is
, the inner and the outer radius of each sector correspond to 푟1 and 푟2, and the angle subtended by the sector is 휙. Thus, the terrain correction formula is
2 2 2 2 ∆𝑔푇 = 훾휌휙 푟1 + ℎ − 푟1 − 푟2 + ℎ − 푟2 (3.18)
The terrain correction at the gravity station is obtained by summing up the contributions of all sectors. The terrain corrections are generally necessary if a topographic difference within a sector is more than 5% of its distance from the station.
Fig. 3.3: Terrain correction chart
3.2.9.4.4 Latitude correction
Both the rotation of the earth and its equatorial bulge produce an increase of gravity with latitude. If we want to correct the gravity readings to the reference spheroid, and the measured gravity is an absolute value, the magnitude of correction produced by this factor can be obtained using Eq.(3.14). It must be subtracted from the measured gravity.
30
3.2.9.4.5 Tidal correction
Gravity measured at a fixed location varies with time because of periodic variation in the gravitational effects of the Sun and Moon associated with their orbital motions, and correction must be made for this variation in a high precision survey. They cause the elevation of an observation point to be altered by a few centimeters and thus vary its distance from the center of the mass of the Earth. The periodic gravity variations caused by the combined effects of Sun and Moon are known as tidal variations. They have a maximum of some 3gu and a maximum period of about 12 hours. The tidal variations are automatically removed during the drift correction.
3.2.10 Free air and Bouguer anomalies
After we make all corrections mentioned above to the measured gravity, we obtain an anomaly which is in fact comes from the density contrast of the Earth‟s interior.
This anomaly is called Bouguer anomaly (∆𝑔퐵),
∆𝑔퐵 = 𝑔표푏푠 − ∆𝑔푡ℎ ± (∆𝑔퐹퐴퐶 − ∆𝑔퐵푃) + ∆𝑔푇 + ∆𝑔푡푖푑푒 (3.19)
In some cases spatially when the survey is made on sea, only the free-air correction is made and the resulting anomaly is called Free-air anomaly, ∆𝑔퐹퐴,
∆𝑔퐹퐴 = 𝑔표푏푠 − ∆𝑔푡ℎ ± ∆𝑔퐹퐴 (3.20)
The free-air or Bouguer anomaly is a combined effects of the shallow structures and deep or broad structures which are called residual anomaly and regional anomaly, respectively.
3.2.11 Accuracy of Bouguer anomaly
The estimated error of the final Bouguer anomaly value depends mainly on the accuracy of the station elevations. It can be computed using the following equation:
31
2 2 2 2 ∆𝑔퐵 = ∆𝑔0 − ∆𝑔휙 + (퐶. ∆ℎ) (Ibrahim 1993) (3.21) where:
∆𝑔퐵: estimated error in the Bouguer anomaly
∆𝑔0: estimated error in the observed gravity value
∆𝑔휙 : estimated error in the theoretical gravity value 퐶 : elevation correction factor ∆ℎ: estimated error in the elevation.
3.2.12 Rock densities
Gravity anomalies result from the difference in density, or density contrast, between a body of rock and its surroundings. The sign of the density contrast determines the sign of the gravity anomaly.
Most common rocks types have densities in the range between 1.60 and 3.20g/cm3. The density of a rock is dependent on both its mineral composition and porosity. In sedimentary rock sequences the porosity tends to decrease with depth (due to compaction) and with age (due to progressive cementation) and thus the density increase. In igneous and metamorphic rocks the density gradually increases as acidity decreases. Density ranges from common rock types and ores are presented in Tab. (3.1).
A knowledge of rock density is necessary both for application for the Bouguer and terrain corrections and for the interpretation of gravity anomalies. Density is commonly determined by direct measurements on rock samples. The density value employed in interpretation then depends upon the location of the rock. It should be stressed that the density of any particular rock type can be quite variable. Consequently, it is usually necessary to measure several tens of samples of each particular rock type in order to obtain a reliable mean density and variance.
Other several indirect methods are also used. They usually provide a mean density of particular rock unit which may be internally quite variable. In situ methods do,
32 however, yield valuable information where sampling is hampered by lack of exposure or made impossible because the rocks concerned occur only at depth.
The measurement of gravity at different depths beneath the surface using special borehole gravimeter or, more commonly, a standard gravimeter in a mineshaft provides a measure of the mean density of the material between the observation levels. Gravity has been measured at the surface and at a depth immediately below. If 𝑔1 and 𝑔2 are the values of gravity obtained at the two levels, then applying free-air and Bouguer corrections, one obtains
𝑔1 − 𝑔2 = 3.086ℎ − 4휋훾휌ℎ (3.22)
The Bouguer correction is double that employed on the surface as the slab for rock between the observation levels exerts both a downward attraction at the surface location and an upward attraction at the underground location. The density 휌 of the medium separating the two observations can then be found from the difference in gravity. Density may also be measured in boreholes using a density (gamma- gamma) logger.
Nettleton's method of density determination involves taking gravity observations over a small isolated topographic prominence. Field data are reduced using a series of different density for the Bouguer and terrain corrections (Fig. 3.4). The density value that yields a Bouguer anomaly with the least correction (positive or negative) with the topography is taken to represent the density of the prominence. The method is useful in the case that no borehole or mineshaft is required, and a mean density of the material forming the prominence is provided. A disadvantage of the method is that isolated relief features may be formed of anomalous materials which are not representative of the area in general.
Density information is also provided from the P-wave velocities of rocks obtained in seismic surveys. Fig. 3.5 shows graphs of the logarithmic of p-wave velocity against density for various rock types (Gardner et al. 1974), and the best-fitting
33 linear relationship. Other workers (e.g. Birch 1960, Batyrmurzaev et al. 1961; Christensen and Fountain 1975) have derived similar relationships. The empirical velocity-density curve of Nafe and Dark (1963) indicates that velocities estimated from seismic velocities are probably no more accurate than about ±0.10kg m-3. This, however, is the only method available for the estimation of densities of deeply buried rock units that cannot be sampled directly.
Tab. (3.1): Densities of rocks and minerals
(after Telford et al. 1990)
34
Fig. 3.4: Nettleton's method for estimating surface density.
Fig. 3.5: P-wave velocity density relationship for different lithologies (the dotted represents Gardner's Rule: 휌 = 푎푣0.25 (after Gardner et al. 1974).
35
3.2.13 Regional and residual anomaly separation
The Bouguer anomaly is composed of two components, one is the regional and the other is a residual. The regional anomalies are the effect of the large-scale, broad and deep-seated structures, while the residual anomalies are the effect of small, confined and shallow structures such as basins and ore bodies. The regional anomalies have relatively long-wavelength and low curvature (low-amplitude) whereas; the residual anomalies have short-wavelength and high curvature (high- amplitude) (Skeels 1966 and Lowrie 1997).
After Bouguer anomaly has been calculated and before the interpretation is made, the anomalies of interest (residual anomalies) must be separated from the others of no interest (regional anomalies). The separation procedure can be thought of as predicting the value expected from deep features and then subtracting them from observed values, so as to leave the shallower effects. The expected value of the regional is generally determined by averaging values in the area surrounding the station. There are several methods for removing the unwanted regional, some of them are graphical and others are grid and numerical methods. These methods are described in the next section.
3.2.13.1 Graphical methods of estimating the regional effects
There are three degrees of refinement which are commonly used. The simplest method is that of drawing smooth contours and subtracting this set of contours from those of the observed map to contour the residual features.
A more refined method is to plot profiles along lines crossing the regional contours or regional geologic trends, to draw smooth regional curves on these lines, and to use these smooth curves to determine the location of the regional contours.
A still more elaborate method is to plot profiles on a network of intersecting lines. Smooth regional curves on these lines are drawn. The two regional values at each
36 intersection point must be reconciled by modifying and adjusting the curves, and then the regional values are contoured.
In areas where borehole data are available (i.e. having depth to basement and densities of sediments and basement), the regional anomaly value at the borehole is computed using the following equation:
𝑔푅푒𝑔 = 𝑔퐵 − 2휋훾∆휌ℎ (3.23) where, 𝑔푅푒𝑔 is the regional anomaly, 𝑔퐵 is Bouguer anomaly , ∆휌 is the density contrast between sediments and basement, is depth to basement.
Once the regional is determined and contoured, it may be subtracted from the observed map either graphically or numerically to obtain residual anomaly map.
3.2.13.2 Grid or numerical methods
The dependence on personal judgment and the required considerable labor by experienced personnel in the graphical method, have led to the development of numerical methods which are intended automatically to isolate local anomalies by rapid routine calculations. These methods operate on a regular spaced array or grid of values. The methods have been developed by two independent approaches, one largely empirical and the other analytical.
3.2.13.2.1 Empirical gridding residual methods
Griffin (1949) practically defined the residual gravity as follows:
∆𝑔 = 𝑔 푟, 휃 − 𝑔 (푟) (3.24) where, 𝑔 푟, 휃 is the gravity value at a given point on the gravity map (Fig. 3.6), and
𝑔 푟 = 𝑔 푟, 0 + 𝑔 푟, 휃1 + 𝑔 푟, 휃2 + ⋯ + 𝑔 푟, 휃푛−1 /푛 (3.25) where, 푟 and 휃 are polar coordinates of 𝑔.
37
Fig. 3.6: Schematic representation of application of Eq. (3.23) (after Griffin 1949).
The residual anomalies are thus obtained depend somewhat on the number of points selected but even more on the radius of the circle. The radius must not be too small to lose a part of the anomalies and not be too large to bring other anomalies. It is likely be of the same order of magnitude as the depth of the anomaly to be emphasized. The grid spacing for point to be calculated is generally about half the radius used for averaging.
3.2.13.2.2 Analytical methods
3.2.13.2.2.1 Second vertical derivative methods
The importance of the second vertical derivative arises from the fact that the double differentiation with respect to the depth tends to emphasize the smaller, shallower anomalies at the expense of larger, regional features (Elkins 1951).
The computation of the second derivative from gravity data distributed over a surface has been discussed by Elkins (1951), whom his work is based on an earlier paper by Peters (1949). He stated that, if value of gravity 𝑔 푥, 푦, 0 is known everywhere in the horizontal plane 푧 = 0, and 𝑔 is the arithmetic mean on a circle with radius 푟 and center P, the second derivative of 𝑔 at P can be obtained from the following relation:
38
휕2𝑔 휕𝑔 (푟) 2 = −4 2 (3.26) 휕푧 푝 휕 푟 푟=0
This means that the second derivative at P equals four times the negative slope of 𝑔 푟 at 푟2 = 0.
Because of the inaccuracy of determining the slope by this method, the equivalent numerical methods were introduced. Thus, several formulae were obtained for calculating the second derivative maps (Evjen 1936, Peters 1949, Henderson and Zietz 1949, Elkins 1951, Saxov and Nygaard 1953, Swartz 1954 and Daneš 1962). Different formulae give quite different numerical results and different grid spacing give different results with the same formula. All of them have the dimension mgal/distance squared. Thus, the second derivative maps are considered as convolution maps. So, they are not suitable for quantitative calculations but they could be an extremely useful tool for revealing the presence and location of small anomalies which could be detected only with great difficulty on Bouguer maps (Elkins 1951, Nettleton 1954 and Skeels 1966).
All of the second derivative formulas have the following form:
퐶 퐷 = 푊 퐻 + 푊 퐻 + 푊 퐻 + ⋯ (3.27) 푆2 0 0 1 1 2 2 where D is the second derivative value; 퐻0 is the center point value; 퐻 1, 퐻 2, … are average values at rings 1, 2, …; 푊0, 푊1, 푊2, … are weighting factors; C is a numerical coefficient; and S is the grid spacing.
3.2.13.2.2.2 Least-squares residual methods
Agocs (1951) stated that "the residual anomaly is defined as the deviation from the regional surface. The regional surface which best fits the observed anomaly data may be determined by the least squares. For the case of the simple plane, the equation of the regional would be
푍 = 푐00 + 푐10푥 + 푐01푦 (3.28)
39 and the residual anomaly would be
푅 = 퐺 − 푍 = 퐺 − (푐00 + 푐10푥 + 푐01푦) (3.29)
Where 퐺 is the observed value at the station whose coordinates are 푥 , 푦. The constants of the equation of the regional may be determined by using the normalizing equations
휕푅 푅 = 0 (3.30a) 휕푐00 휕푅 푅 = 0 (3.30b) 휕푐10 휕푅 푅 = 0 (3.30c) 휕푐01
Given the coordinates and the observed values, the regional may be determined, and the residual for the area calculated rapidly".
In some cases, the regional features would be more complex and not satisfy the simple plane. So, Simpson (1954) developed the simple plane to a polynomial surface of higher orders as represented by the following equation:
푛 푛−푖 푖 푗 푍 = 푖=0 푗 =0 푐푖푗 푥 푦 (3.31a)
In the case of the profile (2D) the regional is as follows:
푛 푖 푍 = 푖=0 푐푖푥 (3.31b)
Where, n is the selected order and equals 1,2,3,…….
Several normalizing equations equal to the number of coefficients for the selected order are set and solved to obtain the coefficients.
By using this method some distortion in computed residuals should be expected because the regional is computed from all input data points including the anomalous ones. To solve this problem, Skeels (1966) postulated that only the
40 values for the parts that we considered to be unaffected anomalies, as demonstrated in Fig. (3.7) will be used. The areas of these values can be determined by inspection or from a second derivative map or any other convolution map, or they may be determined by first calculating a preliminary regional using all of the points, determining the preliminary residuals from this map, and then calculating a new regional map from the original map, omitting the data in the areas that are anomalous on the preliminary residual map.
Fig. 3.7: Areas not used in regional calculation. (a) White points. (b) Circled area.
3.2.13.2.2.3 Downward continuation
Peters (1949) stated that the potential field measured at the earth's surface can be modified mathematically to that which will be if it is measured at a horizontal plane over the earth's surface or below it. The last is called downward continuation. It can be used to determine anomalies arising from sources near to the regional background. The method can also detect source beneath the surface which has unapparent effect. In so doing it makes the broad anomaly sharper. Thus, the downward continuation is effectively used to separate the residual anomaly from the regional one. Also it can be used to determine the shape of the buried source that gives sharp anomaly.
41
There are various methods for executing the downward continuation; one of them is Taylor series. The gravity field, 𝑔(푥, 푦, ℎ), at a depth can be expressed as Taylor series as follows:
휕𝑔 휕2𝑔 ℎ2 𝑔 푥, 푦, ℎ = 𝑔 푥, 푦, 0 + 푥, 푦, 0 ℎ + 푥, 푦, 0 + ⋯ Dobrin (1976) (3.32) 휕푧 휕푧 2 2!
The first and second derivatives are only used, but sometimes only the first derivative is adequate. The second derivative is computed as stated in Sec. (3.2.13.2.2.1). In alike manner as the second derivative is computed, Evjen (1936) proposed a method for computing the first derivative and thus he obtained the following equation
휕𝑔 𝑔 𝑔 𝑔 = 푧0 + 푧1 + 푧2 + ⋯ (3.33) 휕푧 2푟1 2푟2 2푟3
where 𝑔푧 0 = 𝑔푧0 is gravity value at the center of the circles, 𝑔푧 1 , 𝑔푧 2 , 𝑔푧 3 ,… are the averages of gravity values around circles of radii 푟1, 푟2, 푟3, … which equal 푆, 푆 2, 푆 5, … in the case of squared grid with spacing 푆.
Practically, the computation is made for a series of depths. When the field becomes unstable, the computation is stopped, and then the depth at which the anomaly is sharper is considered the depth of the crest of the source.
3.2.14 Gravity interpretation
After removal of regional effects the residual gravity anomaly must be interpreted in terms of an anomalous density distribution. Modern analyses are based on iterative modeling using high-speed computers. Earlier methods of interpretation utilized comparison of the observed gravity anomalies with the computed anomalies of geometric shapes. The ambiguity in the interpretation arises here from the fact that different density distributions can give the same anomaly.
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3.2.14.1 Gravity effect of a sphere
The sphere can be used to model diapiric structures. The contour lines on a map of the anomaly are centered on the diapir, so all profiles across the center of the structure are equivalent.
The gravity effect of a sphere at a point P (Fig. 3.8), directed along r, is as in Eq. (3.34) (Telford et al. 1990).
4휋훾휌 푎3푧 𝑔 = 3 (3.34) 3(푥 2+푧 2) 2 where, z is the depth to the sphere center, a is the sphere radius
When x=0, the vertical component of gravity is
−3 3 2 𝑔 = 𝑔푚푎푥 = 27.5 × 10 휌푎 /푧 (푎 , 푧 are in meters)
= 8.52 × 10−3휌푎3/푧2 (푎 , 푧 are in feet) (3.35)
𝑔푚푎푥 When, 𝑔 = , 푧 = 1.3푥1 (3.36) 2 2
Where 푥1 is half the width at the half-maximum value, 𝑔푚푎푥 . 2
Fig. 3.8: Gravity effect of a sphere.
43
The mass of the sphere (M) also can be expressed in terms of 푥1 and 𝑔푚푎푥 as 2 follows
2 푀 = 25.5𝑔푚푎푥 (푥1 ) tones (푥 is in meters) 2 2 = 2.61𝑔푚푎푥 (푥1 ) tones (푥 is in feet) (3.37) 2
3.2.14.2 Gravity effect of a horizontal rod (line element)
Many geologically interesting structures extend to great distances in one direction but have the same cross-sectional shape along the strike of the structure. If the length along the strike were infinite, the two-dimensional variation of density in the area of cross-section would be sufficient to model the structure. The gravity effect of a horizontal rod is
𝑔 = 2훾푚/푧(1 + 푥2/푧2) (3.38) then
푧 = 푥1/2 (3.39)
3.2.14.3 Gravity effect of a horizontal slab
The gravity anomaly across a vertical fault increases progressively to a maximum value over the uplifted side (Fig. 3.9a). This is interpreted as due to upward displacement of the denser material, which causes a horizontal density contrast across a vertical step of height (Fig. 3.9b). The faulted block can be modeled as a semi-infinite horizontal slab of height and density contrast ∆휌 with its mid-point at depth 푧0(Fig. 3.9c) (Lowrie 1997).
Let the slab be divided into thin semi-infinite horizontal sheets of thickness 푑푧 at depth 푧. Thus, the whole effect of the slab is
휋 1 푧 + ℎ 2 푥 휋 푥 𝑔 = 2훾∆휌ℎ + 0 푡푎푛−1 = 2훾∆휌ℎ + 푡푎푛−1 (3.40) 2 ℎ 푧0− ℎ 2 푧 2 푧0
44
The second expression in the brackets of the left hand side is a mean value, thus it is replaced by the value at the mid-point of the step, at depth 푧0.
Fig. 3.9: (a) The Gravity anomaly across a vertical fault; (b) Structure of a fault with vertical displacement , and (c) Model of the anomalous body as a semi-infinite horizontal slab of height .
3.2.14.4 Gravity effect of a complex shape and iterative modeling
The simple geometric models used to compute gravity anomalies in the previous sections are crude interpretations of the real anomalous bodies. Modern method for calculating the effect of complex shapes using an iterative procedure is derived.
Hubbert‟s (1948) derived a method for computing the gravimetric effects of two- dimensional mass distributions by taking line-integration around the body using the following equation
∆𝑔 = 2훾∆휌 푧푑휃 (3.41a)
Based on the principle of this method, Talwani et al. (1959) have derived the expression for the line-integration along the bound of a two-dimensional body of arbitrary shape in cross-section, by approximating the shape to an n-sided polygon (Fig. 3.10). Thus, the above equation becomes
45
푛 푐표푠 휃푖 푡푎푛 휃푖−푡푎푛 휙푖 ∆𝑔 = 2훾∆휌 푖=1 푎푖푠푖푛휙푖푐표푠 휙푖 휃푖 − 휃푖+1 + 푡푎푛휙푖퐿푛 푐표푠 휃푖+1 푡푎푛 휃푖+1−푡푎푛 휙푖
2 2 푛 푎푖퐶 1 푋 푖+1+푍 푖+1 = 2훾∆휌 푖=1 2 휃푖 − 휃푖+1 + 퐶퐿푛 2 2 (3.41b) (퐶 +1) 2 푋 푖+푍 푖
푍푖+1−푍푖 where 푡푎푛휙푖 = = 퐶 and 푍푖is the depth to the point 푖, 휙 and 휃 are in radian. 푋푖+1−푋푖
Fig. 3.10: Polygon approximation of an irregular vertical section of a two-dimensional body (after Telford et al. 1990).
Bott (1960) derived a computer method for the calculation of the shapes of two- dimensional sedimentary basins from gravity anomalies using constant density contrast. The body must be assumed to have end sides vertical in order to be confined to a region vertically below the anomaly profile; and its top horizontal in the case of outcropping bodies such as sedimentary basins or outcropping igneous masses, or its base horizontal in the case of buried igneous masses. Based on Fig. 3.11 the gravity effect of the body at a point can be computed from the following equation:
2 2 2 2 푗 푎푖퐶 푋 푖+1+푍 푖+1 푋 1+푍 0 ∆𝑔 = 2훾∆휌{ 푖=1 2 휃푖 − 휃푖+1 + 0.5퐶퐿푛 2 2 + 0.5 푋1퐿푛 2 2 + 퐶 +1 푋 푖+푍 푖 푋 1+푍 1 2 2 푋 푘 +푍 푘 푋푘 퐿푛 2 2 + 푍0 휃푡1 − 휃푡푘 } (3.41c) 푋 푘 +푍 0
Where k is the number of last end of the profile, j is the number of inclined lines, the second and the third terms on the right hand side are the line-integral along the
46 vertical side and the horizontal sides, respectively, and 푍0is the depth to the horizontal surface ; it can be made very small, e.g. 1cm, for outcropping masses.
In some cases, as in Fig (3.11) the thickness of the mass is assumed to remain constant beyond one end of the profile, then the line-integral along the horizontal side and the vertical side becomes 푍0 휃 푡1 − 휋/2 and 푍푘 휋/2 − 휃 푡푘 , respectively.
The practical application of the method is to select a number of points on the anomaly profile, when joined by straight lines they should approximately reproduce the profile. Using the infinite slab formula, Eq. (3.17), a first estimate of the thicknesses of the anomalous mass underlying the point is made. These thicknesses together with the surface define the initial model of the body. Using Eq. (3.41c) the gravity effect of the model is computed at a point at one end of the profile. The gravity effect so obtained is subtracted from the anomaly value and the
Fig. 3.11: An illustration of the parameters used in the computation of Line-integral at point 5 (after Qureshi and Mula 1971). residual anomaly is used to adjust the thickness of the model underneath the point, that means adding the quotient (residual anomaly/ 휋훾∆휌) to the thickness of the point. The model so adjusted is computed at the following point. Thus, when computation has been carried out at all selected points of the profile, the model has been adjusted as many times as the number of points. This completes one cycle of
47 computation. Three or five cycles are adequate for most profiles. A final cycle must be computed without any adjustment (Qureshi and Mula 1971).
3.3 Gravity analysis of the study area
Gravity map of the study area is a part of the gravity map of Central Sudan which was produced by Sun-Oil Company in 1984. The gravity map of Central Sudan covers an area situated between Latitude 16-18ºN and Longitude 32-35ºE. The gravity measurements were conducted on 985 stations at 26 lines. 20 lines are parallel and extend NE-SW. 5 lines extend NW-SE but they aren‟t parallel. One line extends E-W. The spacing between two adjacent lines ranges from 10-60km, whereas for adjacent stations ranges from 3-5km. The small spacing is selected whenever gravity readings are shown to vary rapidly with distance.
All gravity stations were tied with the International Gravity Standardization Network (IGSN).
All corrections mentioned in Sec. (3.2.9.4) were made. The IGF30 was used for latitude correction. The density 2.35g/cm3 was used for Bouguer and Terrain corrections. The total accuracy of Bouguer anomaly was calculated using Eq. (3.21) and found to be (±0.19mgal). Finally, the Bouguer Gravity Map of Central Sudan is produced with contour interval 2mgal and with scale 1:250000.
A base map of gravity stations of Sun Oil and borehole data in the study area between Lat. 16-17.5ºN and Long. 32.5-34.75ºE is constructed (Fig. 3.12). The Bouguer anomaly values at gravity stations are recontoured and a Bouguer anomaly map is reproduced with the same contour interval (Fig. 3.13).
3.3.1 Qualitative interpretation of gravity data of the study area
The Bouguer anomaly map is divided into high anomaly zones, low anomaly zones and steep gradient zones (Fig. 3.14). On the other side, the Bouguer anomaly map
48 is overridden on the geologic map of the area (Fig. 3.15) to correlate the above mentioned zones with the geology.
In Fig. 3.14, four high anomaly zones are shaded by red color and characterized by letters A, B, C and D.
The zone A is situated around Ban Gadid between Sabaloka and Musawarat villages. It approximately takes rectangular shape. Comparing this anomaly with the geology in Fig. (3.15), the western part of the zone A lies over outcrops of the Granulite at Ban Gadid, whereas the eastern part lies over Nubian Sandstone and superficial deposits. Thus, this high anomaly is caused by Granulite.
The zone B occupies the central part of the study area east Musawarat and Shendi, and south Zeidab. It elongates N-S. The maximum gravity value is +12 mgal concentrates northeast Musawarat. This zone lies over Nubian Sandstone (Fig. 3.15). Such high anomalies are caused by high density rocks. From the other hand, Dawoud and Sadig (1988) suggested that the root of Ban Gadid Granulites lies eastward. So, the researcher suggests that these high anomalies, within the zone B, are caused by Granulites.
The zone C occupies the northeastern corner of the area. Although, it lies over Nubian Sandstone, it may be attributed to shallow Basement.
The zone D occupies the southeastern part of the area (Fig. 3.14). It surrounds Umm Shadida village at Butana Plain. The maximum anomaly value equals -20 mgal and concentrates northeast Umm Shadida village. As it is observed in Fig. (3.15), this anomaly lies over sediments, but it is known well that the Butana area was covered with Basement Complex, so this high anomaly is caused by shallow Basement.
49
Fig. 3.12: Base map showing profiles selected for selected interpretation. profiles Fig.showing map 3.12: Base
50
area. study the of map Fig.3.13: anomaly Bouguer
51
on Bouguer anomaly map study area. the of anomaly Bouguer on
zones gradient anomaly low zones steep Fig.and zones, 3.14: anomaly High
52
study the of map area. geologic and Bouguer
Fig.3.15:
53
In Fig. (3.14), six low anomaly zones are observed. They are shaded by blue color. They are characterized by letters E, F, G, H, I and J.
The zone E lies south Sabaloka. It is well correlated with Granitoid of J. Es Sulik.
The zone F lies west Sabaloka. The minimum anomaly value is -54 mgal.
The zone G lies west Shendi. The minimum anomaly value is -56 mgal.
The zone H lies around Zeidab village. The minimum anomaly value is -56 mgal.
The zone I is situated on the northeastern part of the area. It extends southward passing between the zones B and C. The minimum anomaly value is -70 mgal.
The zone J lies on the southeastern corner of the area. The minimum anomaly value is -44 mgal.
All the low anomaly zones (except the zones E and F) lie over Nubian Sandstone and sediments, so they are attributed to sedimentary basins in the area.
Finally, twenty-three steep gradient zones are observed in the area (Fig. 3.14). They are distinguished by red polygons. They are divided into four sets.
The first set extends N-S. It includes the zones 1-6.
The second set extends E-W. It includes the zones 7-14.
The third set extends NE-SW. It includes the zones 15-19.
The fourth set extends NW-SE. It includes the zones 20-23.
Some steep gradient zones coincide with some suggested faults and some wadies (Fig. 3.15).
The zone 1 coincide with fault west Ban Gadid.
The zone 2 coincide with W. Awatib. So, W. Awatib may represent fault zone.
54
The zone 8 coincide with Umm Marahik Fault.
The zone 6 coincide with the boundary between two different types of Nubian Sandstone, so it is suggested to be fault.
The zones 15 and 20 coincide with W. Gangy. So, it may flows along two fault systems.
The zone 17 coincide with the boundary between two different sedimentary facies. So, it is suggested to be fault zone.
Finally, the zones 22 and 23 coincide with Atbara River. So, it may flows along fault zones.
The rest of the steep gradient zones don‟t conform such above mentioned zones. So, they are suggested to be faults affected the subsurface rocks in the area. All steep gradients that extend NW-SE are normal faults, whereas those extend NE- SW are strike slip faults.
3.3.2 Anomaly separation of gravity field of the study area
3.3.2.1 Graphical separation of gravity field of the study area
A total of six profiles are selected to separate residual anomalies which are caused by shallow structures. These profiles are placed where anomaly zones are observed on the Bouguer anomaly map of the study area. The ends of most profiles are extended where the basement rocks appear or are expected to be shallow to estimate the regional anomalies. Also some profiles are placed on and/or near boreholes that reached the basement to estimate the regional anomalies. These profiles are selected to intersect each other in order to adjust the regional anomaly values at the intersection points.
These profiles are: profile AA`, profile BB`, profile BC, profile DD`, profile EE` and profile FF` (Figs. 3.14 and 3.15). They are described below not in an
55 alphabetic arrangement, but they are described in an assigned arrangement depending on priority determination of the regional anomalies.
Profile DD` extends approximately NE-SW. Its length is about 215.5km. It placed over the high anomaly zones A, B and C. It crosses the steep gradient zones 1, 7 and 22. The profile also crosses three boreholes numbers 1, 2 and 6; at which the depths to basement are 57.9, 32 and 60 m, respectively.
The regional anomaly values at the borehole positions are computed using Eq. (3.23) with ∆ρ = -0.4, and then the regional curve is smoothly drawn passing through the computed regional and crossing the Bouguer anomaly curve where outcrops of basement appear. Lastly, the residual anomaly values are obtained (Appendix B) and the residual curve together with the Bouguer and regional curves are drawn (Fig. 3.16).
Profile BB` extends WNW-ESE. Its length is 187km. It is selected to pass anomaly zones G, B, I and D. It crosses the steep gradient zones numbers 3, 4, 16 and 15, successively. It passes near boreholes numbers 4 and 8 at which the depth to basement are 94.8 and 109.7m, respectively. It intersects profile DD`.
Using the regional value at the intersection point and applying the same procedures as in the profile DD`, the residual anomaly values are obtained (Tab. B.2) and the residual curve together with the Bouguer and regional curves are drawn (Fig. 3.17).
Profile AA` extends NE-SW. Its length is 231km. It passes over the anomaly zones A, B and I. It crosses the steep gradient zones numbers 7, 2, 9, 10 and 21, respectively. It intersects profile BB` at the center of the anomaly zones B.
Using the regional anomaly value at the intersection point, the regional curve is smoothly drawn passing through the computed regional and crossing the Bouguer anomaly curve where outcrops of basement appear; and then the residual anomaly
56 values are obtained (Tab. B.3) and the residual curve together with the Bouguer and regional curves are drawn (Fig. 3.18).
Profile BC extends ENE-WSW with length of about189.75km. It passes over the anomaly zones G, B and I, respectively. It crosses the steep gradient zones numbers 5 and 19. It intersects the profile DD`, FF` and AA` at the anomaly zone B, the steep gradient zone numbers 5 and 9, respectively.
Applying the same procedures as in the profile AA`, the residual anomaly values are obtained (Tab. B.4) and the residual curve together with the Bouguer and regional curves are drawn (Fig. 3.19).
Profile FF` extends approximately N-S with length of about 146.97km. It passes over the anomaly zones B, I, B, I and D, respectively. It crosses the steep gradient zones numbers 11, 5, 18, 17 and 15, respectively. It intersects the profiles DD`, BC, AA` and EE` at the zone B, the steep gradient zones 5 and 18, and the zone I west Umm Shadida village, respectively.
Using the regional anomaly values at the intersection point, the regional curve is smoothly drawn passing through the computed regional values; and then the residual anomaly values are obtained (Tab. B.5) and the residual curve together with the Bouguer and regional curves are drawn (Fig. 3.20).
Profile EE` extends approximately NE-SW with length of about 149km. It passes over the anomaly zones I, D and I, respectively. It crosses the steep gradient zones numbers 20, 13 and 23, successively. It passes through the intersection point of the profiles BB` and FF`.
Using the same procedures as in the profile FF`, the residual anomaly values are obtained (Tab. B.6) and the residual curve together with the Bouguer and regional curves are drawn (Fig. 3.21).
57
graphical residual anomaly curves of profile of curves residual BB`. anomaly graphical
Fig. 3.17: Bouguer, regional and and Fig.3.17: regional Bouguer,
Fig. 3.16: Bouguer, regional and graphical residual anomaly curves of profile of curves residual DD`. anomaly graphical and Fig.3.16: regional Bouguer,
58
Bouguer, regional and graphical residual anomaly curves of profile of curves residual AA`. anomaly graphical and regional Bouguer,
Fig.3.18:
Fig. 3.19: Bouguer, regional and graphical residual anomaly curves of profile of curves residual BC. anomaly graphical and Fig.3.19: regional Bouguer,
59
profileEE`.
Fig. 3.21: Bouguer, regional and graphical residual anomaly curves of of curves residual anomaly graphical and Fig.3.21: regional Bouguer,
Fig. 3.20: Bouguer, regional and graphical residual anomaly curves of profile of curves residual FF`. anomaly graphical and Fig.3.20: regional Bouguer,
60
3.3.2.2 Anomaly separation of gravity field of the study area using Least-
squares method As it was previously mentioned in Sec. (3.2.13.2.2.2), the determination of the residual anomalies using Least-square method depends on the regional values that were selected from non anomalous zones. In this case, the non anomalous areas are determined by visual inspection. They represent the shaded areas which are illustrated in Fig. (3.22). As it is observed, these areas lie over outcrops of Basement and/or shallow Basement (Fig. 3.15). The Bouguer anomaly values that lie on the non anomalous areas are used to estimate the regional anomaly of the study area. Using Eq. (3.31a), the polynomial coefficients for n = 1, 2 and 3 are estimated using Least-square method and their values are listed in Tab. (3.8), (3.9) and (3.10), respectively. The regional anomaly values for first, second and third order polynomial and the residual anomaly values for the same orders are then calculated and listed in Tab. (A.1) in Appendix A. The regional anomaly values for the first, second and third orders are contoured to obtain the regional anomaly maps (Fig. 3.23, 3.24 and 3.25, respectively). The residual anomaly values for each order are contoured to obtained residual anomaly maps (Fig. 3.26, 3.27 and 3.28).
The regional trend, as it is observed, is approximately NE-SW. The residual maps have the same similarity with very little differences between them. The residual maps have the same aspect as the Bouguer map but the same contour line for both Bouguer and residual map has different magnitude.
61
Tab. (3.8): First order polynomial Tab. (3.10): Third order polynomial
coefficients coefficients
Coefficient Value Coefficient Value
C00 -28.752266798213 C00 -29.267185251561
C01 0.026703567091634 C01 0.0017752394270544
C10 -0.016323409950571 C02 -0.00026597545110656
-6 C03 -4.5124757089497*10
C10 0.05056847167752
C11 0.0017188367356521 Tab. (3.9): Second order polynomial -6 C12 7.240611279589*10 coefficients
C20 -0.0014969245043348 Coefficient Value -5 C21 -1.0973633460939*10 C00 -30.338625558679 -6 C30 6.7565328079366*10 C01 0.07507528103558
C02 -0.00054372960156707
C10 0.0037541008249829
C11 0.00033423403654958
C20 -0.00019154485674999
62
F D' Zeidab 17.4 N A' C S cale 17.2 km 0 10 20 30 40 Legend: E' 17 Town or Village B agaraw iya B orehole K abushiya 16.8 -40 Contour Line with -30
. interval 2 mgal t B Taragm a a Selected Profile
4 8 10 S hendi L 5 6 16.6 7 E l A w atib39 1 1213 2 11M usaw arat 16.4 S abaloka E r R ibeila Umm Shadida
N aga W ad G asir B' 16.2 El Ban Gadeed U m m H aw iya D 16 A E F'
15.8
32.6 32.8 33 33.2 33.4 33.6 33.8 34 34.2 34.4 34.6 Long.
Fig. 3.22: Bouguer anomaly map showing gravity high zones (shaded Area).
Fig. 3.23: First order regional anomaly map of the study area.
63
Fig. 3.24: Second order regional anomaly map of the study area.
Fig. 3.25: Third order regional anomaly map of the study area.
64
Fig. 3.26: First order residual anomaly map of the study area.
Fig. 3.27: Second order residual anomaly map of the study area.
65
rea.
a tudy tudy s
ap of the of ap m
nomaly nomaly a
esidual
r rder rder o
Third
Fig.3.28:
66
3.3.3 Quantitative interpretation of gravity data of the study area
3.3.3.1 Introduction
The quantitative interpretation is made along the previously mentioned profiles using GravModeler Program. GravModeler Program performs 2D modeling of gravity data. It operates on a PC running Windows 95, 98 or Windows NT. It is based on the line integral approach of the classical Talwani's method (Sec. 3.2.14.4). It deals with data formatted in a text (Tab delimited) format in terms of distance (m or km) and gravity anomaly (mgal). The program accepts simple and complex models in terms of density and depth to compute gravity effect which is correlated with the observed gravity.
A 2D modeling is performed. The residual anomalies and distances are formatted in a text (Tab delimited) format files for each profile. According to the qualitative interpretation the models are constructed in terms of densities and depths (depth- density models). The density of 2.3g/cm3 is used for Nubian Sandstone, the densities of 2.61g/cm3, 2.7g/cm3 and 3.1g/cm3 are used for Basement Complex (Dawoud and Sadig 1988). Every model is adjusted many times till the calculated anomaly fits the observed one (field curve).
3.3.3.2 Depth-density models and geologic models along selected profiles in the study area
The depth-density models along the profiles AA', BB', BC, DD', EE' and FF' are illustrated in Figs. (3.29a, 3.30a, 3.31a, 3.32a, 3.33a and 3.34a), respectively. As it is observed in Figs. (3.29a, 3.30a, 3.31a and 3.32a), the models are constructed in terms of sedimentary basins, Basement Complex and granulites; whereas the models in Figs. (3.33a and 3.34a) are constructed in terms of sedimentary basins and Basement Complex only.
67
The depth-density models are converted into geologic models (Figs. 3.29b, 3.30b, 3.31b, 3.32b, 3.33b and 3.34b). The Basement that their densities are 2.61g/cm3 and 2.7g/cm3 are interpreted as gneissic rocks, the other with the density 3.1g/cm3 are interpreted as granulites, whereas the sedimentary basins with the density 2.3g/cm3 are interpreted as Nubian sandstones. The vertical and semi-vertical segments are interpreted as normal faults. Finally, the granulites that occur in Fig. 3.29a are suggested to be uplifted and thrusted from its source to the east.
The Basement surface in geologic model along each profile is not uniform but varies from place to another because of the structural control that prevail the area. In order to describe the Basement surface in each profile in terms of depths, the Basement surface is divided into several different segments. Each segment represents a straight line. The depths are then picked at the beginning and at the end of each segment.
In Fig. (3.29), the depth of Basement surface at the beginning and end (A and A') of the profile AA' are zero meter. The maximum depth is 3110 m at a distance of 210.524 km from the beginning. The maximum depth of the Granulites surface is 4300 m at a distance of 126.18 km, whereas the minimum depth is 2500 m along the horizontal segment that ranges from a distance of 89.52 km to 93.83 km.
In Fig. (3.30), the depths of Basement surface at the beginning B of the profile BB' is 1010 m, whereas at the end B' of the profile is zero m. The maximum depth is 2200 m at a distance of 116.386 km. The maximum depth of the Granulites surface is 3900 m at a distance of 115.96 km, whereas the minimum depth is 2300 m along two horizontal segments, the first ranges from a distance of 80.71 km to 89.2 km, and the other ranges from a distance of 64.14 km to 72.21 km.
In Fig. (3.31), the depths of Basement surface at the beginning B of the profile BC is 1010 m, whereas at the end C of the profile is 280 m which is the minimum depth. The maximum depth is 2950 m along the horizontal segment that ranges
68 from a distance of 145.3812 km to 172.3682 km. The maximum depth of the Granulites surface is 4550 m at a distance of 39.17 km, whereas the minimum depth is 3750 m along the horizontal segment that ranges from 66.6 km to 74.34km.
In Fig. (3.32), the depths of Basement surface at the beginning D of the profile DD' is zero m, whereas at the end D' of the profile is 500 m. The maximum depth is 1210 m at a distance of 84.899 km. The maximum depth of the Granulites surface is 4500 m at a distance of 91.78 km, whereas the minimum depth is 3800 m at a distance of 142.66 km.
It is clear that the uplifted granulites concentrate in an area that starts from a distance of about 50 km east Musawarat and terminates at distance of about 30 km southwest Zeidab. The surface of these uplifted granulites is deep towards the north.
In Fig. (3.33), the depths of Basement surface at the beginning E of the profile EE' is 500 m, whereas at the end E' of the profile is 690 m. The minimum depth is 90 m along the horizontal segment that range from a distance of 80.3248 km to 92.0019 km. The maximum depth is 2210 m at distance 136.9413 km.
Finally, in Fig. (3.34) the depths of Basement surface at the beginning F of the profile FF' is 2050 m, whereas at the end F' of the profile is 410 m. The minimum depth is 50 m along the horizontal segment that ranges from a distance of 89.7648 km to 93.9179 km. The maximum depth is 2110 m along the horizontal segment that range from a distance of 116.5715 km to 126.4824 km.
69
Fig. 3.29: (a) Depth-density model along profile AA'. (b) Geologic model along profile AA'.
70
Fig. 3.30: (a) Depth-density model along profile BB'. (b) Geologic model along profile BB'.
71
Fig. 3.31: (a) Depth-density model along profile BC. (b) Geologic model along profile BC.
72
Fig. 3.32: (a) Depth-density model along profile DD'. (b) Geologic model along profile DD'.
73
Fig. 3.33: (a) Depth-density model along profile EE'. (b) Geologic model along profile EE'.
74
Fig. 3.34: (a) Depth-density model along profile FF'. (b) Geologic model along profile FF'.
75
3.3.3.3 Depth map of the basement surface of the study area
The depths of Basement surface on each profile are used to construct the structural contour map of Basement surface of the study area (Fig. 3.35). As it is observed, the map contains two major sedimentary basins and about three sub-basins.
One of the two major basins is located at Shendi region. It is a southern extension of Shendi Basin. It has a rectangular shape. The maximum thickness of sediments is about 1400 m.
The other basin is broad and located southeast Ziedab and at the northeastern part of the study area. It is previously defined as Atbara Basin. The maximum thickness of sediments is about 3110 m.
Each of the five sub-basins covers a small area. They are described below.
The first is located east Umm Shadida village. It is shallow sub-basin. The maximum depth is about 600 m. It has an elongated shape. It extends SW-NE.
The second is located WNW Umm Shadida village at a distance of 30 km. It was known as Fadniya basin (Ibrahim 1993). It has a rectangular shape. It extends NW- SE. The maximum depth is about 2400 m.
The third is located SSE Zeidab at a distance of 45 km, and east Kabushiya and Bagarawiya. It has non-uniform shape. The maximum depth is about 2000 m. It represents part of Atbara basin.
It is observed that the above mentioned basins are controlled by normal faults. Some of these faults coincide with some wadies such as W. Awatib, W. Abu Talh, W. El Hawad and R. Atbara. At the northeastern corner of the study area at R. Atbara, the Basement seems to be laterally displaced, thus the researcher suggests that this is a dextral strike slip fault parallel to the Central African Sheer Zone (CASZ).
76
3.3.4 Conclusions
Returning to Fig. (3.15), the gravity low near Sabaloka lies over crystalline basement, some steep gradients lie over R. Atbara and on some wadies such as W. Awatib, W. El Hawad and W. Abu Harik. So, it is concluded that not all gravity lows are always interpreted as sedimentary basins and all major wadies in the area and its adjacent can be referred to as fault zones. Returning to Figs. (3.15, 3.28 and 3.35) the strike slip fault at Sabaloka area appears over basement and disappears before W. Awatib where the basement is covered with sedimentary rocks. This fault is traced again according to the shape of the gravity anomalies at Sabaloka area. The same displaced shape is observed at R. Atbara. So, it is concluded that this is another dextral strike slip fault extends beyond R. Atbara. In Fig. (3.15) the gravity high at Ban Gadeed is caused by granulites. Another strong gravity highs appear over an area that is situated east Shendi and south Umm Ali area. They are interpreted as the source of the granulites which have been uplifted some kilometers and thrusted to Ban Gadeed as indicated by Dawoud and Sadig (1988). Finally, returning to Figs. (3.24 and 3.25) it is observed that the regional anomaly represents a gravity high over sedimentary basins. As the regional anomaly comes from deep seated structure, it is concluded that this regional anomaly is caused by arising of mantle beneath the sedimentary basins so as to compensate the decrease in mass which is caused by the light density of sedimentary rocks.
77
.
rea a
tudy tudy s
urface of the the of urface s
asement
B
ap of of ap
m
ontour ontour c
Structural
Fig.3.35:
78
Chapter Four
Resistivity Method
4.1 Introduction
Geo-electrical resistivity method is a useful technique in groundwater exploration because the resistivity of a rock is very sensitive to its water content. In general, the method is able to map different stratigraphic units in a geologic section as long as the units have resistivity contrasts. Often this is connected to rock porosity and water quality and saturation in the pore spaces.
Geo-electrical resistivity techniques are based on the response of the earth to the flow of electrical current. In these methods, an electrical current is passed through the ground at two electrodes (current electrodes) and another two potential electrodes allow us to record the resultant potential difference between them, giving a way to measure the electrical impedance (resistance) of the subsurface material. The apparent resistivity is then a function of the measured impedance (R) and the geometry of the electrode array. Depending upon the survey geometry, the apparent resistivity data are plotted as 1-D soundings, 1-D profiles, or in 2-D cross-sections in order to look for anomalous regions.
Resistivity measurements associated with varying depths depending on the separation of the current electrodes can be interpreted in terms of a lithology model of the subsurface. Data are called apparent resistivity because the measured resistivity values are actually averaged over the total current path length but are plotted at one depth point for each potential electrode pair.
4.2 Theoretical background
According to Ohm‟s Law the resistance R, in ohms, of a wire is directly proportional to its length L and is inversely proportional to its cross-sectional area A. That is:
79
∆푉 퐿 푅 = = 휌 (4.1) 퐼 퐴 where, ρ (the constant of proportionality) is known as the electrical resistivity, a characteristic of the material which is independent of its shape or size, ∆V is the potential difference across the resistance and I is the electric current through the resistance.
The resistivity method is established according to above principles. If we consider a point source of current, I, placed at the ground surface and that the subsurface is isotropic and homogeneous, the current travels from the point radially in all directions in a hemispherical shape. The hemispherical surfaces are equipotential surfaces which are perpendicular to the current lines. The potential V at point M on the ground surface and at a distance r from the source point is
푉 = 퐼휌/2휋푟 (푉 = 0 푤ℎ푒푛 푟 = ∞) (4.2)
To complete the current cycle we consider another point sink of the current on the surface, then the potential at M is a combination of potential from the two current points. By considering another point N (Fig. 4.1), the potential is calculated in alike manner. Taking the potential difference, rearranging the terms and postulating the fact that the subsurface is not homogeneous, we find that
2휋 휌푎 = [∆푉 /퐼][ 1 1 1 1 ] = RK (4.3) ( − − + ) 푟1 푟2 푟3 푟4 where K is the geometric factor, R is the resistance.
It should be noted that alternating current is used to avoid macroscopic polarization of the subsurface material. An AC frequency in the range 1–100 Hz is sufficient to avoid this problem (Herman 2001).
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Fig. 4.1: Current distribution and equipotential surfaces in homogeneous and isotropic medium.
4.2.1 Electrode configurations
The most commonly used electrode systems are illustrated in Fig. (4.2).They have different geometric factors (K). They are:
퐿 2− 푙 2 - Schlumberger array (at 푥 = 0, K = 휋 ). 2푙 - Wenner array (K=2πa).
- Pole-Dipole array
2휋푎푏 푟 = 푎, 푟 = 푟 = ∞, 푟 = 푏. Then, K = . 1 2 4 3 푏−푎 - Dipole-Dipole array
푟1 = 푟4 = 2푛푙, 푟2 = 2푙(푛 − 1), 푟3 = 푙(푛 + 1). Then, dropping the minus,
K = 2휋푙푛 푛 − 1 (푛 + 1), (Telford et al.1990).
4.2.2 Rock resistivities
The resistivities (ρ) of rocks and minerals display wide ranges. For example, graphite has a resistivity of the order of 102Ohm.m, whereas, some dry quartzite rocks have resistivities of more than 1012Ohm-m (Parasnis 1962).
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Fig. 4.2: Types of electrode configurations. (a) Wenner. (b) Schlumberger. (c) Pole-dipole. (d) Double-dipole (after Telford et al.1990).
In most sedimentary rocks, electricity is conducted through motion of ions of interstitial fluid, and thus resistivity is controlled more by porosity, water content, and water quality than by the resistivities of the rock matrix. Clay minerals, however, are capable of conducting electricity electronically, and the flow of current in a clay layer is both electronic and electrolytic. Resistivity values for unconsolidated sediments commonly range from less than 1 ohm-m for certain clays or sands saturated with saline water, to several thousand ohm-m for dry
82 basalt flows, dry sand and gravel. The resistivity of sand and gravel saturated with fresh water ranges from about 15 to 600 ohm-m. The following table displays of some types of rocks.
Tab. (4.1):Resistivities of various rocks and sediments. Tab. (4.2): Variation of rock resistivity with water content.
(After Telford, et al. 1990)
4.2.3 Field work procedures
4.2.3.1 Field equipment
The required field equipment to acquire resistivity data include Resistivity Meter, High-Voltage batteries, at least four insulated wire reels, steel electrodes, hummers, GPS instrument, calculators, log-log papers and resistivity worksheets.
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4.2.3.2 Survey types
Resistivity surveys can be conducted in different ways:-
- Vertical electrical sounding (VES). - Horizontal electrical profiling.
The Vertical Electrical Sounding technique arises from the fact that the current will penetrate deep when the current electrodes are spread outward. So, the technique is suitable for investigating formations that vary with depth. The technique can be carried out with Schlumberger, Wenner and Dipole-Dipole configurations, but it is more effective with the Schlumberger configuration. The technique is carried by spreading out the current electrodes after every measurement. The measured values are resistances (R) in ohm. When the current electrode spacing becomes very large (compared to potential electrode spacing), the potential difference will be very small. This may causes an error in the resulting apparent resistivity value. The distance MN should always be kept comparable to AB such that MN ≥ AB/5. This is to improve the sensitivity of the measuring tools.
During the measurements, the measured values are recorded in a work-sheet against electrode spacing values and K values. The apparent resistivity values are plotted versus current electrode spacing values in Log-Log graph to obtain an apparent resistivity curve. The apparent resistivity curve rises at 45˚ when the current penetrates basement rock (high resistive rock). In this case, the measurements at the point are stopped. The measurements are carried out at new points in the same manner till the selected area is sufficiently covered with VES measurements.
The Lateral Profiling technique is particularly useful in mineral exploration. The technique can be carried out with all arrangements. In this technique, fixed electrode spacing is chosen (i.e. a fixed depth is tapped) and the whole electrode array is moved along a profile after each measurement is made. The value of
84 apparent resistivity is plotted, generally, at the geometric center of the electrode array. Maximum apparent resistivity anomalies are obtained by orienting the profiles at right angles to the strike of the geologic structure. The results are presented as apparent resistivity profiles or apparent resistivity maps, or both.
4.2.4 Geo-electric parameters
A geologic section could differ from a geo-electric section as geologic layers do not always coincide with the boundaries between layers marked by different resistivities (Zohdy et al. 1974). For example, when the salinity of groundwater in a given type of rock varies with depth, several geo-electric layers may be distinguished within a lithologically homogeneous rock. In the opposite situation layers of different lithologies or ages, or both, may have the same resistivity and thus form a single geo-electric layer. A geo-electric layer is described by two fundamental parameters, its resistivity ρi and its thickness hi, where the subscript i indicates the position of the layer in the section. Other geo-electric parameters are derived from its resistivity and thickness. These are:
1. Longitudinal conductance, Si = hi/ρi.
2. Transverse resistance, Ti = hiρi.
3. Anisotropy, 휆 = 휌푡 /휌퐿.
Where: 휌푡 is the average transverse resistivity and
휌퐿 is the average longitudinal resistivity.
These secondary geo-electric parameters are particularly important to describe a geo-electric section consisting of several layers (Fig. 4.3). For n layers, the total longitudinal conductance (S)
푛 ℎ푖 푆 = 푖=1 (4.4) 휌푖
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Fig. 4.3: Columnar prism used in defining the geo-electric parameters of a section.
The total transverse unit resistance is
푛 푇 = 푖=1(ℎ푖휌푖) (4.5) the average longitudinal resistivity is
푛 ℎ 퐻 휌 = 푖=1 푖 = (4.6) 퐿 푛 ℎ푖 푆 푖=1 휌 푖 the average transverse resistivity is
푇 휌 = (4.7) 푡 퐻
The study of the parameters S, T, ρL, ρt and 휆 is an integral part of the analysis of electrical sounding data and also is the basis of important graphical procedures (for example, the auxiliary point method) for the interpretation of electrical sounding curves (Kalenov 1957; Orellans and Mooney 1966; Zohdy 1965).
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4.2.5 Types of vertical electrical sounding (VES) curves over horizontally stratified media
The form of the curve obtained by sounding over a horizontally stratified medium is a function of the resistivities and thicknesses of the layers, as well as of the electrode configuration.
4.2.5.1 Homogeneous and isotropic medium
If the ground is composed of a single homogeneous and isotropic layer of infinite thickness and finite resistivity then the apparent resistivity curve will be a straight horizontal line whose ordinate is equal to the true resistivity 휌1 of the semi-infinite medium.
4.2.5.2 Two-layer medium
In the case that the ground is composed of two layers (homogeneous and isotropic layer of finite thickness underlain by an infinitely thick sub-stratum) then the sounding curve begins, at small electrode spacings, with a horizontal segment. As the electrode spacing is increased, the curve rises or falls when the resistivity of the first layer is less than or greater than the resistivity of the second layer, respectively.
4.2.5.3 Three-layer medium
If the ground is composed of three layers of, resistivities ρ1, ρ2, and ρ3, and thicknesses h1, h2, and h3 = ∞, the type of the curve is described according to the relation between the values of ρ1, ρ2, and ρ3. Thus, there are four possible types:
- H-type: ρ1>ρ2<ρ3.
- A-type: ρ1<ρ2<ρ3.
- K-type: ρ1<ρ2>ρ3.
- Q-type: ρ1>ρ2>ρ3.
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Fig. 4.4: Three layers curve types.
4.2.5.4 Multi-layer medium
As it is observed above, the type of three layers curve is described by one letter. In the case of four layer the type can be described by two of such letters (e.g. HA,HK,…etc). In general, an n-layer curve (where n≥3) is described by (n-2) letters.
4.2.6 Analysis of vertical electrical sounding (VES) curves
When an area is investigated, the sounding curves generally are not all of the same type (for example H, A, K, Q, and HA). Thus, some of the qualitative and quantitative methods of interpretation of electrical sounding data are described below:
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4.2.6.1 Qualitative interpretation
The qualitative interpretation of the sounding data involves: 1. Preparation of type-map. The Type map shows the distribution of curve types on a map of the survey area.
2. Preparation of apparent resistivity maps. Each map is prepared by plotting the apparent resistivity value, as registered on the sounding curve, at a given electrode spacing (common to all soundings) and contouring the results. An apparent resistivity map for a given electrode spacing indicates the general lateral variation in electrical properties in the area
3. Preparation of apparent resistivity pseudo-sections. These pseudo-sections are constructed by plotting the apparent resistivities, as observed, along vertical lines located beneath the sounding stations on the chosen profile. The apparent resistivity values are then contoured. Generally a nonlinear (logarithmic) vertical scale is used.
4. Preparation of S-map. In H, A, KH, HA, and similar type sections the terminal branch on the sounding curve often rises at an angle of 45º. This usually indicates igneous or metamorphic rocks of very high resistivity. The total longitudinal conductance S is determined from the slope of the terminal branch of a VES curve, rising at an angle of 45º (here called the S-line). The value of S equals the value of
AB/2 at the intercept of the extension of the S-line with the horizontal line (ρa = 1 Ohm-m).
Increases in the value of S from one sounding station to the next indicate an increase in the total thickness of the sedimentary section, a decrease in average longitudinal resistivity (ρL), or both. From S and ρL the total thickness of sedimentary section can be determined Eq. (4.6).
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These maps, sections and profiles constitute the basis of the qualitative interpretation which should precede quantitative interpretation of the electrical sounding data.
4.2.6.2 Quantitative interpretation
4.2.6.2.1 Introduction
The mathematical analysis for quantitative interpretation of resistivity results is most highly developed for the depth probing or drilling technique. As in other geophysical methods where quantitative interpretation is possible, the assessment of results should progress from rough preliminary estimates made in the field towards more sophisticated methods of interpretation.
4.2.6.2.2 Quantitative interpretation of two horizontal beds
To compute 휌푎 due to two horizontal beds using Schlumberger array (as an example), the image analysis method is used. Considering Fig. (4.2b) with x=0, the center of P1 and P2 becomes the same center of C1 and C2. Using the image analysis method (Telford et al. 1990), the potential (V1) at P1 due to current source and sink at C1 and C2 is
퐼휌 1 푘푚 1 푘푚 푉 = 1 + 2 ∞ − + 2 ∞ (4.8a) 1 2휋 퐿−푙 푚=1 퐿−푙 2+(2푚푧 )2 퐿+푙 푚=1 퐿+푙 2+(2푚푧 )2
Where, 퐿 half current electrode spacing, 푙 half potential electrode spacing, k reflection coefficient and z thickness of the first layer.
the potential (V2) at P2 due to current source and sink at C1 and C2 is
퐼휌 1 푘푚 1 푘푚 푉 = 1 + 2 ∞ − + 2 ∞ (4.8b) 2 2휋 퐿+푙 푚=1 퐿+푙 2+(2푚푧 )2 퐿−푙 푚=1 퐿−푙 2+(2푚푧 )2
퐼휌 2 2 1 1 ∆푉 = 1 − + 4 ∞ 푘푚 − (4.9a) 2휋 퐿−푙 퐿+푙 푚=1 1 1 퐿−푙 1+ 2푚푧 2/ 퐿−푙 2 2 퐿+푙 1+ 2푚푧 2/ 퐿+푙 2 2
When L>> 푙,
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1 1 2푙 1 − 1 ≈ 3 퐿−푙 2+ 2푚푧 2 2 퐿+푙 2+ 2푚푧 2 2 퐿2 1+ 2푚푧 /퐿 2 2
Then the potential difference becomes
퐼휌 2푙 푘푚 퐼휌 2푙 ∆푉 = 1 1 + 2 ∞ ≈ 1 1 + 퐷 ′ (4.9b) 휋퐿2 푚=1 3 휋퐿2 푠 1+ 2푚푧 /퐿 2 2
The exact expression for apparent resistivity is
퐿+푙 푘푚 퐿−푙 푘푚 휌 = 휌 1 + ∞ − ∞ 푎 1 푙 푚=1 1 푙 푚=1 1 1+ 2푚푧 2/ 퐿−푙 2 2 1+ 2푚푧 2/ 퐿+푙 2 2
= 휌1(1 + 퐷푠) (4.10a)
Approximately, we have
푚 ∞ 푘 휌푎 ≈ 휌1 1 + 2 푚=1 3 = 휌1(1 + 2퐷푠′) (4.10b) 1+ 2푚푧 /퐿 2 2
When the electrode spacing is very small (L< When the electrode spacing (L) is very large compared to z (the depth of the bed), the Eq. (4.10b) becomes: ∞ 푚 휌푎 ≈ 휌1 1 + 2 푚=1 푘 (4.10c) Since 푘푚 < 1, we can write the summation term in the form: 1 ∞ 푘푚 = − 1 푚=1 1−푘 Substituting 푘 = (휌2 − 휌1)/(휌2 + 휌1), we get 휌푎 = 휌2. That is to say, at very large spacing, the apparent resistivity is practically equals to the resistivity in the lower formation. Crude interpretation. Before applying more complicated methods of interpretation, it is useful to consider few ideas. We can get some information of 91 the unknown parameters 휌2, 휌1 and z from the field curve. Thus, part of the curve at small electrode spacings is roughly horizontal, it approximately equals 휌1. At larger spacings also it becomes semi-horizontal, it approximately equals 휌2. The depth to the interface (z) equals the spacing at the inflection point, approximately. Curve matching. A much more accurate method of interpretation in electric drilling involves the comparison of field curve with the characteristic curves. Theoretical resistivity curves (master curves). The master curves are prepared with dimensionless coordinates (Telford et al. 1990). The 휌푎 in Eq. (4.10c) is divided by 휌1. The ratio 휌푎 / 휌1 is then plotted against L/z in logarithmic paper. All characteristic curves are preserved in shape by making 휌1 = 1 and making z as large as 1km. The sets of curves are constructed either for various values of k between ±1 or for various ratios of 휌2/ 휌1 between ±∞. A typical set of curves is shown in Fig. (4.5). Fig. 4.5: Two layers master curves of Wenner configuration. The field data of a VES point is plotted in a transparent Log-Log paper (AB/2 at the abscissa and 휌푎 at the ordinate). The transparent paper is then passed over the set of master curves of the same array maintaining the parallelism of the abscissa and ordinate of both transparent paper and master curves until the field curve coincides more or less with one of the master curves (or interpolated between 92 adjacent master curves). The point where 휌푎 / 휌1 = 퐿/푧 = 1 on the master sheet is marked on the transparent paper. From the marked point a line is drawn vertically downward to read the value of z at the abscissa and horizontally to read 휌1 at the ordinate. From k or 휌2/ 휌1 values of the master curve that fits the field curve, the value of 휌2 is obtained. 4.2.6.2.3 Quantitative interpretation of multiple horizontal beds When there are more than two horizontal beds, the above mentioned crude interpretation is first used for relatively small spacing to obtain the depth and resistivity of the upper layer. Next the conductance or minimum conductance of all layers above the bottom one is determined as described in Sec. (4.2.6.1). 4.2.6.2.3.1 Partial curve matching This technique requires matching of small segments of the field profile with theoretical curves of two or three horizontal layers (Telford et al. 1990). The procedure for matching successive left-to-right segments of a field sounding is as follows: 1. The same procedure as was described in two layers curve matching is applied here. 2. The transparent paper is transferred to appropriate auxiliary curve set where the cross is placed at the origin and the same (휌2/ 휌1) curve of the auxiliary as that of the master curve is drawn in a pencil on the transparent paper. 3. Replacing the transparent paper on the master sheet and maintaining the (휌2/ 휌1) line from step 2 on the master origin, a second master segment further to the right is fitted to the sounding curve. The second auxiliary point is marked over the master origin, 휌푒2 and ze2 where ze2 =z1+ z2 and 푧 푧 +푧 푧 푧 푒2 = 1 2 = 1 + 2 휌푒2 휌푒2 휌1 휌2 We also obtain (휌3/ 휌푒2) and hence 휌3 from the fitted segment. 4. The transparent paper is return to the auxiliary and step 2 is repeated. 93 5. Repeat step 3 to get 휌푒2, ze2 as well as 휌4 from the third cross. 6. Repeat the steps 4 and 5 until the sounding curve is completely fitted. A check on the (휌푒 , ze) values may be taken at any juncture, using the relation in step 3. Also the minimum conductance may be found and employ for the same purpose. 4.2.6.2.3.2 Complete curve matching The expression for surface potential over two beds may be expressed in integral forms as: 퐼휌 ∞ 푉 = 1 1 + 2푟 푘 휆 퐽 휆푟 푑휆 (Telford et al. 1990) (4.11) 2휋푟 0 0 Where 푘 휆 = 푘 exp −2휆푧 / 1 − 푘 exp(−2휆푧) and 퐽0 is the zero order Bessel Function. This expression is suitable for solving any number of layers (Keller and Frischknecht 1966 and Zohdy 1973). Employing the Schlumberger array, the resistivity relation can be written as follows: ∞ 2 (4.12) 휌푎 = 휌1 1 + 2퐿 0 푘 휆 퐽1 휆퐿 휆푑휆 Where ′ 퐽1 휆퐿 = −퐽 0 휆퐿 is the first order of Bessel function, ′ 퐽 0 is the first derivative of 퐽 0 and we have replaced r by L, half the current electrode separation. The product 푘 휆 퐽1 휆퐿 is known as Stefanescu function. 94 The solution of this general expression may be obtained by expanding the integral as an infinite series or by numerical integration, both methods being suitable for computer programing. The following system (Fig. 4.6) offers possibilities of doing the quantitative interpretation in a convenient way (Johansen 1977). Through a trial-and-error procedure the interpreter interacts with the computer until a layer sequence (휌푖 , 푑푖) agreeing qualitatively with the measured curve as well as with the geological concept has been found. This model (휌푖, 푑푖) is then used as input to an iterative least square procedure (LSP) which performs the quantitative adjustment of 0 0 (휌푖, 푑푖). The output from the LSP consists of the optimum parameter set (휌푖 , 푑푖 ) minimizing the weighted sum of squares of residuals Q, and certain "extreme parameter sets" characterizing the confidence surfaces in parameter space. input: field measurements trial-and-error program using graphic display terminal adequate starting model in accordance with geological concept iterative least squares program using singular value decomposition output: "best" solution and extreme parameter sets fixed known parameters at relevant values Fig. 4.6: Sequence of operations in the interpretation of VES data (after Johansen 1977). 95 4.2.7 Ambiguity in sounding interpretation The errors in the interpretation of sounding data arise from errors in the measured data which are caused by extraneous factors in one hand (e.g. power line, metallic fence, streams, dray ground, etc…) and by subsurface inhomogeneities in the other hand. The forms of these errors are described below in some details. 4.2.7.1 Extraneous effects on resistivity measurements Geo-electrical measurements are in general affected by extraneous effects such as high voltage power lines, elongated good conductors like a metallic fence with galvanic contact to the ground and elongated resistive bodies like road beds and dykes. To avoid such of these extraneous effects and obtained good data quality, the profiles mustn't be parallel to the bodies and must be at safety distance (1.5 to 2 times the expected penetration depth) and good contact between the electrodes and the ground must be obtained. If the soil around the electrodes is completely dry, water must be added to obtain good contact between the electrodes and the ground (Zohdy 1968b). 4.2.7.2 Distortion of sounding curves The electrical sounding curves may be distorted by lateral inhomogeneities in the ground in different forms which must be taken into consideration in the interpretation. These forms are formation of cusps, sharp maximum and curve discontinuities; they are described below in some details. 4.2.7.2.1 Formation of cusps The formation of a cusp on a Schlumberger sounding curve generally is caused by a lateral heterogeneity (Zohdy 1968b). A resistive lateral inhomogeneity, in the form of a sand lens, produces a cusp like the one shown in curve A (Fig. 4.7a); and a conductive inhomogeneity, in the form of a buried pipe or a clay pocket, produces a cusp as the one shown in curve B (Fig. 4.7b). 96 4.2.7.2.2 Sharp maximum The maximum or peak value on a K-type sounding curve is always gentle and broad, and should never have a sharp curvature where the ground is horizontally homogeneous. The formation of a sharp peak generally is indicative of the limited lateral extent of the buried (middle) resistive layer (Alfano 1959). Fig. 4.7a: Distortion of sounding curves by cusps caused by lateral inhomogeneities (after Zohdy 1969a). 4.2.7.2.3 Curve discontinuities Two types of discontinuities are observed on Schlumberger sounding curves. The first type is observed when the spacing MN is enlarged (with AB constant) and the value of the apparent resistivity, for the larger MN spacing, does not conform to the theoretical magnitude for such a change in MN (Deppermann 1954).The repetition of such a discontinuity when MN is changed to a larger spacing for the second time indicates a lateral inhomogeneity of large dimensions. When the discontinuities are not sharp, the curve can, be corrected easily by shifting the distorted segment of the curve vertically to where it should be. The second type of discontinuity is less common, and occurs during the expansion of the current electrode spacing AB when sounding with a Schlumberger array. In 97 general, the curve is displaced downward, that is, the value of the apparent resistivity at the larger AB is much less than the previous reading. This type of discontinuity generally is caused by a narrow, shallow, dike-like structure which is more resistive than the surrounding media and whose width is small in comparison to the electrode spacing (Kunetz 1955, 1966 and Zohdy 1969a) (Fig. 4.7b). The abscissa value at which the discontinuity on the sounding curve occurs is equal to the distance from the sounding center to the dike-like structure. Fig. 4.7b: Discontinuities on Schlumberger Curves Caused by Shallow Dike-like Structure (after Zohdy 1969a). 4.2.7.3 Principle of equivalence Equivalence means that two resistive or conductive layers have different resistivities and thicknesses give the same transverse resistivity or longitudinal conductance, respectively. Thus, a resistivity curve can represent several layer contributions. 4.2.7.4 Principle of suppression Suppression occurs where a resistive layer lies in between two conductive layers or vice versa. If a relatively thin resistive layer lies in between two conductive layers, it may only be possible to determine the transverse 98 resistivity of the layer. Resistive layers should have a thickness more than 1.5–2 times the layers above it to be detected on the sounding curve. In the opposite case, where a conductive layer lies in between two resistive layers, it may only be possible to determine the longitudinal resistivity of the layer. The conductive layer also has to be about 1.5–2 times as thick as the layers in total above it to be determined by both its thickness and resistivity separately. 4.2.7.5 Principle of anisotropy Anisotropy occurs when the formation resistivities measured parallel (ρpara) and perpendicular (ρperp) to the bedding plane are not equal. The ratio (λ) of ρperp/ρpara is called a coefficient of anisotropy. The coefficient of anisotropy can be obtained by dividing the computed thickness of a layer by its real thickness obtained from borehole. Alternatively, it can be investigated by conducting two perpendicular VES near boreholes. Then the ratio of the interpreted thickness gives an estimate to the coefficient of anisotropy (λ). 4.3 Resistivity analysis of the study area 4.3.1 General description Geo-electrical resistivity measurements are made in the study area (Musawarat Area) using VES technique and Schlumberger configuration. A total of 105 VES points were conducted in the area around Musawarat village. The area is bounded by Latitudes 16.275º-16.653ºN and Longitudes 33.148º-33.441ºE (Fig. 4.8). In December 2002 the VES points 61-71 were conducted in Shendi region by groundwater research staff using OYO meter. In March 2003, the same staff fulfilled additional measurements in the area using the same meter. These measurements represent VES points 78-82. The VES points 1-28 were conducted in the area before 2009 using SAS1000 meter for graduation projects. The rest of the VES points were conducted in the area during the period of the present study 99 using SAS1000 meter. The maximum spacing AB/2 ranges from small spacings (150, 250 and 300) at the western part to large spacing (800, 900 and 1000m) at the northeastern part. The positions of the VES points are determined with navigator GPS with an accuracy of ±10m in the horizontal direction and ±2m in the vertical direction. Some of these VES points are located near boreholes for subsequent calibration. 4.3.2 Qualitative interpretation of resistivity data of the study area It was previously mentioned in Sec. (4.2.6.1) that the qualitative interpretation involves studying the Type-map, apparent resistivity maps, S- map and pseudo sections along selected profiles. In this study, the above mentioned maps and pseudo-sections are prepared for the study area and they are explained below in some details. 4.3.2.1 Type-map of the study area The type-map of the study area is demonstrated in Fig. (4.9).Twenty four curve types are observed. They are divided into three groups according to their similarity in each group:- The first group is HAKH group. It includes HAKH, KHAKH, QHAKH, KHAK, HAKQ and HAK-types. This group covers broad area between Musawarat and El Awatib villages. Most of the sounding curves in this area are of HAKH-type (six layers). 100 Fig. 4.8: Base-map of resistivity and borehole data in the study area. 101 The second group is group HKHKH. It includes HKHKH, HKHKHKH, QHKHKH, HKHK, HKHA, HKH, QHKH, QHK and HK-types. The first two types concentrate on the northeastern part of the area (east Wad Masa village), whereas the rest types are distributed around El Awatib and Es Salama villages. The third group is HAAKH group. It includes HAAKH, KHAAK, HAAK, KQHAA, HAAKQ, HAAAK, QHAAK, HAAA and HAA-types. The first three types concentrate in small area north and northeast Musawarat villages. The remaining types are found everywhere in the study area. 4.3.2.2 Apparent resistivity maps of the study area Apparent resistivity maps of the area for AB/2= 4, 50, 100, 200, 400 and 600 m are constructed in order to know how do the apparent resistivities of the subsurface of the area are distributed to take an idea about the nature of the subsurface. These maps are represented in Figs. (4.10, 4.11, 4.12, 4.13, 4.14 and 4.15), respectively. 102 Fig. 4.9: Type-map of the study area. 103 In Fig. (4.10) high apparent resistivity zones (more than 100) concentrate on the western, eastern and central (between Musawarat and El Awatib) parts of the area. Low apparent resistivity zones (less than 100) concentrate on the southern part and northern part that includes El Awatib, Es Salama and Wad Masa villages. Because the map is prepared for small electrode spacing, the apparent resistivity approximately equals the true resistivity of the surface layer. So, when correlating this map with the surface geology, the high apparent resistivity zones can be attributed to sand and sandstone, whereas the low ones can be attributed to clay. Figs. (4.11, 4.12, 4.13, 4.14 and 4.15) give similar same results. They have high apparent resistivity zones on the central part of the area. They may be attributed to shallow Basement. Also, they have low apparent resistivity zones on the northern part. They are parallel to R. Nile and surround El Awatib, Es Salama and Wad Masa villages. These may be attributed to thick clay layer. Also, the maps have a steep gradient zone on the southern part. It extends N-S and conformable with W. Awatib. It can be attributed to fault zone. Another two steep gradient zones are developed in Fig. (4.13, 4.14 and 4.15). They are distinguished by letters A and B. The zone A extends N-S, whereas the zone B extends E-W. They may be attributed to fault zones in the lower Formations. 104 Fig. 4.10: Apparent resistivity map of the study area for AB/2=4 m. 105 Fig. 4.11: Apparent resistivity map of the study area for AB/2=50 m. 106 Fig. 4.12: Apparent resistivity map of the study area for AB/2=100 m. 107 Fig. 4.13: Apparent resistivity map of the study area for AB/2=200 m. 108 Fig. 4.14: Apparent resistivity map of the study area for AB/2=400 m. 109 Fig. 4.15: Apparent resistivity map of the study area for AB/2=600 m. 110 4.3.2.3 Pseudo-sections of the study area A total of eight pseudo-sections are constructed along the profiles in Fig. (4.8). The pseudo-section along profile AA' is illustrated in Fig. (4.16). Below VES104 two high apparent resistivity zones are observed. The upper zone may be caused by gravel or sand, whereas the lower zone may be caused by Basement. The upper part of the section shows low apparent resistivity zones. They may be attributed to sandy-clay or saturated sand. The lower part shows high apparent resistivity zones. They may be attributed Basement. Below VES105 and VES102 the contour lines concave downward. So, the sediments there may be thick. The pseudo-section along profile BB' is illustrated in Fig. (4.17). Below VES94, VES93, VES21, and VES59 high apparent resistivity zones are observed. They may be attributed to dry sand or sandstone. Another two high apparent resistivity zones are observed below VES91, VES92 and VES58. They may refer to dry sandstone. Below VES93, VES89 and VES57 three synclinal shapes on contour lines are observed. They may refer to thick sediments. The pseudo-section along profile CC' is illustrated in Fig. (4.18). High apparent resistivity zones are observed below VES92, VES91, VES97, VES27 and VES28. They may be attributed to sandstone or Basement. Two synclinal shapes on contour lines are observed below VES90 and VES88. They may refer to thick sediments. The pseudo-section along profile DD' is illustrated in Fig. (4.19). The low resistivity zones cover the upper part of the pseudo-section except that the area lies below VES53 with high apparent resistivity zone. The low apparent resistivity zones may be attributed to saturated sediments or clay, whereas the high one may be attributed to boulders, gravels or sand. The lower part of the pseudo-section shows high apparent resistivity zones. They may refer to Basement rocks. 111 NNW Distance (km) SSE 0 5 10 15 20 25 A V E S 10 V E S 24 V E S 105 V E S 104 V E S 103 V E S 102 V E S 101 V E S 100A' 1 10 ) m ( 2 / B A 100 Fig. 4.16: Pseudo-section along profile AA'. NW Distance (km) SE B 0 5 10 15 20 25 B' V E S 29 V E S 95 V E S94 V E S 93 V E S 21 V E S 92 VE S91 V E S 90 V ES 89 V E S 59 V E S 58 V ES 57 V E S 56 1 10 ) m ( 2 / B A 100 1000 Fig. 4.17: Pseudo-section along profile BB'. 112 NNW Distance (km) SSE C 0 5 10 15 20 V E S 92 V E S 91V E S 90 V E S 60 V E S 88 V E S 97 V E S 98 V E S 27 V E S 99 V E S 28 C' 1 10 ) m ( 2 / B A 100 1000 Fig. 4.18: Pseudo-section along profile CC'. NW Distance (km) SE D 0 5 10 15 20 25 D' V E S 13 V E S 30 V E S 42 V E S 41 V E S 40 V E S 39 V E S 53 VES3 V E S 82 V E S 78 1 10 ) m ( 2 / B A 100 1000 Fig. 4.19: Pseudo-section along profile DD'. 113 NW Distance (km) SE E 0 5 10 15 20 E' V E S 31 V E S 14 V E S 15 V E S 16 V E S 17 1 10 ) m ( 2 / B A 100 1000 Fig. 4.20: Pseudo-section along profile EE'. NW Distance (km) SE F 0 5 10 15 F' V E S 34 V E S 71 V E S 62 V E S 48 V E S 64V E S 47 V E S 46 V E S 45 V E S 44 1 10 ) m ( 2 / B A 100 1000 Fig. 4.21: Pseudo-section along profile FF'. 114 W Distance (km) E 0 5 10 G V E S 105 V E S 88 V E S 59 VES7 VES6 VES5 VES3 V E S 83 V E S 35 V E S 55 G' 1 10 ) m ( 2 / B A 100 1000 Fig. 4.22: Pseudo-section along profile GG'. SW Distance (km) NE 0 5 10 15 20 25 30 35 H' H V E S 22 V ES19 V ES94 V E S 41 V E S 15 V E S 62 VE S 70 V ES69 V E S 68 1 10 ) m ( 2 / B A 100 1000 Fig. 4.23: Pseudo-section along profile HH'. 115 The pseudo-section along profile EE' is illustrated in Fig. (4.20). The whole pseudo-section shows low apparent resistivity zone, except that the area lies in the lower part below VES16 shows high apparent resistivity zone. The low apparent resistivity zone may be attributed to saturated sediments, clay or sandy-clay, whereas the high one can be attributed to Basement rocks. The pseudo-section along profile FF' is illustrated in Fig. (4.21). The whole pseudo-section shows low apparent resistivity zone, except that the area restricted between VES46 and VES44 shows high apparent resistivity zones in the upper and the lower parts of the pseudo-section. The low apparent resistivity zone can be attributed to saturated sediments, clay or sandy-clay, whereas the high one in the upper part may be attributed to gravels or sands, and that in the lower part can be attributed to Basement rocks. The pseudo-section along profile GG' is illustrated in Fig. (4.22). The area lies between VES59 and VES56 in the upper part of the pseudo-section shows high apparent resistivity zone. It may be attributed to boulders, gravels or sands. Another high apparent resistivity zone is placed in the lower part of the pseudo- section between VES57 and VES55. This zone can be attributed to Basement rocks. The rest of the pseudo-section show low apparent resistivity zones. They may be attributed to sandy-clay or saturated sediments. The pseudo-section along the profile HH' is illustrated in Fig. (4.23). In the upper part of the pseudo-section and below VES94 and VES68 high apparent resistivity zones are observed. It may be attributed to gravels, boulders or sands. Another high apparent resistivity zone is observed in the lower part in the area restricted between VES94 and VES15. It may be attributed to Basement rocks. The rest of the pseudo-section show low apparent resistivity zones. They may be attributed to sandy-clay or saturated sediments. 116 Finally, in all pseudo-sections, it is observed that the high apparent resistivity zones in the upper part are attributed to boulders, gravels or dry sands; in the lower part are attributed to Basement rocks and in the middle parts are attributed to dry sandstones. The low apparent resistivity zones in the upper parts are attributed to clay or sandy-clay, in the middle parts are attributed to claystones or saturated sandstones and in the lower parts are attributed to weathered Basement rocks. In the other hand, some pseudo-sections horizontally show different apparent resistivity zones. These may refer to lateral inhomogeneities in some subsurface formation or may refer to some homogeneous formation and it has been saturated with water during season of rainfall and unsaturated when the rain doesn't fall during a long period of time. If the VES data are collected when the formation is saturated and unsaturated, and then the data are combined together into one pseudo-section, the horizontally different apparent resistivity zones are observed. 4.3.2.4 Total longitudinal conductance map(S-map) of the study area The total longitudinal conductance map (S-map) generally gives an idea about the total thickness of sediments. As it was previously explained in Sec. (4.2.6.1), the S-map of the study area is constructed (Fig. 4.24). The VES data that their curves have terminal branches that rise approximately at an angle of 45 are used to construct the s-map. As it is observed in Fig. (4.24), the large S values (13 and 12) mho concentrate in the northern part east and west Wad Masa village, respectively, and then the values decrease gradually to the south. At Es Salama and El Awatib villages the S value is about 5 mho. At Musawarat area to the south towards El Nagaa village, the S value is about 2.5 mho. Thus, the researcher suggests that the thickness of sediments is large in the northern part of the study area and decreases gradually to the south and west. 117 Fig. 4.24: Total longitudinal conductance map (S-map) of the study area. 118 4.3.3 Quantitative interpretation of resistivity data of the study area 4.3.3.1 Introduction The quantitative interpretation of resistivity data of the study area is made using computer program. The computer program used here is IPI2Win. IPI2Win is designed for automated and interactive semi-automated interpreting of vertical electric sounding and/or induced polarization data obtained with any of a variety of most popular arrays used in the electrical prospecting. IPI2Win can be run on any computer with Windows 95/98/NT operating system. Monitor should be in 256 colors or higher. By this program, a model for each sounding data point is constructed starting with VES points which were conducted near borehole to give an idea about real resistivities of subsurface layers which are used to control the rest of the sounding data points those have the same or similar curve types. Each model is adjusted many times till the calculated curve fits the observed one. Finally, the results are obtained and put in Appendix (C) to subsequently make geo-electric sections. Based on VES survey, the electrical resistivities in the area can be summarized as: - Gravels (surface) > 200 Ω.m - Sands (surface) 57-176 Ω.m - Clayey sands 33-49 Ω.m - Clays + Sandy clays (surface) 13-30 Ω.m - Sandstones (saturated) 21-189 Ω.m - claystones 11-14 Ω.m - Silicified (sandstones/claystones) > 200 Ω.m - Crystalline B.C. > 200 Ω.m 119 4.3.3.2 Geo-electric sections along selected profiles in the study area A total of eight geo-electric sections are constructed along the previously mentioned profiles (Fig. 4.8). They are illustrated in Figs. (4.25, 4.26, 4.27, 4.28, 4.29, 4.30, 4.31 and 4.32). These geo-electric sections are described below in some details. Fig. (4.25) is a geo-electric section along profile AA'. It contains six resistivity layers. The ends of the first layer are adjacent to VES 24 and VES 101. The depth of its bottom surface ranges from zero meter to 2.7 m. Its resistivity ranges from 13 Ω.m to 852 Ω.m. The depth of the bottom surface of the second layer ranges from 2.27 m to 5.86m. Its resistivity ranges from 22 Ω.m to 176 Ω.m. The depth of the bottom surface of the third layer ranges from 9.23 m to 24.1 m. Its resistivity ranges from 24 Ω.m to 194 Ω.m. The depth of the bottom surface of the fourth layer ranges from 27.2 m to 63.1 m. Its resistivity ranges from 618Ω.m to 3602Ω.m. Two odd resistivity zones appear within this layer, the first zone lies below VES 10 and VES 19 with resistivities of 182 Ω.m and 24 Ω.m, respectively, whereas the second one lies below VES 103 with resistivity of 28 Ω.m. The depth of the bottom surface of the fifth layer ranges from 80.3 m to 130 m. Its resistivity ranges from 33 Ω.m to 82 Ω.m. The resistivity of the six layer ranges from 267 Ω.m to 1350 Ω.m. Fig. (4.26) is a geo-electric section along profile BB'. It contains six resistivity layers. The depth of the bottom surface of the first layer ranges from 0.77 m to 4.77 m. Its resistivity ranges from 49 Ω.m to 588 Ω.m. The depth of the bottom surface of the second layer ranges from 4.06 m to 12.8 m. Its resistivity ranges from 16 Ω.m to 95 Ω.m. The depth of the bottom surface of the third layer ranges from 16.5 m to 32.8 m. Its resistivity ranges from 25 Ω.m to 130 Ω.m. An odd resistivity zone appears within this layer, it lies below VES 58 with resistivity of 406 Ω.m. The depth of the bottom surface of the fourth layer ranges from 37.5 m to 80.2 m. Its resistivity ranges from 214 Ω.m to 2462 Ω.m. The depth of the bottom surface of the fifth layer ranges from 81.9 m to 132 m. Its resistivity ranges from 26 Ω.m to 113 Ω.m. The resistivity of the six layer ranges from 272 Ω.m to 771 Ω.m. 120 Fig. (4.27) is a geo-electric section along profile CC'. It contains six resistivity layers. The depth of the bottom surface of the first layer ranges from 0.89 m to 2.89 m. Its resistivity ranges from 27 Ω.m to 272 Ω.m. The depth of the bottom surface of the second layer ranges from 7.41 m to 9.8 m. Its resistivity ranges from 27 Ω.m to 89 Ω.m. An odd resistivity zone appears within this layer, it lies below VES 90, VES 60 and VES 88 with resistivities of 16 Ω.m, 21 Ω.m and 11Ω.m, respectively. The depth of the bottom surface of the third layer ranges from 17.2 m to 30.7 m. Its resistivity ranges from 35 Ω.m to 182 Ω.m. The depth of the bottom surface of the fourth layer ranges from 44 m to 75.6 m. Its resistivity ranges from 548 Ω.m to 4864 Ω.m. The depth of the bottom surface of the fifth layer ranges from 122 m to 141 m. Its resistivity ranges from 36 Ω.m to 138 Ω.m. The resistivity of the six layer ranges from 496 Ω.m to 1150 Ω.m. Fig. (4.28) is a geo-electric section along profile DD'. It contains six resistivity layers. The depth of the bottom surface of the first layer ranges from zero meter to 3.13 m. Its resistivity ranges from 15 Ω.m to 1617 Ω.m. The depth of the bottom surface of the second layer ranges from 4.86 m to 12.5 m. Its resistivity ranges from 33 Ω.m to 115 Ω.m. Three odd resistivity zones appear within this layer, the first zone lies below VES 30 with resistivity of 1 Ω.m, the second zone lies below VES 41 with resistivity of 210 Ω.m, whereas the third one lies below VES 53 with resistivity of 278 Ω.m. The depth of the bottom surface of the third layer ranges from 13.8 m to 31.9 m. Its resistivity ranges from 21 Ω.m to 186 Ω.m. The depth of the bottom surface of the fourth layer ranges from 23.2 m to 94.2 m. Its resistivity ranges from 223 Ω.m to 1434 Ω.m. The depth of the bottom surface of the fifth layer ranges from 108 m to 132 m. Its resistivity ranges from 23 Ω.m to 172 Ω.m. The depth of the top surface of the sixth layer ranges from 30 m to 132 m. Its resistivity ranges from 467 Ω.m to 8873 Ω.m. Fig. (4.29) is a geo-electric section along profile EE'. It contains six resistivity layers. The depth of the bottom surface of the first layer ranges from zero meter to 3.6 m. Its resistivity ranges from 57 Ω.m to 165 Ω.m. The depth of the bottom surface of the second layer ranges from 4.14 m to 9 m. Its resistivity ranges from 21 Ω.m to 35 Ω.m. The depth of the bottom surface of the third layer ranges from 16.5 m to 27.8 m. Its 121 resistivity ranges from 63 Ω.m to 120 Ω.m. An odd resistivity zone appears within this layer, it lies below VES 31 with resistivity of 8 Ω.m. The depth of the bottom surface of the fourth layer ranges from 17 m to 90.5 m. Its resistivity ranges from 278 Ω.m to 490 Ω.m. The depth of the bottom surface of the fifth layer ranges from 71.2 m to 127 m. Its resistivity ranges from 85 Ω.m to 175 Ω.m. An odd resistivity zone appears within this layer, it lies below VES 31 and VES 14 with resistivities of 14 Ω.m and 11 Ω.m, respectively. The resistivity of the six layer ranges from 194 Ω.m to 353 Ω.m. Fig. (4.30) is a geo-electric section along profile FF'. It contains six resistivity layers. The depth of the bottom surface of the first layer ranges from zero meter to 7.86 m. Its resistivity ranges from 18 Ω.m to 544 Ω.m. The depth of the bottom surface of the second layer ranges from 3.76 m to 20.2 m. Its resistivity ranges from 21 Ω.m to 175 Ω.m. An odd resistivity zone appears within this layer, it lies below VES 46 and VES 45 with resistivities of 449 Ω.m and 308 Ω.m, respectively. The depth of the bottom surface of the third layer ranges from 19.4 m to 40.6 m. Its resistivity ranges from 39 Ω.m to 189 Ω.m. The depth of the bottom surface of the fourth layer ranges from 63.1 m to 83.5 m. This layer is divided into two parts according to their resistivity ranges. The resistivity of the first part ranges from 18 Ω.m to 179 Ω.m, whereas the resistivity of the second one ranges from 272 Ω.m to 1362 Ω.m. The depth of the bottom surface of the fifth layer ranges from 92.3 m to 168 m. Its resistivity ranges from 22 Ω.m to 171 Ω.m. The resistivity of the six layer ranges from 206 Ω.m to 1105 Ω.m. Two odd resistivity zones appear within this layer, the first zone lies below VES 34 with resistivity of 8 Ω.m, whereas the second one lies below VES 46 with resistivity of 162 Ω.m. Fig. (4.31) is a geo-electric section along profile GG'. It contains six resistivity layers. The depth of the bottom surface of the first layer ranges from 0.59 m to 4.68 m. Its resistivity ranges from 41 Ω.m to 1239 Ω.m. The depth of the bottom surface of the second layer ranges from 4.97 m to 10.6 m. Its resistivity ranges 122 from 21 Ω.m to 176 Ω.m. An odd resistivity zone appears within this layer, it lies below VES 88 with resistivity of 11 Ω.m. The depth of the bottom surface of the third layer ranges from 17.2 m to 35.75 m. Its resistivity ranges from 25 Ω.m to 127 Ω.m. An odd resistivity zone appears within this layer, it lies below VES 83 with resistivity of 1493 Ω.m. The depth of the bottom surface of the fourth layer ranges from 42.3 m to 90.4 m. Its resistivity ranges from 267 Ω.m to 5320 Ω.m. The depth of the bottom surface of the fifth layer ranges from 85.2 m to 138 m. Its resistivity ranges from 42 Ω.m to 182 Ω.m. The resistivity of the six layer ranges from 267 Ω.m to 1898 Ω.m. Fig. (4.32) is a geo-electric section along profile HH'. It contains six resistivity layers. The depth of the bottom surface of the first layer ranges from zero meter to 5.82 m. Its resistivity ranges from 28 Ω.m to 527 Ω.m. The depth of the bottom surface of the second layer ranges from 3.13 m to 12.5 m. Its resistivity ranges from 36 Ω.m to 172 Ω.m. An odd resistivity zone appears within this layer, it lies below VES 70 and VES 69 with resistivities of 13 Ω.m and 12 Ω.m. The depth of the bottom surface of the third layer ranges from 12.5 m to 40.8 m. Its resistivity ranges from 17 Ω.m to 120 Ω.m. The depth of the bottom surface of the fourth layer ranges from 33.2 m to 88.7 m. Its resistivity ranges from 278 Ω.m to 771 Ω.m. Two odd resistivity zones appear within this layer, the first zone lies below VES 19 with resistivity of 23.8 Ω.m, whereas the second one is restricted between VES 62 and VES 68 with resistivities range from 115 Ω.m to 223 Ω.m. The depth of the bottom surface of the fifth layer ranges from 80.2 m to 165 m. Its resistivity ranges from 22 Ω.m to 117 Ω.m. An odd resistivity zone appears within this layer, it is restricted between VES 70 and VES 68 with resistivities range from 10 Ω.m to 13 Ω.m. The resistivity of the six layer ranges from 140 Ω.m to 620 Ω.m. 4.3.3.3 Geologic sections along selected profiles in the study area The above mentioned geo-electric sections are converted into geologic sections (Figs. 4.25, 4.26, 4.27, 4.28, 4.29, 4.30, 4.31 and 4.32). The first layer in all geo-electric sections, which has resistivity ranges (13-1617 Ω.m), is interpreted as superficial deposits. These superficial deposits represent clay, sandy- 123 A' 42 423 186 SSE 1350 VES100 49 657 194 25 VE S101 1062 Distance (km) Silicified Sandstones Superfacial Deposits 42 332 618 100 VES102 20 rofileAA'. p 82 28 24 1350 V ES103 ection along along ection s 58 56 449 VE S104 3602 15 eologic g - 62 25 267 VES 105 1650 Geoelectric 79 VE S24 506 712 117 10 Fig.4.25: Basement Complex sandy-clay Sandstone (Lower and Upper Aquifer) 5 33 24 28 620 V E S 19 0 48 54 VE S10 182 NNW 0 50 A D e p t h ( m ) 100 124 B' 84 24 SE 618 113 214 V E S 56 25 71 19 V E S 57 527 108 527 Fault Superfacial Deposits 45 27 440 406 V E S 58 1493 Distance (km) 20 68 57 36 353 367 V E S 59 45 56 631 852 V E S 89 36 16 506 130 V E S 90 1020 rofileBB'. p 61 89 571 120 V E S 91 1585 15 ection along along ection s 58 61 95 618 V E S 92 1898 Silicified Sandstones Sandy-clay eologic 26 g 390 771 115 V E S 21 - 33 771 390 V E S 93 10 Geoelectric 33 40 319 771 Fig.4.26: V E S 94 5 41 70 283 2462 V E S 95 Basement Complex Sandstone (Lower and Upper Aquifer) 0 56 25 272 232 NW V E S 29 0 50 B D e p t h ( m ) 100 125 C' 85 135 141 VES 28 4864 SSE 84 27 538 113 VES99 20 4144 Superfacial Deposits C lay S andy-clay 98 58 138 VES27 4580 Distance (km) 15 56 35 670 100 VES98 1350 rofileCC'. p ection along along ection s 63 55 726 756 108 VES97 10 eologic g - Geoelectric 42 35 11 548 VE S88 1150 62 21 496 887 182 Fig.4.27: 5 VE S60 36 16 506 130 VE S90 1020 Basement Complex Sandstone (Lower and Upper Aquifer) Silicified Sandstones 61 89 571 120 1585 VES91 0 58 61 95 618 V ES92 1898 NNW 0 C 50 100 150 D e p t h ( m ) 126 D' 38 45 467 346 1434 V E S78 SE 71 33 923 111 1128 VES82 25 Fault Superfacial Deposits 31 146 980 382 108 VES3 697 165 852 158 278 V ES 53 Distance (km) 20 35 887 102 278 141 VES39 rofileDD'. p 50 802 172 923 186 15 VE S 40 S andy-clay C lay G ravels ection along along ection s eologic g 71 62 684 210 - V ES 41 10 Geoelectric 21 51 332 1752 V ES 42 Fig.4.28: 5 1 85 224 8873 VE S 30 Basement Complex Sandstone (Lower and Upper Aquifer) Silicified Sandstones 0 0 15 852 223 117 VES13 NW 0 D 50 D e p t h ( m ) 100 127 E' 85 548 382 108 VES17 SE Fault Superfacial Deposits 20 398 175 490 108 VES16 Distance (km) 15 rofileEE'. p ection along along ection s C laystone Silicified Sandstones Sandy-clay 10 eologic g - 194 117 278 120 165 VE S15 Geoelectric 5 Fig.4.29: 11 63 127 3531 VES14 0 Basement Complex Weathered Basement Sandstone (Lower and Upper Aquifer) 14 50 27 631 VES31 NW 0 50 E 100 D e p t h ( m ) 128 F' SE VES 44 83 171 127 213 1362 15 VES 45 31 49 450 608 189 308 Superfacial Deposits VES46 32 38 26 162 339 449 23 89 18 VES47 272 175 Distance (km) 1105 22 43 48 V ES64 267 307 158 rofileFF'. 10 p 23 33 58 25 V E S 48 294 ection along along ection s eologic Silicified Sandstones Sandy-clay G ravels g - 22 38 V ES62 206 179 127 Geoelectric 5 Fig.4.30: 23 47 39 21 VES 71 206 Basement Complex Weathered Basement Sandstone (Lower and Upper Aquifer) 0 8 NW 31 19 37 VES 34 194 0 F 50 150 100 D e p t h ( m ) 129 G' E 49 V E S 55 182 127 2833 59 92 35 V E S 35 267 1406 Fault Superfacial Deposits 91 31 38 VE S 83 1898 1128 1493 Distance (km) 31 V E S 3 146 980 382 108 10 38 V E S 5 548 182 980 155 '. 70 40 V E S 6 527 835 GG rofile p 50 21 Sandy-clay C lay VES7 128 5320 ection along along ection s eologic g - 5 68 57 36 V E S 59 353 367 Geoelectric 42 35 11 V ES 88 548 1150 Fig.4.31: Basement Complex Sandstone (Lower and Upper Aquifer) Silicified Sandstones 0 W 62 25 267 176 V E S105 1650 0 G 50 D e p t h ( m ) 150 100 130 H' 13 19 194 115 172 NE VES68 10 22 12 140 130 V E S 69 35 12 19 13 194 223 VES70 Fault Superfacial Deposits 22 38 206 179 127 VES62 30 Distance (km) 25 rofileHH'. p 20 35 ection along along ection 194 117 278 120 s VES15 C lay Silicified Sandstones Sandy-clay eologic g - 15 71 62 684 210 VES41 Geoelectric 10 Fig.4.32: 33 40 73 319 771 V E S 94 5 33 24 28 78 620 VES19 Basement Complex Weathered Basement Sandstone (Lower and Upper Aquifer) 0 25 17 210 313 251 VES22 SW 0 50 H D e p t h ( m ) 150 100 131 clays, clayey sands, sands and gravels. The second layer in all geo-electric sections which has resistivity ranges (16-176 Ω.m) is interpreted as a layer consists of sandy-clays, clayey sands and sands. The low and high resistivity ranges (4-16 Ω.m and 210-449 Ω.m) within this layer are interpreted as clay and gravels, respectively. The third and fifth layers which have similar resistivity ranges (21-189 Ω.m and 22- 182 Ω.m) are interpreted as saturated sandstones, thus they considered as upper and lower aquifers, respectively. The low resistivity values (10-14 Ω.m) within the lower aquifer are interpreted as claystones, whereas that of the high values (406 and 1493 Ω.m) within the upper aquifer are interpreted as non porous sandstones. The fourth layer of resistivity ranges (214-5320 Ω.m) is interpreted as aquifuge layer (non porous sandstones or likely silicified sandstones/claystones). The low resistivity ranges 24-182 Ω.m within the layer is interpreted as saturated sandstones. The sixth layer of resistivity ranges (210-8873 Ω.m) is interpreted as Basement, whereas that of the ranges 140-194 Ω.m is interpreted as weathered Basement. It is observed that the lower aquifer and Basement are affected by several normal faults. 4.3.3.4 Subsurface geologic maps of the study area From the above mentioned geoelectric sections, five maps are constructed. They are depth map of the top surface of the upper aquifer, thickness map of the upper aquifer, depth map of the top surface of the lower aquifer, thickness map of the lower aquifer and depth map of Basement surface (Figs. 4.33, 4.34, 4.35, 4.36 and 4.37). In Fig. (4.33), the depth of the top surface of the upper aquifer changes gradually from 3m west W. Awatib and east Musawarat village to 19 m at the northeastern part of the study area. 132 The claystones and non porous sandstones that appear within this aquifer (Sec. 4.3.3.3) are located here (Fig. 4.33) east Es Salama and around Musawarat villages, respectively, the areas where groundwater is not available. In Fig. (4.34) the thickness of the upper aquifer changes rapidly from 5 m to 30 m in the southern part of the area. In the rest of the area, the thickness is of the order of 10 m to 20 m. In Fig. (4.35) the depth of the top surface of the lower aquifer ranges from 20 m west W. Awatib to 95m at the eastern edge of the area. Around Musawarat village, the depth is of the order of 75-90 m, whereas at El Awatib, Es Salama and Wad Masa villages, is of the order of 35-45 m. These large variations in depth are caused by faulting. Thus, the area that includes El Awatib, Es Salama and Wad Masa villages is uplifted by normal faults related to the area that includes Musawarat village. The weathered basement that appears within this aquifer (Sec. 4.3.3.3) are placed here (Fig. 4.35) in two areas east Wad Masa village and east Es Salama village including Wad Masa village. In Fig. (4.36) the thickness of the lower aquifer increases rapidly from 34 m to 74 m in the southern part of the area and east Wad Masa, and then changes gradually from place to another within the rest of the area. In the area between El Awatib and Musawarat, the thickness reaches the maximum value (74 m) in the middle of the area. In an area that restricted between Musawarat, Es Salama and Wad Masa, it reaches the minimum value (34 m) in the middle of the area. In an area of southeast Wad Masa, it is in the order of 85 m, which is the largest value in the whole area. In Fig. (4.37) from Musawarat to the north, east and west (adjacent to W. Awatib), the Basement is deep. At El Awatib, Es Salama and Wad Masa, and west W. Awatib, the Basement is shallow; because it is uplifted by the same faults those were illustrated in Fig. (4.35). 133 4.3.4 Conclusions Two aquifers are delineated based on the interpretation of geoelectrical resistivity data of the study area. The upper aquifer is free aquifer, whereas the lower one is confined aquifer. The confined aquifer is restricted between basement and silicified sandstones. Both aquifers have small depth west W. Awatib and large depth east of it because of the normal fault that is represented with W. Awatib. The water is not available within the upper aquifer at Musawarat and Es Salama areas (the areas of high and low resistivities which are interpreted as silicified sandstones and claystones, respectively) (Fig. 4.33). The lower aquifer disappears beneath the area that lies east of El Awatib and south of Es Salama. The aquifer here is replaced by the uplifted basement (Fig. 4.35). Finally, although the lower aquifer is the confined aquifer, it can be recharged through the large wadies that flowing over the area from one side and through permeable sandstones that appear within the silicified sandstones from the other side (Figs. 4.25, 4.30 and 4.32). 134 Fig. 4.33: Depth map of the top surface of the upper aquifer. 135 Fig. 4.34: Thickness map of the upper aquifer. 136 Fig. 4.35: Depth map of the top surface of the lower aquifer. 137 Fig. 4.36: Thickness map of the lower aquifer. 138 Fig. 4.37: Depth map of Basement surface. 139 Chapter Five Results and Discussion Geophysical and borehole data indicated that the Bara, Kosti, Khartoum and Atbara basins contain less than 5 km of sedimentary and magmatic fill (Jorgenson and Bosworth 1989; and Wycisk et al. 1990) and the maximum thickness of sediments in Atbara basin is about 3100 m (Jorgenson and Bosworth 1989). In the present study, again Atbara, southern part of Shendi and Fadniya basins are revealed from gravity data. The maximum thickness of sediments in Atbara basin is found to be 3110 m. Some normal faults that are delineated from geo-electrical resistivity data and some steep gradient zones of gravity data, which are referred to here as normal faults, coincide with some wadies such as W. Awatib, W. Abu Talh, W. El Hawad and R. Atbara. This means that these normal faults affecting the Mesozoic sedimentary rocks which fill the above mentioned basins, but it is well known that these faults were formed during the first and second rifting phase. Thus, it is suggested that these faults were reactivated during the third rifting phase during Late Eocene/Miocene. It is found that the subsurface of the area of Musawarat, El Awatib, Es Salama and Wad Masa contains six geologic layers. From borehole data, it is concluded that the above mentioned layers are: - Superficial deposits. - Sandy-clays, clayey sands and sands. - Porous sandstones (upper aquifer). - Silicified sandstones (aquifuge). - Porous sandstones (lower aquifer). - Basement complex. 140 From lithology, it is found that the third, fourth and fifth layers are sandstones. The resistivies of the third and fifth layers are low, whereas the resistivity of the fourth one is high. Comparing these resistivities with the theoretical ones (Tab. 4.1) as well as those obtained by Lashkaripour and Nakhaei (2005), it is found that the resistivities of the third and fifth layers lie within the range of the resistivities of saturated sandstones, so they are considered as upper and lower aquifers, whereas the resistivity of the fourth layer is found within the range of resistivities of dry sandstones. The depth to the top surface of the lower aquifer is about 95m and the static water level is about 39 m. This means that the lower aquifer is a confined aquifer. From other hand, the fourth layer is restricted between two aquifers. So, the fourth layer is nonporous sandstones. It may be silicified sandstones; thus it is considered as aquifuge. The granulites of Sabaloka inlier are found to be of Pan-African age (Kröner 1987). The Pressure/Temperature (PT) calculation based on coexisting mineral pairs of the granulites indicates that the granulites are formed at depth of more than 25 km. Using statistical analysis of the relationship between Bouguer gravity anomaly, topography and depth to the Moho, the crustal thickness of the Sabaloka inlier is found to be 41 km (Sadig 1969). The early recumbent folding in Sabaloka area implying that the crustal shortening which was associated with the Pan- African orogeny and accretion of island arcs to the east in the Red Sea Hills, resulted in thickening of the crust at Sabaloka and thus facilitated granulites metamorphism (Dawoud and Sadig 1988). Thus, the granulites represent the infrastructure of this part of the Nubian Shield, but their exposure at Sabaloka was interpreted as due to several factors. The second phase of the recumbent folding, faulting and rafts in the granulites indicate that the granulites were thrusted from their root zone to the east (Dawoud and Sadig 1988). In the present study, the body that caused the high gravity anomaly east Musawarat, Shendi, Kabushiya and Bagarawiya is interpreted as granulites root. It is suggested to be uplifted first to a depth of less than 2.5 km, and then thrusted to the west to form the granulites of 141 Sabaloka inlier. The uplifting is indicated by the steep gradients that surround the high anomaly. Wycisk et al. (1990) and Bosworth (1992) concluded that the Sudanese rift basins (Central African Rift System (CARS) in Sudan) had undergone extension during three rift phases. The first rifting phase occurred during Late Jurassic/Early Cretaceous (Albian). During the rifting phase the Blue Nile basins and Bara basin underwent extension. At this rifting phase the principal extension direction was approximately E-W. The second rifting phase occurred during Late Cretaceous/Early Tertiary (Turonian-Paleocene), during which the extension shifted to a NE-SW orientation. During this rifting phase all known Mesozoic basins of Sudan (e.g. Atbara and Shendi basins) were reactivated. The third rifting phase occurred during Late Eocene/Miocene. During this phase Khartoum basin has probably underwent significant inversion (Bosworth 1992). 142 Conclusions and Recommendations Two major sedimentary basins and several sub-basins are delineated from the interpretation of gravity data of the study area (Fig.3.35). One of the two major basins is located at Shendi region. It is a southern extension of Shendi Basin. The maximum thickness of sediments is about 1400m. The other basin is broad and located southeast Ziedab at the northeastern part of the study area. It was previously defined as Atbara Basin. The maximum thickness of sediments is about 3110m. The first sub-basin is located east Umm Shadida village with maximum depth is about 600m. It has an elongated shape and extends SW-NE. The second is located WNW Umm Shadida village at a distance of 30km. It was known as Fadniya basin (Ibrahim 1993). It has a rectangular shape extending NW-SE. The maximum depth is about 2400m. The last one is located SSE Zeidab at a distance of 45km, and east Bagarawiya. It has non-uniform shape. The maximum depth is about 2000m. All of these basins are filled with Nubian Sandstones. The above mentioned basins are controlled by normal faults. Some of these faults coincide with some wadies such as W. Awatib, W. Abu Talh, W. El Hawad and R. Atbara. At the northeastern corner of the study area at R. Atbara, the Basement seems to be laterally displaced, thus it is concluded that this is another dextral strike slip fault. In Fig. (3.15), the gravity high at Ban Gadeed is shown to be caused by granulites. The granulites have been emplaced tectonically at Ban Gadeed. Another strong gravity high appears over an area that is situated east Shendi and south Umm Ali area. It is interpreted as the source of the granulites which have been uplifted some kilometers and then thrusted to Ban Gadeed as it was indicated by Dawoud and Sadig (1988). 143 Returning to Figs. (3.24 and 3.25), it is observed that the regional anomaly represents gravity high concentrates over sedimentary basins. As the regional anomaly comes from deep seated structure, it is concluded that this regional anomaly is caused by rising of mantle beneath the sedimentary basins so as to compensate for the deficiency in mass material caused by the light density of sedimentary rocks. From the interpretation of the geoelectrical resistivity data of Musawarat, El Awatib, EsSalama and Wad Masa areas, six geologic layers are delineated (Figs. 4.25-4.32). They are: - Superficial deposits. - Sandy-clays, clayey sands and sands. - Porous sandstones (upper aquifer). - Silicified sandstones (aquifuge). - Porous sandstones (lower aquifer). - Basement complex. The third and fifth layers are found to be groundwater aquifers, so they are referred to as upper and lower aquifers, respectively. The lower aquifer is thicker than the upper one, so it is concluded that it has a lot of water enough for drinking and irrigation purposes. The water in the upper aquifer is available everywhere in the study area except at Musawarat and Es Salama areas (Fig. 4.33). The water in the lower aquifer is available everywhere in the study area except the area that lies east of El Awatib and south of Es Salama. The aquifer here is replaced by the uplifted basement (Fig. 4.35). So, this area is considered the poorest one in groundwater. Although the lower aquifer is the confined aquifer, it can be recharged through the large wadies that flowing over the area from one side and through permeable sandstones that appear within the silicified 144 sandstones from the other side (Figs. 4.25, 4.30 and 4.32). The depth of the upper aquifer at El Awatib, Es Salama and Wad Masa is about 6m (Fig.4.33). The depth of the lower aquifer at Musawarat is about 80m, at Naga about 85m, east Wad Masa about 70m (Fig. 4.35). The depth of the basement at Musawarat is about 130m, east Wad Masa is about 145m, whereas at Wad Masa, Es Salama, El Awatib and west W. Awatib is about 60m. Some faults are delineated according to rapid change in the depth (Figs. 4.35). One of them coincides with W. Awatib. Thus, it is suggested that the area includes Musawarat and east Wad Masa area is subsided related to the area that includes west W. Awatib, El Awatib, Es Salama and Wad Masa. Comparing the gravity results with the geoelectrical resistivity ones, it is observed that the faults are revealed in both (Figs. 3.35 and 4.37). In other side, the depth of the basement at Musawarat area is found to be about 130m as a result of the geoelectrical resistivity interpretation, whereas from the interpretation of gravity data is found to be about 400m. This difference comes from the fact that upper part of the basement is influenced by uplifting and removal of load as well as weathering, thus its density tends to decrease towards the density of sedimentary rocks. Several basins are delineated from the interpretation of gravity data of the study area. Several wadies are flowing over these basins, so they recharge them. Thus, these basins may contain good groundwater aquifers. Recommendations: 1. Seismic refraction and resistivity measurements must be conducted in the area to investigate the structures, sedimentary sequence as well as the groundwater conditions. 145 2. 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Zohdy, A. A. R., Eaton, G. P. and Mabey, D. R. (1974). Application of surface geophysics to ground-water investigation. Techniques of water-resources investigation, U. S. Geological Survey, 116 p. 157 Shendi Sabalaka Fig. 2.1: Geological Map of the Study Area (from Geological Map of Sudan produced by GRAS 1988). Fig. 1.2: Satellite Image of the Study Area. Resistivity-depth Models of of theModelsResistivity-depth Study Area Appendix (C) 179 Fig. C.1: Resistivity-depth Model of VES3. 180 Fig. C.2: Resistivity-depth Model of VES5. Fig. C.3: Resistivity-depth Model of VES6. 181 Fig. C.4: Resistivity-depth Model of VES7. Fig. C.5: Resistivity-depth Model of VES10. 182 Fig. C.6: Resistivity-depth Model of VES13. Fig. C.7: Resistivity-depth Model of VES14. 183 Fig. C.8: Resistivity-depth Model of VES15. Fig. C.9: Resistivity-depth Model of VES16. 184 Fig. C.10: Resistivity-depth Model of VES17. Fig. C.11: Resistivity-depth Model of VES19. 185 Fig. C.12: Resistivity-depth Model of VES21. Fig. C.13: Resistivity-depth Model of VES22. 186 Fig. C.14: Resistivity-depth Model of VES24. Fig. C.15: Resistivity-depth Model of VES27. 187 Fig. C.16: Resistivity-depth Model of VES28. Fig. C.17: Resistivity-depth Model of VES29. 188 Fig. C.18: Resistivity-depth Model of VES30. Fig. C.19: Resistivity-depth Model of VES31. 189 Fig. C.20: Resistivity-depth Model of VES34. Fig. C.21: Resistivity-depth Model of VES35. 190 Fig. C.22: Resistivity-depth Model of VES39. Fig. C.23: Resistivity-depth Model of VES40. 191 Fig. C.24: Resistivity-depth Model of VES41. Fig. C.25: Resistivity-depth Model of VES42. 192 Fig. C.26: Resistivity-depth Model of VES44. Fig. C.27: Resistivity-depth Model of VES45. 193 Fig. C.28: Resistivity-depth Model of VES46. Fig. C.29: Resistivity-depth Model of VES47. 194 Fig. C.30: Resistivity-depth Model of VES48. Fig. C.31: Resistivity-depth Model of VES53. 195 Fig. C.32: Resistivity-depth Model of VES55. Fig. C.33: Resistivity-depth Model of VES56. 196 Fig. C.34: Resistivity-depth Model of VES57. Fig. C.35: Resistivity-depth Model of VES58. 197 Fig. C.36: Resistivity-depth Model of VES59. Fig. C.37: Resistivity-depth Model of VES60. 198 Fig. C.38: Resistivity-depth Model of VES62. Fig. C.39: Resistivity-depth Model of VES64. 199 Fig. C.40: Resistivity-depth Model of VES68. Fig. C.41: Resistivity-depth Model of VES69. 200 Fig. C.42: Resistivity-depth Model of VES70. Fig. C.43: Resistivity-depth Model of VES71. 201 Fig. C.44: Resistivity-depth Model of VES80. Fig. C.45: Resistivity-depth Model of VES82. 202 Fig. C.46: Resistivity-depth Model of VES83. Fig. C.47: Resistivity-depth Model of VES88. 203 Fig. C.48: Resistivity-depth Model of VES89. Fig. C.49: Resistivity-depth Model of VES90. 204 Fig. C.50: Resistivity-depth Model of VES91. Fig. C.51: Resistivity-depth Model of VES92. 205 Fig. C.52: Resistivity-depth Model of VES93. Fig. C.53: Resistivity-depth Model of VES94. 206 Fig. C.54: Resistivity-depth Model of VES95. Fig. C.55: Resistivity-depth Model of VES97. 207 Fig. C.56: Resistivity-depth Model of VES98. Fig. C.57: Resistivity-depth Model of VES99. 208 Fig. C.58: Resistivity-depth Model of VES100. Fig. C.59: Resistivity-depth Model of VES101. 209 Fig. C.60: Resistivity-depth Model of VES102. Fig. C.61: Resistivity-depth Model of VES103. 210 Fig. C.62: Resistivity-depth Model of VES104. 211 Fig. C.63: Resistivity-depth Model of VES105.