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OES Theses and Dissertations Ocean & Earth Sciences
Spring 1999
Stratal Architecture in a Prograding Shoreface Deposit, Eastern Shore, VA: Relationship to Grain Size, Permeability, and Facies Distribution
Andrew C. Miller Old Dominion University
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Recommended Citation Miller, Andrew C.. "Stratal Architecture in a Prograding Shoreface Deposit, Eastern Shore, VA: Relationship to Grain Size, Permeability, and Facies Distribution" (1999). Doctor of Philosophy (PhD), Dissertation, Ocean & Earth Sciences, Old Dominion University, DOI: 10.25777/fgpa-9e17 https://digitalcommons.odu.edu/oeas_etds/64
This Dissertation is brought to you for free and open access by the Ocean & Earth Sciences at ODU Digital Commons. It has been accepted for inclusion in OES Theses and Dissertations by an authorized administrator of ODU Digital Commons. For more information, please contact [email protected]. STRATAL ARCHITECTURE IN A PROGRADING SHOREFACE
DEPOSIT, EASTERN SHORE, VA: RELATIONSHIP TO GRAIN
SIZE, PERMEABILITY, AND FACIES DISTRIBUTION
by
Andrew C. Muller B.S., May 1989 Adelphi University M.S., August 1992, Old Dominion University
A Dissertation Submitted to the Faculty of Old Dominion University in Partial Fulfillment of the Requirement for the Degree of
DOCTOR OF PHILOSOPHY
OCEANOGRAPHY
OLD DOMINION UNIVERSITY May 1999
Approved by’
Donald J.P. Swift (Director)
Ronald E. Johnson (Member)
G. Richard Whittecar (Member)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT
STRATAL ARCHITECTURE IN A PROGRADING SHOREFACE DEPOSIT, EASTERN SHORE, VA: RELATIONSHIP TO GRAIN SIZE, PERMEABILITY, AND FACIES DISTRIBUTION
Andrew C. Muller Old Dominion University, 1999 Director Dr. Donald J.P. Swift
A fundamental concern of the stratigrapher is to develop predictive models of
stratigraphic organization. In sedimentology one of the most significant problems that
has yet to be resolved is the fact that there is a lack of quantitative information
regarding the relationship between geometry of beds, thickness o f beds, grain size and
sedimentary structures in sandy environments, especially shallow marine deposits.
Scientists have also realized the need to correlate quantitative permeability to
sedimentary structures and scales of stratigraphic organization. The purpose of the
study is to investigate the scales of stratigraphic organization that control the variation
of grain size and permeability in shallow marine deposits. A model of stratal
architecture is constructed in order to relate scales of stratigraphic organization to these
properties. The hypothesis tested is that models of stratal architecture are more
efficient predictors of grain size and permeability than are facies models in shallow
marine sands. Several methods are used to test the hypothesis, including mapping of
stratal geometry, measuring stratal characteristics, and the construction of facies
distribution through measured sections. These techniques are used to erect the stratal
architecture of strand plain deposits at Oyster, Virginia. ANOVA, Tukey-Kramer Means
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Comparisons tests and variograms are performed to test the statistical significance of
mean grain size and permeability variability over multiple scales of stratigraphic
organization. Results from this study demonstrate that multiple levels of stratigraphic
organization are statistically significant with respect to the spatial variability of grain
size and permeability, and that one-dimensional facies models are clearly unable to
resolve these important stratigraphic scales. The study also revealed that a parabolic
relationship exists between mean grain size and set thickness, and is thought to be the
evolutionary consequence of the progressive sorting process.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS
Page
LIST OF TABLES...... viii
LIST OF FIGURES...... xi
Chapter
L INTRODUCTION...... 1
GENERAL INTRODUCTION...... 1 Statement of the Problem...... 1 Heterogeneity in Sedimentary Deposits ...... 1 Numerical Models ofPhysical Heterogeneity...... 3
GRANULOMETRIC PROPERTIES OF SEDIMENTS...... 4 General...... 4 Primary Properties ...... 5 Mineralogy and Fabric ...... 5 Grain Size and Sorting...... 6 Shape and Roundness ...... 8 Secondary Properties ...... 9 Porosity...... 9 Permeability...... 10 Permeability and Grain Size ...... 11
LEVELS OF STRATIGRAPHIC ANALYSIS...... 14 General...... 14 Small Scale Architecture...... 15 GeneraL...... 15 Small Scale Architecture: McKee and Weir (1953)...... 16 Classification of Cross-Stratification...... 20 Mesoscale Architecture (Facies and Facies Models) ...... 26 Vertical Architectural Patterns...... 28 Hierarchy of Bounding Surfaces ...... 33 Large Scale Architecture (Depositional Sequences) ...... 35 Architectural Classification used in this Study...... 39
THE STUDY AREA...... 44 General Geology o f the Eastern Shore...... 44 The Oyster Site as a Natural Lab...... 49 Facies Erected in the Study Area...... 51
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HYPOTHESIS TO BE TESTED...... 52
THESIS LAYOUT...... 52
0. METHODS OF STUDY...... 53
INTRODUCTION...... 53 Approach...... 53 Data Collected...... 54
FIELD METHODS...... 54 Opening of Pit Faces ...... 54 Measured Sections ...... 55 Geological Mapping...... 55 Sampling Procedures ...... 56 Grain Size...... 58 Permeability...... 58 Stratal Geometry Measurements...... 58
LABORATORY METHODS...... 59 Grain Size Analysis ...... 59 Geostatistical Analysis ...... 59 Textural Properties ...... 59 Normalization of Textural Properties to Set Geometry. 60 Variogram Construction...... 60 Analysis o f Variance ( ANOVA)...... 61
ffl. ARCHITECTURE OF THE OYSTER SITE...... 67
INTRODUCTION...... 67
FACIES ARCHITECTURE...... 67
STRATAL ARCHITECTURE...... 75 General...... 75 Coset A...... 77 Coset B ...... 80 Coset C ...... 87 Coset D...... 89
VERTICAL PATTERNS...... 94 Set Thickness...... 94 Grain Size...... 95
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Chapter Page
IV. GEOSTATISTICAL ANALYSIS OF THE OYSTER SITE...... 106
INTRODUCTION...... 106
STRATAL ARCHITECTURAL MAPS...... 106 Coset A...... 107 Distribution of Grain Size Samples...... 107 Distribution of Permeability Samples ...... 107 Coset B ...... 107 Distribution of Grain Size Samples ...... I ll Distribution of Permeability Samples ...... I l l Coset C ...... 111 Distribution of Grain Size Samples...... 111 Distribution o f Permeability Samples...... 116 Coset D ...... 116 Distribution of Grain Size Samples...... 117 Distribution of Permeability Samples ...... 117
BIVARIATE STATISTICS...... 117 General...... 117 Textural Properties ...... 118 Mean Grain Size vs. Sorting...... 118 Mean Grain Size vs. Skewness ...... 118 Mean Grain Size vs. Percent Gravel ...... 120 Sorting vs. Percent Gravel ...... 120 Mean Grain Size vs. Permeability...... 120 Sorting vs. Permeability...... 123 Mean Grain Size vs. Set Thickness ...... 123
ANALYSIS OF VARIANCE RESULTS...... 123 General...... 123 Tukey-Kramer Means Comparison T est ...... 127 Coset Variability...... 128 Grain Size...... 128 Permeability...... 132 Set Variability...... 136 General...... 136 Coset A...... 137 Coset A: Grain Size Results...... 137 Coset A: Permeability Results ...... 138 Coset B ...... 141 Coset B: Grain Size Results ...... 141 Coset B: Permeability Results ...... 141
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Coset C ...... 145 Coset C: Grain Size Results...... 145 Coset C: Permeability Results ...... 146 Coset D ...... 146 Coset D: Grain Size Results...... 146 Coset D: Permeability Results...... 149
VARIOGRAM RESULTS...... 152 General ...... 152 Variogram Modeling...... 155 Coset A...... 155 Grain Size Results ...... 155 Permeability Results ...... 156 Coset B ...... 156 Grain Size Results ...... 156 Permeability Results ...... 161 Coset C ...... 161 Grain Size Results ...... 161 Permeability Results ...... 167
V. CONCLUSIONS...... 171
INTRODUCTION...... 171
SIGNIFICANCE OF THE OYSTER SITE ARCHITECTURAL RESULTS...... 173 Facies Architecture...... 173 Stratal Architecture...... 174 Progressive Sorting on the Nassawadox Shoreface...... 178 General...... 178 Mean Grain Size vs. Set Thickness ...... 184
SIGNIFICANCE OF ANOVA RESULTS...... 187
SIGNIFICANCE OF VARIOGRAM RESULTS...... 189
GENERAL CONCLUSIONS...... 189
FUTURE RESEARCH...... 190
BIBLIOGRAPHY...... 192
VITA...... 198
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TABLE Page
1.1 Granulometric properties o f sediments ...... 5
1.2 Grain size classification scale (after Wentworth 1922) ...... 7
1.3 Relative affects of primary granulometric properties on secondary properties (after Pettijohn et al. 1986)...... 15
1.4 Comparison of quantitative terms used to describe stratification (after McKee and Weir 1953) ...... 20
1.5 Classification of cross-stratified units (after McKee and Weir 1953) ...... 21
1.6 Types of cross-stratification, grouped by lower bounding surface shape, grouping, scale and formation processes (after Allen 1984) ...... 27
1.7 Comparison of stratigraphic organization terminology of the McKee and Weir system vs. Campbell’s terminology...... 27
1.8 Scales of stratigraphic organization used in this study ...... 44
2.1 Bata collected...... 54
3.1 Textural properties of each facies ...... 74
3.2 Petrographic facies classification...... 75
3.3 Summary of average stratal geometry measurements of Coset A...... 80
3.4 Textural properties of Coset A...... 83
3.5 Summary of the average stratal geometry measurements of Coset B ...... 83
3.6 Summary of textural properties for Coset B ...... 87
3.7 Summary of stratal geometry measurements for Coset C ...... 89
3.8 Textural properties of Coset C ...... 91
3.9 Summary of stratal geometry measurements for Coset D ...... 94
3.10 Textural properties of Coset D ...... 94
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TABLE Page
3.11 Results of significance tests for correlation between set position and mean grain size ...... 101
4.1 Coset A: grain size set statistics ...... 109
4.2 Permeability set statistics: Coset A...... 110
4.3 Coset B: grain size set statistics ...... 114
4.4 Permeability set statistics: Coset B ...... 115
4.5 Coset C: grain size set statistics ...... 116
4.6 Permeability set statistics: Coset C ...... 116
4.7 Coset D: grain size set statistics ...... 117
4.8 Permeability set statistics: Coset D ...... 117
4.9 ANOVA results for grain size of cosets ...... 130
4.10 Means comparison results o f cosets: grain size ...... 132
4.11 ANOVA results for permeability of cosets ...... 136
4.12 Means comparison test for permeability of cosets ...... 136
4.13 ANOVA results of grain size for Coset A...... 138
4.14 Grain size means comparisons results: Coset A...... 140
4.15 ANOVA results for set permeability: Coset A...... 140
4.16 Means comparison results for permeability. Coset A...... 142
4.17 ANOVA results for grain size: Coset B ...... 144
4.18 Means comparison results for grain size: Coset B...... 144
4.19 ANOVA results of permeability. Coset B ...... 145
4.20 Means comparison results of permeability Coset B ...... 148
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TABLE Page
4.21 ANOVA results of grain size: Coset C ...... 149
4.22 Means comparison results of grain size: Coset C ...... 149
4.23 ANOVA results of permeability: Coset C ...... 149
4.24 Means comparison results of permeability for Coset C ...... 151
4.25 ANOVA results of grain size: Coset D...... 151
4.26 Means comparison test results o f grain size: Coset D ...... 151
4.27 ANOVA results of permeability: Coset D...... 151
4.28 Means comparison test results o f permeability: Coset D ...... 152
4.29 Number ofdata pairs for horizontal variogram: Coset A, grain size...... 159
4.30 Number of data pairs for vertical variogram: Coset A, grain size ...... 160
4.31 Number of data pairs for horizontal variogram: Coset A, permeability...... 160
4.32 Number of data pairs for vertical variogram: Coset A, permeability...... 161
4.33 Number of data pairs for horizontal variogram: Coset B, grain size ...... 164
4.34 Number of data pairs for vertical variogram: Coset B, grain size...... 165
4.35 Number of data pairs for horizontal variogram: Coset B, permeability...... 165
4.36 Number of data pairs for vertical variogram: Coset B, permeability...... 166
4.37 Number of data pairs for horizontal variogram: Coset C, grain size...... 166
4.38 Number of data pairs for vertical variogram: Coset C, grain size...... 167
4.39 Number of data pairs for horizontal variogram: Coset C, permeability...... 170
4.40 Number of data pairs for vertical variogram: Coset C, permeability...... 170
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF FIGURES
FIGURE Page
1.1 Permeability trends in a cross-bedded sand, showing the influences of sedimentary structure on fluid flow (after Pryor 1973) ...... 13
1.2 Sub-aqueous bedforms produced as a result of increasing stream power and grain diameter (after Allen 1963)...... 17
1.3 Diagram illustrating the terminology used to define stratification (after Allen 1984) ...... 19
1.4 Diagram illustrating the classification of cross-stratification (after McKee and Weir 1953)...... 22
1.5 Diagram illustrating cross-strata set scale, set grouping, base relationship (after Allen 1963,1984) ...... 24
1.6 Classification of cross-strata shape and lower bounding surface shape (after Allen 1963,1984)...... 25
1.7 The complete turbidite (after Walker 1984) ...... 30
1.8 Vertical patterns of stratification and their related grain size patterns (after Allen 1984) ...... 31
1.9 Hierarchy of bounding surfaces (after Brookfield 1977) ...... 34
1.10 Six fold hierarchy of bounding surfaces for fluvial deposits. A to E represents successive enlargements of fluvial unit showing the rank of bounding surfaces indicated by the circled numbers (after Miall 1985)...... 36
1.11 Fluvial architectural elements (after Miall 1985) ...... 37
1.12 Features o f a sequence and it’s associated system tracts, boundaries within systems traces are parasequences. HST is high stand systems tract, LST is low stand system tract, TST is transgressive systems tract, SB1 is type 1 sequence boundary and mfs is maximum flooding surface (after Vail 1987) ...... 40
1.13 Stratigraphic consequences of eustatic sea level changes (after Vail etal. 1979)...... 41
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FIGURE Page
1.14 The Eastern Shore of Virginia, showing the positions of the Accomack and Butlers BlufFMembers...... 45
1.15 Cross section showing the stratigraphic relationship of the members of the Nassawadox Formation (after Mixon 1985)...... 48
1.16 Evolution of the Nassawadox Spit ...... 50
2.1 Sample grid used to place samples on the outcrop face...... 57
2.2 Definition sketch for a normative set and the normalization of samples to set geometry...... 62
2.3 Definition sketch of a typical variogram ...... 63
3.1 Photograph of trough cross-stratification at the Oyster Site. Note the basal gravel lags in cross strata sets (arrows)...... 68
3.2 Photograph illustrating sediments from the lower Butlers Bluff Member...... 68
3.3 Facies distribution between easting 958 and 964 (after Parsons 1998) ...... 70
3.4 Facies distribution between easting 964 and 970 (after Parsons 1998) ...... 71
3.5 Facies distribution between easting 970 and 976 (after Parsons 1998) ...... 72
3.6 Facies distribution between easting 976 and 982 (after Parsons 1998) ...... 73
3.7 Percentage of facies within the Butlers BIuffMember...... 76
3.8 Petrographic facies vs. classical facies ...... 76
3.9 Mesoscale architecture of the Oyster Site...... 78
3.10 Photomosaic of Coset A...... 79
3.11 Histogram of lamina thickness for Coset A...... 81
3.12 Histogram of lamina width for Coset A...... 81
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FIGURE Page
3.13 Histogram of set thickness for Coset A...... 82
3.14 Histogram of set width for Coset A...... 82
3.15 Photograph of the stratal geometry of Coset B ...... 84
3.16 Histogram of lamina thickness for Coset B ...... 85
3.17 Histogram of lamina width for Coset B ...... 85
3.18 Histogram of set thickness for Coset B ...... 86
3.19 Histogram of set width for Coset B ...... 86
3.20 Photomosaic of Coset C, illustrating parallel laminations and set breaks...... 88
3.21 Histogram of set thickness for Coset C ...... 90
3.22 Histogram of set width for Coset C ...... 90
3.23 Photograph illustrating the break between Cosets C and D, and the general characteristics of Coset D...... 92
3.24 Histogram of set thickness for Coset D...... 93
3.25 Histogram of set width for Coset D...... 93
3.26 Vertical pattern of set thickness for easting 964 ...... 96
3.27 Vertical pattern of set thickness for easting 966 ...... 97
3.28 Vertical pattern of set thickness for easting 968 ...... 98
3.29 Vertical pattern of set thickness for easting 970 ...... 99
3.30 Vertical pattern of set thickness for easting 972 ...... 100
3.31 Vertical distribution of mean grain size for easting 965.3 ...... 102
3.32 Vertical distribution of mean grain size for easting 966 ...... 103
3.33 Vertical distribution of mean grain size for easting 968 ...... 104
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FIGURE Page
3.34 Elevation vs. mean grain size ...... 105
4.1 Stratal architecture o f the Oyster Site: Coset A...... 108
4.2 Stratal architecture o f the Oyster Site: Coset B and C ...... 112
4.3 Stratal architecture o f the Oyster Site: Coset C and D ...... 113
4.4 Mean grain size vs. sorting...... 119
4.5 Mean grain size vs. skewness...... 121
4.6 Mean grain size vs. % gravel...... 121
4.7 Sorting vs. % graveL ...... 122
4.8 Mean grain size vs. permeability ...... 122
4.9 Sorting vs. permeability ...... 124
4.10 Mean grain size vs. set thickness ...... 124
4.11 Example of box plots used in this study (after JMP Statistical Guide 1995) ...... 126
4.12 Definition sketch of means comparison circles (after JMP Statistical Guide 1995)...... 129
4.13 Coset box plots for grain size, and means comparison circle plot ...... 131
4.14 Example of the normal quantile plot (after JMP Statistical Guide 1995)...... 133
4.15 Q-Q plot Coset A...... 133
4.16 Q-Q plot Coset B ...... 134
4.17 Q-Q plot Coset C ...... 134
4.18 Q-Q plot Coset D ...... 135
4.19 Coset box plots and means comparison circles of permeability...... 135
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FIGURE Page
4.20 Box plots and means comparison circles of grain size: Coset A...... 139
4.21 Box plots and means comparison circle for permeability: Coset A...... 139
4.22 Box plots and means comparison circles of grain size: Coset B ...... 143
4.23 Box plots and means comparison circles of permeability: Coset B ...... 143
4.24 Box plots and means comparison circles of grain size: Coset C ...... 147
4.25 Box plots and means comparison circles of permeability: Coset C ...... 147
4.26 Box plots and means comparison circles of grain size: Coset D ...... 150
4.27 Box plots and means comparison circles of permeability: Coset D ...... 150
4.28 Definition sketch of parameters used to construct the directional variogram (after Pannatier 1996)...... 154
4.29 Horizontal variogram of grain size: Coset A...... 157
4.30 Vertical variogram of grain size: Coset A...... 157
4.31 Horizontal variogram of permeability: Coset A...... 158
4.32 Vertical variogram of permeability: Coset A...... 158
4.33 Horizontal variogram of grain size: Coset B ...... 162
4.34 Vertical variogram of grain size: Coset B ...... 162
4.35 Horizontal variogram of permeability: Coset B ...... 163
4.36 Vertical variogram of permeability: Coset B ...... 163
4.37 Horizontal variogram of grain size: Coset C ...... 168
4.38 Vertical variogram of grain size: Coset C ...... 168
4.39 Horizontal variogram of permeability: Coset C ...... 169
4.40 Vertical variogram of permeability: Coset C ...... 169
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FIGURE Page
5.1 The formation of cross strata sets, notice the scour formed in front of the migrating dune...... 176
5.2 The progressive sorting mechanism acting through time steps T1-T3 (after Swift et al. 1991a)...... 180
5.3 Textures and structures of depositional systems that have undergone progressive sorting (after Swift et al.1991b)...... 182
5.4 Progressive sorting on the Nassawadox shoreface...... 183
5.5 Hjulstrom curve, relating grain size to velocity (after Seibold and Berger 1982) ...... 186
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CHAPTER I
INTRODUCTION
GENERAL INTRODUCTION
Statement of the Problem
The construction of predictive models o f stratigraphic organization is a
fundamental concern of the stratigrapher. Pettijohn and colleagues (1973) have pointed
out that one of the most important unresolved problems in sedimentology is that there is
a lack of detailed information on the geometry, thickness of beds, grain size, and
sedimentary structures in sandy environments. Another significant problem in
sedimentology is that there is an extraordinary lack of quantitative permeability data
correlated to sedimentary structures and stratigraphic organization (Chandler et al.
1989; Davis et aL 1993; Doyle and Sweet 1995). Furthermore, there is a continual need
to incorporate detailed sedimentological data into predictive models of stratigraphic
organization.
Heterogeneity in Sedimentary Deposits. Scientists have realized that sediments
and sedimentary structures are generally not homogeneous or uniformly random in
nature. Sedimentary deposits typically display multiple layers o f contrasting grain size
and permeability at discrete or continuous scales. These layers may range from
millimeters to tens of meters thick and are often geometrically anisotropic and
discontinuous (Allen 1963; Cushman 1990). Therefore, a hierarchy o f sedimentary
bodies can be erected over a range of spatial scales and used to describe the
The journal model used for this dissertation was the Journal of Sedimentary Research.
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heterogeneity in sedimentary deposits. The term “architecture” is used to describe the
two and three dimensional study o f the geometry o f individual sediment bodies, and their
stratigraphic organization (Allen and Allen 1990). Studies of stratigraphic architecture
have focused almost exclusively on mesoscale and large scale architecture, and have only
been conducted in aeolian or fluvial deposits (Brookfield 1977; Miall 1985; Miall 1988;
Davis et al. 1993; Cowan 1991; Jordan and Pryor 1992). Small scale architecture
(centimeter scale) o f marine deposits have been almost entirely ignored. I believe that in
order to develop predictive models of stratigraphic organization that relates primary
properties such as bed structure and grain size to secondary properties of permeability
and porosity, we need to understand how small scale heterogeneity fits into a
classification o f large scale heterogeneity at the basin scale. Only then can we fully
describe the true heterogeneity of a deposit. I propose to investigate the architectural
controls o f permeability, grain size and facies distribution in shallow marine deposits.
Stratigraphers have been constructing qualitative models o f sedimentary
architecture over the past several decades; however the development of more powerful
computational techniques have made it possible to incorporate detailed sedimentary
characteristics into simulations of fluid flow. Therefore there is a need for detailed
quantitative information on sedimentary structures over several spatial scales.
Hydrologists have led the way in applying geo statistical techniques to granular properties
of sediments, but have often overlooked the stratigraphic order at larger spatial scales.
Geologists have been constructing architectural models on large spatial scales often
times missing the importance of small scale organization. It is essential to bridge the gap
between the large scale studies of geologists and the smaller scale studies of hydrologists
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(Walker 1984; Leeder 1982; Chandler et aL 1989; Davis et aL 1993,1997; Doyle and
Sweet 1995).
Numerical Models o f Physical Heterogeneity. The characteristics of petroleum
reservoirs, such as permeability, porosity and grain size have become vital components
to petroleum production, as have the characteristics o f ground water aquifers for water
resources and pollutant transport. Field studies of Freyberg, 1986, Garabedian et aL
1991, and Davis et aL 1993, have all shown that geological heterogeneity is the dominant
control on the migration and dispersion o f ground water contaminant plumes. Other
studies have been successful in showing that enhanced oil recovery is mainly dependent
on the detailed characterization o f reservoir properties over a range o f spatial scales
(Lake and Carroll 1986; Lake et al. 1991). Numerical models that use governing
equations to solve subsurface fluid flow usually require maps of spatially variable
hydraulic properties. In most studies, the complete three-dimensional structure of
hydraulic properties as well as the geologic structures have not been measured.
Therefore, modelers have incorporated numerous methods to interpolate between the
data points obtained. Koltermann and Gorelick (1996) recognize three basic image
creation techniques in order to get a complete picture of the heterogeneity of an aquifer.
The first group of techniques are structure imitating methods. These methods utilize a
number o f techniques including probabilistic rules, correlated random fields and
deterministic constraints based on facies recognized. Structure imitating techniques also
include sedimentation pattern matching and spatial statistical algorithms. The second
group o f techniques are defined as process imitating methods, and include various
calibration methods for the aquifer model as well as geological process models. The
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third group o f techniques are known as descriptive methods. Descriptive methods
attempt to define zones of hydraulic properties within an aquifer by coupling geologic
observations with one dimensional facies models. The current transport models in use
today do an inadequate job of predicting the small scale heterogeneities that control
pollutant dispersal in aquifers (Cushman 1990; Hess et aL 1992). Therefore, accurate
descriptions o f the local geometry o f sub-units must be conducted because they are
essential in defining flow field boundaries and preferential pathways of solute transport.
Koltermann and Gorelick (1996) have pointed out that models that incorporate three
dimensional surface flow fields, and hybrid methods that can utilize all of the available
geologic, geophysical and hydrological information are missing from the literature.
Determining how the architecture o f a deposit controls the spatial distribution of
permeability and grain size is an important basic sedimentological problem that will
enhance future modeling efforts for amplified oil recovery and solute transport problems
that currently dominate environmental problems o f today and most likely the next
century. Quantification of the stratal architectural controls of aquifer properties will give
solute transport modelers the ability to incorporate “reaT’ sedimentary structures into
their models which will significantly increase the predictive ability of these models.
Modeling solutions that contain this detailed type of sedimentological information wifi be
invaluable to scientists and managers who need to make difficult decisions regarding
various environmental problems.
GRANULOMETRIC PROPERTIES OF SEDIMENTS
General
Sedimentologists are primarily interested in the processes that transport and
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. deposit sediments. As a consequence the sedimentologist often uses granulometric
properties o f the sedimentary body in order to infer how the deposits were formed.
Granulometric properties of a sedimentary deposit are also known as the texture of the
sediment, and may be divided into two general categories, primary characteristics and
secondary characteristics. Primary granulometric properties o f sands are the mineralogy,
grain size, sorting, shape o f particles, roundness, surface texture, and the fabric.
Secondary properties are properties o f the sedimentary body that are dependent upon the
fundamental properties listed above. These properties include porosity, permeability,
saturation and the bulk density (Table 1.1), (Pettijohn et aL 1987; Berg 1986; Miall
1990).
Table 1.1.- Granulometric properties o f sediments
Primary Secondary mineralogy porosity grain size permeability sorting saturation shape bulk density roundness surface texture fabric
Primary Properties
Mineralogy and Fabric. Terrigenous sands are commonly composed of quartz,
feldspars and rock fragments. The matrix which is the finer grained material between the
grains in sandstones typically comprises clay minerals such as kaofinite, Qlite and
montmorillonite. Quartz is the dominant mineral o f most sands and sandstones because
it is the most resistant to both chemical and physical weathering. The cementing material
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that holds the sandstone together is commonly a precipitated overgrowth of silica,
carbonate or iron oxides during early or late stage diagenesis (Folk 1974; Pettijohn et aL
1987; Berg 1986).
Grain Size and Sorting. Grain size and sorting are the most frequently
measured granulometric properties o f sands and sandstones, and are used to infer the
transporting agent, the strength of the transporting agent, and the conditions under
which the deposits were formed. It can also be used to deduce the sediment transport
direction, and for these reasons it is no wonder that there is a tremendous body of
literature on the techniques and interpretations o f grain size analysis. Several methods
are currently used to measure grain size, and include sieving, pipetting, sediment tubes,
microscopy as well as Electrozone and laser particle counters. Geologists classify
particle sizes according to the standardized scheme of Wentworth. Table 1.2 illustrates
the Wentworth scale. Grain size is commonly reported using the phi (
The grain size diameter in phi units is equal to the negative log base 2 of the diameter in
millimeters. Sieving is the most common method for granulometric analysis for fine
sands up through gravels. Pipette analysis is widely used for silts and clays, and for
sandstones, thm section microscopy is the only method accepted. Sedimentation tube
methods gained popularity in the late 1970's and throughout the 1980's because of the
smaller sample sizes required, the speed of the analysis and the idea that settling velocity
is an important hydraulic property o f the sediment as compared to the sieve method.
Recently, the pharmaceutical industry and engineers have led the way in particle size
characterization with new developments in Electrozone and laser diffraction particle
analyzers. These methods are beginning to gain acceptance in the sedimentological
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Table 1.2.- Grain size classification scale (after Wentworth 1922)
Diameter Diameter Class Sediment Rock
(mm) 256 -8 Boulders 64 -6 Cobbles Gravel Conglomerate 4 -2 Pebbles 2 -1 Granules I 0 Very Coarse 05 1 Coarse 0.25 2 Medium Sand Sandstone 0.125 3 Fine 0.062 4 Very Fine 0.031 5 Coarse 0.015 6 Medium sot Siltstone 0.007 7 Fine 0.004 8 Very Fine <0.004 <8 Clay Clay Claysrone community (Folk 1974; Lewis 1984; Anderson and Kurtz 1979; Gibbs 1974; Middleton 1976). Statistical measurements that are derived from granulometric analysis include sorting, skewness and the kurtosis. Many attempts have been made by researchers to use these statistical parameters in discriminating between different depositional environments. These measurements may be estimated using graphical techniques or they may be calculated as moment measurements. Sorting is the measure o f the dispersion around the central tendency, and is therefore the standard deviation o f the grain size distribution. Sorting is considered an important textural property because it is used as an Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8 indication o f the energy level within the depositional environment. Sediments that are classified as well sorted are those in which two-thirds o f the grain size falls within less than one Wentworth grade. Moderately sorted sediments contain sizes that range between one and two Wentworth grades, and poorly sorted sediments range over more than two Wentworth grades. Beach and dune sediments are typically the best sorted, while the poorest sorting tends to be in glacial tills and mudflows. Skewness and kurtosis are the least important of the statistically derived properties from granulometric analysis. Skewness refers to the degree o f asymmetry, and ranges from positive values for a finely skewed sediment to negative values for a coarsely skewed deposit. The kurtosis is a measure o f the peakedness o f the curve, (Folk and Ward 1957; Folk 1973; Lewis 1984; Friedman 1961; Visher 1969; Shepard and Young 1961; Middleton 1976). Shape and Roundness. Shape and roundness are important because they contain information about the modification of grains due to abrasion, chemical weathering and sorting. They may also be important in provenance problems. Shape is defined by varying ratios of a particles three axis, and is expressed as sphericity. Sphericity is defined as the degree to which the three axis of a particle have equal dimensions. Roundness refers to the curvature o f the comers o f the grains. Visual estimates o f sphericity and roundness are often used in sedimentological studies, but do not receive nearly as much attention as grain size or sorting. Surface texture is studied with the aid o f a binocular or polarizing microscope, and more recently the scanning electron microscope. Studies on surface texture often reveal a variety o f microstructures such as fracture patterns and striations which may give clues to the transporting agent (Folk 1973; Lewis 1984; Pettijohn et aL 1987). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The fabric of the sediment body refers to the spatial arrangement and orientation of the grains that make up the sediment body, and is dependent on the transporting agent, grain size, shape and roundness. There have not been many studies on grain fabric because o f the difficulty in quantifying this property (Folk 1974; Pettijohn et aL 1987). Secondary Properties Porosity. Porosity is defined as the percent of void space that occurs between or within the individual grains o f a sediment body. Porosity can be classified into four general types, intergranular, intragranular, fracture and solution porosity. Intergranular porosity is defined as the percent of voids between individual grains. Intragranular porosity is the percentage o f voids within the grains. Fracture porosity may be micro or macro and solution porosity is a result of the solution of the cementing material. Solution porosity is commonly known as secondary porosity. Total porosity is simply the measure o f all o f the void spaces whereas effective porosity is a measure o f just the interconnected void spaces. Effective porosity is usually measured instead o f total porosity because it a more meaningful measurement for the flow of fluids. Porosity is typically measured in the laboratory and expressed as percent o f bulk volume. P=(Vp/Vb)lQO=(Vb-Vm)lOO/Vb In equation 1-1, P is the porosity, Vb is the bulk volume, Vp is the pore space volume and Vm is the mineral volume (Berg 1986; Pettijohn et aL 1972; Fetter 1988). Studies have shown that for natural sediments, porosity is a function of grain Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10 size, sorting, shape, fabric and the amount of cementing material. The packing of sedimentary grains contributes significantly to the fabric of the sand body, and is believed to be the most important factor controlling porosity. Cubic packing has the loosest arrangement of grains, and therefore the highest porosity. At the other end of the spectrum is rhombohedral packing which has the tightest arrangement and therefore theoretically the lowest porosity (Morrow et aL 1969; Rodgers and Head 1961; Thickell and Hiatt 1938; Fraser 1935). Permeability. The capacity o f a sediment body to transmit a fluid is known as the permeability. Permeability is dependent upon the connected voids within the sediment body, and many researchers believe that it is also a function of grain size, shape, sorting and porosity. In Darcy’s (1856) classic paper, he showed that the rate of flow through a porous medium such as sand is directly proportional to the head loss and inversely proportional to the length o f the sand column. Q--KA{hl -h2)/L (1' 2) Q in equation 1-2 is the volume rate o f flow, K is known as the constant o f proportionality, A is the cross sectional area and the difference between the heights of the water (hi and 2) is the head loss. Permeability is usually expressed in terms o f volume flux, and equation 1-3 can be written in the more familiar form known as Darcy’s Law. V-Q/A - -K(dh/dL) ( l' 3) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 11 K is known as the constant o f proportionality or hydraulic conductivity, V is the volume flux and dh/dL is the head loss per unit length in the above equation. The Darcy is the unit of choice for hydrogeologists and engineers and is defined as: Darcy=(Q/A)(\x)(dL/dp){ 1.0133.H 06) (1-4) In this definition, Q/A is the flow volume per unit area, p. is the viscosity, dL/dp is the pressure gradient and the last part is a conversion factor (Fetter 1988; Berg 1986; Fraser 1935). It is important to distinguish permeability from hydraulic conductivity. Permeability is an intrinsic property of a porous medium. Unlike hydraulic conductivity it does not depend on the properties of the particular fluid. Hydraulic conductivity does depend on the fluid properties. Therefore the hydraulic conductivity is specific to the particular fluid and takes into account the density and viscosity of the fluid at standard temperature and pressure. Typical unites for hydraulic conductivity are meters/day. Permeability and Grain Size. There have been numerous attempts to correlate permeability to grain size over the past several decades and several empirical equations have been developed by both engineers and geologists. The reasoning behind the attempts to correlate grain size and permeability stems from studies that have shown that have shown a fourfold increase in pore throat area occurs when there is a doubling in the diameter of particles (Fraser 1935). This realization has lead to the very familiar empirical relationship used to calculate hydraulic conductivity from grain size. K=cd2 (1-5) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12 K is the hydraulic conductivity, d is the diameter o f the particles and c is a dimensionless constant. Krumbein and Monk (1943) developed an empirical equation that relates grain size and sorting to permeability. K = cd2e ,33° (1-6) The diameter in equation 1-6 is measured as the geometric mean diameter, c is a constant and a is the sorting (Russel and Shepherd 1990; Pettijohn et aL 1986; Potter and Mast 1962; Mast and Potter 1962). In a widely cited study by Beard and Weyl (1973), artificial mixtures o f sands were used to relate permeability and porosity to grain size and sorting. They concluded that permeability decreased with decreasing grain size and that porosity increased with sorting. Pryor (1973) took 922 samples of porosity and permeability from various depositional environments including river bars, dune and beach environments and related them to grain size, sorting and sedimentary structure. The results indicated that permeability increased with sorting, and porosity increased with grain size for river bar sands only. Also, the results suggest that there are greater variations o f grain size and permeability within bedding than between, and that depositional processes have a strong affect on porosity and permeability distributions (Fig. 1.1). Byers and Stephens (1983) conducted a statistical analysis of hydraulic conductivity and particle size in a fluvial sand. They concluded that the strongest correlation between hydraulic conductivity and grain size is that o f the log o f hydraulic conductivity and the effective grain size d,0 (10% finer particle size). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 13 Permeability Boundary Fig. 1.1.- Permeability trends in a cross-bedded sand, showing the influences of sedimentary structure on fluid flow (after Pryor 1973). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 14 They also suggest that grain size and hydraulic conductivity contain different spatial correlation structures in the vertical plane. According to Byers and Stephens, the grain size pattern is more structured than hydraulic conductivity and follows the observed stratigraphy. However, the hydraulic conductivity was best modeled as a simple random variable. Several problems exist with this study. First, when comparing the geometric mean grain size and effective grain size, coefficients o f correlation (R2) are not reported; however when calculated they reveal no significant difference between them. This means that it does not matter whether one uses effective grain size or mean grain size, they are both equally poor in predicting permeability from empirical equations. Also, a hierarchy of sedimentary structures was not used to interpret the hydraulic conductivity structure. Recently, Panda and Lake (1995) attempted to improve permeability predictions by incorporating the entire particle size distribution. Table 1.3 shows the relative effects primary granulometric properties have on secondary properties. Although several studies have been conducted on this subject, clearly there is a need for more work in this field. LEVELS OF STRATIGRAPHIC ANALYSIS General As stated earlier, one of the primary objectives of the stratigrapher is to describe and interpret the three dimensional nature of stratigraphic organization o f the sedimentary basin fill, which is referred to as the architecture o f the sedimentary body. Small scale to mesoscale architecture is largely a function o f subsidence, sea level and the sedimentary dynamic processes that govern the formation o f depositional environments and depositional systems. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 15 Table 1.3.- Relative affects o fprimary granulometric properties on secondary properties (after Pettijohn et al. 1986) Primary Properties Secondary Properties grain size Permeability decreases with grain size, porosity maybe unchanged, or may decrease sorting As sorting gets poorer, permeability and porosity decrease fabric Permeability and porosity decrease with tighter packing, permeability may follow bedding structures cement permeability and porosity decrease with increasing cement At this level of stratigraphic organization, sedimentary properties are measured on scales o f millimeters to tens o f meters. Meso scale to large scale architecture usually involves the sub-disciplines o f lithostatigraphy, chrostratigraphy and biostratigraphy. The principal objective on the large scale is the reconstruction of major depositional sequences, and often employ the use of seismic sections and the application of sequence stratigraphic concepts (Miall 1990; Walker 1984; Leeder 1982). Small Scale Architecture General. For several decades sedimentologists have known that sandstones may be sub-divided into genetically related strata by an hierarchically ordered set o f bedding contacts (Allen 1963). Strata may be horizontally deposited, or they may be formed as cross strata. Cross strata are defined as being compositionally or texturally distinct layers that are more or less steeply inclined to the principal bedding axis. Most cross strata are due to the movement of ripples and dunes. Strata that are horizontally or consist of low angle parallel lamina have bedding planes that are flat. Flat or parallel bedding usually occurs in medium to fine grained sand, and may be rich in mica. Lamina in flat beds are Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. often only a few grain diameters thick making it difficult to measure individual lamina thicknesses. In medium to fine grained sands and sandstones that have relatively little mica, parallel or horizontal laminations are indicative of upper flow regime conditions. Parallel laminations may also form under lower flow regime conditions if the critical velocity for ripple formation has not been reached. Fig. 1.2 illustrates the resultant sub aqueous bedforms with varying grain diameter and stream power (Allen 1964,1970; Jopling 1962; McBride et aL 1975; Bridge 1978; Co Hinson and Thompson 1982). The first detailed account of cross bedding was conducted by HaH (1843), who used the term “diagonal bedding”. Sorby (1859), showed that cross strata could arise from Gilbert- type delta building through flume experiments. He called this type of bedding “drift bedding”. Sorby also described a smaller scale o f cross strata that he called ripple drift, and showed that these structures formed as result o f net deposition occurring with current ripple migration. Small Scale Architecture: McKee and Weir (1953). McKee and Weir's (1953) classification of stratification and cross stratification is the first attempt to categorize stratigraphic organization, and starts by recognizing three basic groups o f terms that should be applied to sedimentary deposits. The first group contains qualitative terms such as stratum and cross stratum. These terms emphasize the attitude and relation o f rock units without any implication of scale. The second group refers to quantitative terms that are related to the thickness of stratification. These terms include thick- bedded, thin-bedded and laminated- The third basic group also relates to quantitative terms, however, this group is concerned with the thickness of splitting within stratified units. These terms include massive, slabby and flaggy. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced Stream Power ( ergs/cm A2/sec) 20,000 10,000 2.000 4.000 g,000 1,000 6,000 400 200 60 80 40 100 stream power and grain diameter (after Allen 1963). Allen (after diameter grain and power stream Fig. 1.2.- Sub-aqueous bedforms produced as a result o f f increasing o result a as produced bedforms Sub-aqueous 1.2.- Fig. 0 .2 0 .4 O .6 0 .8 0 .1 .09 .08 .07 .06 .OS .04 .03 .02 .01 Cross-Lamina Ripples Plane Bed Plane Jm No Sediment Movement NoSediment X c ) (cm D X Cross-Bedding Dunes Upper Flow Regime Flow Upper Lower Flow Regime Flow Lower Plane Bed Plane 17 18 These three groups of terms are a good way to begin describing the nature of stratified sedimentary rocks. Stratification is the first term to be described in the qualitative term group. This term is used to describe layering in sedimentary deposits. A stratum is defined as the basic unit or single layer o f homogenous or gradational Iithology, and a scale is not implied. McKee and Weir (1953) point out that this term is not synonymous with the terms of bed or lamina because these terms imply a scale. Cross stratification refers to layers deposited at one or more angles to the dip of the formation. A group of strata that are genetically related constitutes a set. Strata within a set are separated by erosional surfaces, or by an abrupt change in character such as Iithology. A group o f two or more sets is designated as a coset, a group that is composed of strata and cross-strata is known as a composite set. This is a large sedimentary unit that has a constant or gradational Iithology (Fig. 1.3), (McKee and Weir 1953). The quantitative terms are important because they imply a scale to be used. The term bed is reserved for any sedimentary stratum that is greater than 1 cm. thick. Lamina refers to stratum that are 1 cm. or less in thickness. Therefore, a cross-bedded deposit is a single unit containing homogeneous or gradational Iithology deposited at an angle to the original dip and greater than 1 cm thick (Table 1.4). This classification sets up specific limits for the terms thick-bedded and thin-bedded. Table 1.4 also shows the relationship of the splitting properties. McKee and Weir (1953) also proposed a general classification for cross stratified units based on seven criteria. The criteria used are: (1) The character of the lower bounding surface, (2) The shape of the cross strata set, (3) The cross strata set axis Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 19 Fig. 1.3.- Diagram illustrating the terminology used to define stratification (after Allen 1984). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 20 Table 1.4.- Comparison o f quantitative terms used to describe stratification (after McKee and Weir 1953) Stratification Cross Thickness Splitting Terms Stratification Property Terms Terms Very thick- Very thickly cross bedded cross beds Greater than 120 Massive cm. Thick-bedded Thickly cross bedded 120 cm to 60 cm Blocky Thin-bedded Thinly cross bedded 60 cm to 5 cm. Slabby Very thin- Very thinly cross bedded 5 cm to 1 cm Flaggy bedded f jmnmfwj cross laminated Cross lamina 1 cm to 2 mm. Shaiy (sthstooe) Platy (sandstone) Thinly- Thinly cross laminated 2 mm o r less Papery laminated attitude, (4) Axis symmetry of the cross strata, (5) The arching of the cross strata, (6) Cross strata dip and (7) Individual cross strata length (Table 1.5). From these seven criteria, three major types of cross-stratification can be recognized (Fig. 1.4). Type 1 is referred to as a simple set of cross strata. This deposit is called a simple set because the lower bounding surface is a surface o f non deposition instead of an erosional surface. A simple set is formed by deposition alone. A planar set o f cross strata makes up the second type of cross-stratification, and has a lower bounding surface which is a planar surface o f erosion. This deposit is formed from beveling and subsequent deposition. The third type of cross-stratification is call a trough set. This deposit results from channeling and subsequent deposition. In this classification system, the basic criterion that determines the type o f cross strata is the nature o f the lower bounding surface. Classification o f Cross-Stratification. Allen (1963) proposed a descriptive classification for cross-stratified sediments based on six elements that are similar to the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 21 McKee and Weir classification. Allen made a refinement to this classification in order to incorporate all of the known kinds of structures. A second goal of this paper was to give possible origins for the known types of cross-stratification. Table 1.5. - Classification o f cross-stratified units (after McKee and Weir 1953) Primary Secondary Attributes Attributes Bounding Set shape Axis Cross-strata Cross-strata Cross- Cross-strata Cross- surface of cross- attitude of symmetry arching strata dip length strata strata set cross-strata type Nonerosional Lenticular Plunging Symmetric Concave High angle Small scale Simple surfaces (>20 (< 1 foot) degrees) Planar surfaces Tabular Noo- Asymmetric Straight Medium Planar o f erosion pfunging scale (I to 20 feet) Curved surfaces Wedge- Convex Low angle Large scale Trough o ferosion shaped (<20 (> 20 feet) degrees) Allen's basic criticism ofMcKee and Weir’s (1953) work was that it did not include cross-stratification associated with small scale ripple marks or the possibility that some sets or cosets may occur as solitary units. Allen recognized that some sets occur alone with deposits of different structures. Solitary sets are fundamentally different from a group o f genetically related cross-stratified sets. Solitary sets in marine deposits have been interpreted to form as the result o f the construction of isolated shallow banks. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 22 Simple cross-stratification The lower bounding surfaces o f Sets are non-erosional surfaces. Planar cross-stratification The lower bounding surfaces of Sets are planar surfaces of erosion. Trough cross-stratification The lower bounding surfaces o f Sets are curved surfaces of erosion. Fig. 1.4.- Diagram illustrating the classification of cross-stratification (after McKee and Weir 1953). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 23 In this classification system, the lower bounding surface is considered important, but the grouping property and the magnitude o f the cross-stratified sets are considered more important. This scheme uses six primary criteria for classifying cross-strata. The first criteria is the degree of grouping o f the set. The cross-stratified unit may be solitary or grouped to form a coset. A cross-stratified unit is considered a solitary set if it is composed of a single set of cross-strata, bounded by non-cross-stratified deposits, or by different cross-stratified units. The scale of the set thickness, is the second criteria. Cosets that contain sets that are mainly less than 5 cm. thick are classified as small-scale cross-stratified units. The third most important criteria is the character o f the lower bounding surface. The bounding surface may be erosional or non-erosional in nature. The bounding surface may also be gradationaL Number four in this classification is the shape o f the lower bounding surface. The fifth criteria deals with the angular relation between the cross strata in a set and the lower bounding surface. The last characteristic used is the degree of litho logical uniformity. Fig. 1.5 illustrates the descriptive terms used in Allen's classification o f Set scale, Set grouping, the Cross-strata base relationship and Cross-strata texture. Fig. 1.6 illustrates Cross-strata shape and the shape o f the lower bounding surface. Using these six criteria, fifteen different types o f cross stratification have been recognized (Table 1.6) (Allen 1963). Campbell (1967) modified the McKee and Weir (1953) classification because he believed that the former classification system was inadequate for quantitative descriptions of stratigraphic organization Campbell sets up four component layers o f a sedimentary body. These layers are from smallest to largest, lamina, Iammasets, beds, and bedsets. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 24 Cross-Strata Set Set Grouping Scale (Thickness) Small scale Large scale Solitary Grouped (<0.04m thick) (X).04m thick) Cross-Strata; Base Relationship Cross-Strata Texture Concordant Discordant Homogeneous Heterogeneous Fig. 1.5.- Diagram illustrating cross-strata set scale, set grouping, base relationship (after Allen 1963, 1984). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 25 Cross-Strata Shape Rolling Shape o f Lower Bounding Surface Sharp regular Sharp Irregular Planar/Tabular Curved Cylindrical Scoop Trough Gradational Fig. 1.6.- Classification of cross-strata shape and lower bounding surface shape (after Allen 1963, 1984). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 26 The four layers are genetically similar, but differ in areal extent and the time interval under which they were formed. In this classification system, lamina are the smallest observable structure within the sedimentary body. A lamina set is a group of individual lamina that are conformable and form a distinct structure within a bed. According to Campbell, the bed reveals the principal layering, and is therefore the basic building block of the sedimentary body. A bedset contains a number of superimposed genetically related beds.The main difference between the McKee and Weir classification system and that o f Campbell’s, is that Campbell does not impose a limit on bed thickness unlike the greater than one centimeter limit that McKee and Weir use. In Campbell’s classification system, beds may be composed of lamina sets. This classification system differs from other hierarchical systems that are less widely used in that it does not force adjacent beds to be different lithologically, and the bed does not have to be composed of a homogeneous Iithology. Table 1.7 shows a comparison between McKee and Weir’s terminology and that of Campbell’s (Campbell 1967; McBride 1962; Bridge 1993). Mesoscale Architecture (Facies and Facies Models) Meso scale architecture refers to the study of textures and sedimentary structures on the scale o f outcrops and well sections. This usually involves defining sedimentary facies and constructing one dimensional vertical facies assemblages and facies models. In 1669, Steno introduced the concept o f facies, in which he defined facies as “the characteristics o f part of the Earth’s surface during a particular interval o f time” (Teichert 1958). Grossly (1838) introduced the modem usage of the facies term by defining it as the complete attributes of a stratigraphic unit including both paleontological and litho logical characteristics. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 27 Table 1.6.- Types o f cross-stratification, grouped by lower bounding surface shape, grouping scale and formation processes (after Allen 1984) Set Scale Set Grouping Lower Bounding Process Cross- Surface Shape Strata Types Large Scale Solitary Planar or irregular Due to migration of Alpha. Bela, solitary banks, sub- Gamma, Epsilon aerial or sob- and Xi aqueous, containing curving or linear fronts Large Scale Solitary Cylindrical, sooop shaped or Bade filled Zeta, Eta, Them, shaped hollows due to and Iota cutting and fiUing o f isolated channels, pits or hollows. Cutting and filling may not be simultaneous Small or Large Grouped Various Due to the A. Small Scale; migration of Kappa, Lambda, different sized Mu and Nu ripple trams B. Large Scale: Omikron and Pi Table 1.7.- Comparison ofstratigraphic organization terminology o f the McKee and Weir system vs. Campbell’s terminology __ McKee and Weir (1953) Campbell (1967) ______ lamina or bed lamina bfnin^ set set (lamina or bed) bed coset bedset composite set Walker (1984), suggests that the spatial relationships of rock volumes and their internal characteristics must be compared to other modem well studied stratigraphic units in order to properly identify facies. The reason for this is that it is generally assumed that a facies designation will eventually be given an environmental interpretation. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 28 Facies architecture is a term commonly used for mesoscale to large scale architectural studies. Most facies architectural techniques involve the construction o f vertical facies assemblages and eventually facies models. A facies assemblage is defined as the total attributes of a sedimentary body. This includes the geometry, areal extent, continuity o f the litho logic units, rock types, fossils and sedimentary structures o f the sedimentary body (Potter 1959; Miall 1990). A facies model is the depositional environmental interpretation of the facies assemblage. Litho facies tend to organize into depositional systems. A depositional system is defined as an assemblage of process related facies (Fisher and McGowen 1967; Swift et al. 1991). The construction o f facies assemblages and facies models relies heavily on the application o f Walther’s Law. Walther’s Law states that facies found in a vertical sequence were formed adjacent to one another (Walker 1984; Miall 1990). This concept has great implications for stratigraphers, because it implies that lateral facies relationships can be predicted by investigating vertical facies successions. Walker (1984) states that any facies model must fulfill three functions. First, the model must be the generalized case for a particular depositional environment. Therefore, the model is to be used as a comparative tool for local examples. The second function of a facies model is that it must set up a framework to be used with future observations, and the third function is that it must act as a predictor under newly encountered situations. Fig. 1.7 is an example of a classic facies model, the Bouma sequence (Walker 1984). Vertical Architectural Patterns. Vertical architectural patterns within sets and co sets are thought to be the result of changing textural properties. Sets or cosets can be homogeneous or heterogeneous with respect to textural properties and can create Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 29 recognizable patterns such as the above Bouma sequence. Visher (1965) described systematic vertical variations of grain size within and between sedimentary structures of fluvial origin in the Missourian of Oklahoma. Visher’s vertical depositional pattern consists o f a basal unit containing trough cross bedding, followed by a laminated sand zone. Above the laminated zone is a unit that is composed o f fine grained symmetrical ripples. The top unit is a laminated clay and fine grained sand zone. This depositional sequence has been recognized by Visher in both recent and ancient fluvial deposits. In this vertical sequence, the mean and maximum grain size decreased upwards within cosets as well as between cosets. The sorting also becomes poorer as you move up the sequence. Visher interpreted this textural trend within the sequence as being the result of an upward decrease in energy. Allen (1984) reports that field observations have illustrated the vertical patterns of grain size in cross laminated cosets. Fig. 1.8 shows Allen’s summary o f the recognized patterns of vertical grain size variations that have been reported. In this summary, letters A, B, and S refer to specific types of climbing ripple or ripple drift cross lamina sets. Type A ripple drift cross lamination consists o f climbing sets o f lee side lamina. The stoss side is not preserved at all, and the preserved lee side lamina may be either concave up or sigmoidal in shape. Type B ripple drift cross lamina is recognized by climbing sets of lee side lamina and complete preservation o f the stoss side lamina. Stoss side lamina are relatively thick. Co sets o f type B, usually do not contain graded bedding. Type S, refers to sinusoidal ripples, and the stoss side is usually equal in thickness to the lee side (Jopling et al. 1968; Allen 1973b). Parallel lamination is represented by the P in Fig. 1.8 and D is the grain size diameter. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 30 E(h) Hemipefagic mud E(t) Tarbidite mod (D) Interlaminations of silt and day C Rippled Bed B Upper Flat Bed Sandy parallel laminations Rapid deposition, Quick bed ? • > s • , • '**. .1 • »,. • Massive or gradded bed* Fig. 1.7.- The complete turbidite (after Walker 1984). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 31 Stratification Sequence Gram Size Profiles Pattern t Pattern 3 t e s t ”t a me* Pattern 4 r 7 r r r E&33S A w !?*» Kara R^e r 3 * -=~=_ A aa 1 i L Fig. 1.8.- Vertical patterns of stratification and their related grain size patterns (after Allen 1984). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 32 Pattern 1 has been recognized in the field by several researchers, (Sorby 1908; McKee 1965; McKee et al. 1967; Coleman 1969) and shows a vertical sequence of structures that grade from parallel lamina through type A and B cross lamina into S typecross lamination. This type of vertical sequence of structures is usually found in fluvial sediments, although some have been reported in glacial meltwater and turbidite deposits. The grain size typically decreases vertically within and between cosets of this sequence. Allen (1972b), reports that although it is rare to find a coarsening upward o f mean grain size in pattern I sequences, they exist in the Uppsala Esker. Allen (1984), states that pattern 2 is a special geometrical condition in which the angle o f climb is uniform vertically. There is typically no vertical variation o f grain size within and between cosets in this pattern. R.G. Walker in 1963 reported a type C cross lamination in which the angle o f climb within cosets remained constant in muddy sand and silty deposits. In this case, the mean grain size decreased upwards. Pattern 2 is usually representative of turbidite, fluvial or deltaic facies. Jopling and Walker 1968 described vertical grain size distributions in cosets illustrated by pattern 3. In this case, grain size typically increases within and between cosets as you move upwards in the sequence. Pattern 3 cycles are quite infrequent and are usually found only in glacial lake deltas (Allen 1984). Pattern 4 illustrates repetitive cosets of various cross lamination types. This pattern of cross lamina cosets usually consist of an upward fining o f the grain size, and has been recognized from turbidite facies by Sorby (1908), and in the Uppsala Esker by Allen (1972). In rare cases, an upward coarsening o f grain size has been recorded (Allen 1984). All o f these previous studies on vertical trends in grain size are good preliminary attempts to understand the relationship between stratal architecture and grain Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 33 size variations, but much more work must be done in order to understand the full spatial significance and relationship to grain size and permeability over several scales. Facies models have been used by stratigraphers for quite some time, and they have been very useful for the description of clastic environments but they are not adequate for understanding large scale architecture (depositional sequences) or small scale heterogeneities (Miall 1990; Bridge 1993). In order to folly understand the three dimensional nature o f sedimentary bodies, we need to break free o f one dimensional vertical models. Hierarchy o f Bounding Surfaces. In the previous section I explained that a sedimentary body could be divided into a hierarchy of genetically related strata by bedding contacts, and that McKee and Weir followed by Campbell were the first to formalize classification systems. Brookfield (1977) showed that a four order bedform hierarchy could be erected for aeolian deposits. The hierarchical bedform order of Brookfield consists of impact ripples, aerodynamic ripples, dunes and draas. This hierarchy of bedfbrms are separated by three internal bounding surfaces (Fig. 1.9). First order surfaces are laterally extensive and are either convex up or flat lying bedding planes that separate draas. Bounding sets of cross strata are second order surfaces. Second order surfaces are analogous to McKee and Weir’s set designation. Third order surfaces bind bundles of lamina in cross strata sets and are designated as reactivation surfaces. This surface is probably analogous to Campbell’s bminasets. Allen (1983) made the first attempt to formalize a hierarchy of bounding surfaces for fluvial deposits. He also recognized three major bounding surfaces, but reversed the numbering order o f Brookfield so that an opened ended numbering scheme was Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 34 Third Order Cross-strata set bounding surfaces Fig. 1.9.- Hierarchy o f bounding surfaces (after Brookfield 1977). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 35 developed. In Allen's classification of bounding surfaces, first order surfaces bound individual sets o f McKee and Weir. Second order surfaces are analogous to the coset designation o f McKee and Weir, however they contain more than one lithofacies type. Third order surfaces are laterally extensive. Miall (1988) expanded Allen's work to incorporate the basin scale heterogeneity. In doing this, a six fold hierarchy was created for fluvial sediments. The six fold hierarchy o f Miall is illustrated in Fig. 1.10. From this classification system, Miall forwarded the idea of architectural elements, which has gained wide spread use in recent years. An architectural element is defined as Iithosome characterized by geometry, facies and scale. The implication of the architectural element is that it represents the depositional product o f sedimentary processes (Miall 1985, 1988). Fig. 1.11 illustrates the basic architectural elements defined by Miall in fluvial deposits. In this classification system, first order surfaces are equivalent to Allen’s set boundaries. The coset, as defined by McKee and Weir are bound by second order surfaces in this system. Third order surfaces represent growth increments of macroforms such as point bars or sand flats, and fourth order surfaces bound Miall’s architectural elements. Fifth order surfaces are those that bound major sand sheets (channel fill complexes), and six order surfaces bound channel groups or paleovalleys. The architectural elements ofMiall clearly represents either facies or facies assemblages, and this classification system has been extended to include large scale architecture. Large Scale Architecture (Depositional Sequences) Large scale architecture refers to the geometric relationships o f sediment bodies at the basin scale. The concepts of sequence stratigraphy have been the most useful in recent years in describing basin wide architecture. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 36 W-K)*m -IO, -IO * km B. flot CH bar OA LA 10-3000m- Fig. 1.10.- Six fold hierarchy of bounding surfaces for fluvial deposits. A to E represents successive enlargements of fluvial unit showing the rank of bounding surfaces indicated by the circled numbers (after Miall 1985). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 37 CH Channel LA Lateral Accretion SG Sediment Gravity Flow GB Gravel Bar and Bedform SB Sand Bedform DA Downstream Accretion LS Laminated Sand OF Overbank Fines Fig. 1.11.- Fluvial architectural elements (after Miall 1985). Reproduced with permission of the copyright owner Further reproduction prohibited without permission. 38 Sequence stratigraphy is defined as the study o f the geometric relationship o f repetitive, genetically related strata bounded by surfaces o f erosion or non-deposition, or their correlative conformities, put within a chronostratigraphic framework (Van Wagoner et aL 1988). The basic unit of sequence stratigraphy is the depositional sequence. A sequence is recognized as genetically related strata that are bounded by unconformities and their correlative conformities. Each sequence can be sub-divided in smaller units known as system tracts (Mitchum 1977). System tracts are recognized by their position and stacking patterns within the sequence and are composed o f parasequences. Parasequences are defined as a succession of conformable genetically related strata that are bounded by marine flooding surfaces and their correlative surfaces (Van Wagoner 1985; Van Wagoner et aL 1988; Allen and Allen 1990). Marine flooding surfaces are surfaces that represent abrupt changes in water depth and are used to separate older strata from younger strata (Van Wagoner et aL 1988). Parasequences may be grouped into parasequence sets, which are defined as genetically related parasequences. Parasequence sets have been recognized as forming distinctive stacking patterns that are often bounded by marine flooding surfaces (Van Wagoner 1985). Correlating and mapping of sedimentary rocks using this nomenclature, is accomplished by defining the boundaries between sequences, parasequences, and parasequence sets. It is believed that rates of subsidence, eustacy and sediment supply all contribute to the formation of sequences and their stratal components (Fig. 1.12), (Van Wagoner et aL 1988). In 1977, Peter Vail and colleagues from Exxon constructed a chart o f relative sea level versus time. This chart is known in the literature as the Vail curve, and was constructed by using seismic reflection techniques. The limits of onlap and toplap within Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 39 coastal facies of marine sequences as recorded by seismic refection methods are thought to be the best indicators of relative sea level fluctuations. Coastal onlap is considered to be indicative of a relative rise in sea level, whereas coastal toplap is indicative o f a standstill of relative sea level. A relative fell in sea level is represented by a downward shift in coastal onlap. Fig. 1.13 illustrates the geometric relationships of onlap and toplap in relation to relative sea level fall, rise or standstill (Vail et al 1977; Allen and Allen 1990). Stratal architectural models utilizing sequence stratigraphic concepts have been used extensively in order to predict reservoir facies in deep water environments. Self and colleagues (1993) investigated the usefulness o f sequence stratigraphic models in predicting reservoir facies of the Plio-Pleistocene in the Gulf of Mexico. They concluded that current sequence stratigraphic models are too simplistic, and fail to incorporate complex forcing mechanisms other than eustatic sea level fluctuations. Therefore, Self argues that the predicted lithology is often inaccurate when compared to the actual lithology recovered in wells. The authors suggest using an empirical approach which incorporates the correlation of oxygen isotope data and fbraminiferal analysis to sequence boundaries. This study demonstrates the need for a different approach to successfully predict lithology. This approach may work for large scale basin wide architecture, but would not work for the small scale heterogeneity that is often encountered in aquifers. Architectural Classification used in this Study Facies modeling has been the method o f choice for most stratigraphic organization studies and has had some success at describing sedimentary environments. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 40 V///A 7 / / / A btised Valey Fig. 1.12. - Features o f a sequence and it's associated system tracts, boundaries within systems traces are parasequences. HST is high stand systems tract, LST is low stand system tract, TST is transgressrve systems tract, SB1 is type 1 sequence boundary and mfs is maximum flooding surface (after Vail 1987). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 41 (a) RELATIVE RISE (c) GHAOOAL RELATIVE FALL Terrigenous influx Terrigenous influx Coastal Erosional truncation Relafive " v w w a p Rnall la*of sea level encroachment Iniial depositional Chronostrahgrapluc surface surfaces (b) R&AT1VE ST1LLSTAND (d) RAPID RELATIVE FALL Terrigenous M ux Terrigenous Mux — Toplap Underlying unconformity Relative stflbtand Surface associated wMi basinvrard shat Scale If-Y-j Non-marine coastal deposts Tens to thousands of km | | Littoral deposts KH1 Marine deposits Fig. 1.13 - Stratigraphic consequences of eustatic sea level changes (after Vail et al. 1979). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 42 However, one dimensional vertical models are inadequate for the understanding of sedimentary heterogeneity. In an important study conducted by Liu et al. 1996, several permeability and porosity measurements were made on the Triassic Hawkesbury Sandstone in Sydney, Australia. Sedimentological and geo statistical approaches were utilized in order to characterize the horizontal and vertical permeability and porosity variations in braided river depositional systems. The results o f this study revealed that there was a high degree o f variability within the permeability data, and that this variability is not consistent with fractal models based on a Gaussian Normal probability distribution. The authors also discovered that when they sub-divided the sandstone into genetically related sedimentary facies, the predictability o f the permeability distribution was significantly improved. Although Liu has successfully shown that facies analysis greatly increases the ability to predict hydraulic properties, even leading edge facies analysis could stand a significant improvement. Sequence stratigraphic methods have also been used extensively, but this approach is only reasonable on the basin scale, for it also neglects small scale heterogeneity which may be important to secondary textural properties. Architectural elements and numbering o f bounding surfaces are the latest approaches to understanding stratigraphic organization. Numerous studies have been published attempting to relate secondary textural properties to these elements or bounding surfaces. Davis et al. (1997) attempted to relate fluvial bounding surfaces and the permeability correlation structure in outcrops o f the Sierra Ladrones Formation, Albuquerque Basin, New Mexico. The authors concluded that the results suggest that fluvial bounding surfaces provide a geological basis for modeling heterogeneity in Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 43 alluvial deposits. Both of these studies are an excellent start in the understanding of permeability correlation structure and how it relates to geologic structures; however neither of these studies incorporated ideas from Bridge’s (1993) review paper. In his review paper, Bridge (1993) critiques several current methods used to describe and classify sedimentary deposits o f fluvial origin. Bridge argues that the practice of numerically ordering bounding surfaces rather than the strata themselves is often difficult to apply uniformly. He also points out that architectural elements or lithofacies codings are not mutually exclusive, and tend to either be misleading or incorrect. Bridge also states that the use of one dimensional vertical sequences o f litho facies is obsolete, and stresses that a simple classification based on easily measured parameters should be used. I agree with Bridge’s comments on these methods, and therefore suggest that the simple classification of McKee and Weir (1953) be used and extended to the larger stratigraphic scales. In the stratal architecture classification system that I am proposing to use, individual strata (lamina or beds) organize to form sets o f strata, and these sets o f strata organize to form cosets of strata. The coset is the largest category in the McKee and Weir classification system and can vary significantly in sedimentary structures and lithology. Therefore, the term coset overlaps and is analogous to the smallest facies category, that o f facies volume. On larger stratigraphic scales, facies may organize into depositional systems. Depositional systems may consist o f fining upward or coarsening upward facies successions, that rest on or are capped by a source diastem (Swift et a l 1991). Therefore, the depositional system overlaps with the concept o f a parasequence as defined by sequence stratigraphic nomenclature. Depositional systems may further organize into a set o f depositional systems, which is analogous to a sequence, the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 44 fundamental unit o f sequence stratigraphy. It is important to keep in mind that facies and depositional systems are usually autocyclic in nature, while conventional sequence stratigraphic concepts are generally thought to be allocyclic in nature. Table 1.8 illustrates the relationship between successive stratigraphic organization terms. Table 1.8.- Scales o fstratigraphic organization used in this study Stratal (small scale) Facies (mesoscale) Sequence (large scale) cross-stratum cross-strata set cross-strata coset fades depositional system parasequence depositional sequence THE STUDY AREA General Geology of the Eastern Shore The Deknarva Peninsula is part of the Middle Atlantic coastal plain bordered on the west by the Chesapeake Bay and on the east by the Delaware Bay and Atlantic Ocean (Fig. 1.14). The Oyster site is situated on the Iagoonal side o f Virginia’s Eastern Shore landward of the outer barrier island chain. In this area, the coastal plain deposits consist of unconsolidated sediments o f Cenozoic age ranging from 65 million years old to the present. The Upper Pleistocene deposits are composed of gravel, sand and clay formed in marginal marine and estuarine environments during high stands o f sea level (Mixon 1985; Schiedler et aL 1984). The Quaternary was dominated by periods of cyclic growth and retreat o f the polar ice caps, with a period o f approximately 100,000 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 45 38 00' 3745’ 37 30* North 3715* Accomack Member 10 km Butlers Bluff Member 37 00’ 7615’ 76 00’ 7545' 75 30' 7515* Fig. 1.14.- The Eastern Shore o f Virginia, showing the positions o f the Accomack and Butlers Bluff Members. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 46 years. Each ice advance caused sea level to drop about 125 m, and the architecture of the Upper Pleistocene deposits exhibits this pattern. Periods of low stand followed by inter glacial high stands o f sea level resulted in the formation o f a coastwise stepped topography known as terraces. These terraces, which step down towards both the Atlantic Ocean and the Chesapeake Bay, are separated by low tying linear scarps. The scarps (Mappsburg and Cheriton), have been interpreted to be ancient shorelines of marine and estuarine origin (Colquhoun et aL 1991; Mixon 1985). The Chesapeake Bay, the largest estuary in North America, was formed by the drowning o f the lower Susquehanna River during the post glacial sea level rise, amplified by lithospheric subsidence. The modem day configuration of the Bay developed over the past two sea level cycles (Mixon 1985). At approximately 240,000 yrs. BP., the Accomack Spit, precursor of the Eastern Shore Peninsula, built seaward across the mouth of an ancestral Chesapeake Bay during a time when sea level was twenty meters higher than at present. During the 240,000 year high stand, a barrier spit formed as an extension of the barrier system of the Delmarva coast, in response to the southwest transport of sand in the zone o f shoaling and breaking waves. Through stratigraphic analysis o f the Delmarva Peninsula, Mixon (1985) has designated this deposit as the Accomack Member o f the Omar Formation. During the subsequent sea level fall, the shoreline retreated back across the shelf and down onto the upper slope, stranding the Accomack Spit in the re-exposed Susquehanna Valley (Mixon 1985). When sea level rose again, a second barrier spit was emplaced, further restricting the mouth of the Chesapeake Bay. This deposit has been named the Nassawadox Formation (Mixon 1985). Mixon (1985) suggests that this Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 47 deposit accumulated approximately 120,000 years BP. The oceanic side of the Nassawadox Formation is made up of mostly well sorted, medium to coarse grained sand that has been deposited in surf zone and tidal bay mouth environments. This sub unit is known as the Butlers Bluff Member, and was named after exposures at Butlers Bluff, Kiptopeake State Park (Mixon 1985). The Oyster site lies completely within the Butlers Bluff Member. The Bay side of the Nassawadox Formation consists of finer grained sand, richer in clay, which was deposited in a back barrier environment. These deposits have been designated as the Occohannock Member. The Stumptown Member is the third Member o f the Nassawadox Formation, and was deposited in the Eastville paleovalley, incised into older deposits during the earlier sea level fall (Mixon 1985), (Fig. 1.15). The Nassawadox spit pro graded across the ancestral Chesapeake Bay as a result of sand being bypassed along the oceanic side o f the spit driven by the longshore current. As the sand approached the edge o f the spit, some o f it was transported by tidal currents and was deposited onto the tidal sand shoal of the bay mouth. Most of the sand was driven around the tip of the spit by wave refraction. As the fluid power decreased in this area, sand was deposited in incremental steps around the tip of the spit. As time progressed, the edge of the spit prograded across the bay mouth, overrunning the tidal shoaL As a result, time surfaces on the oceanic side of the spit dip seaward, and curve towards the west dipping southward. The Nassawadox spit is underlain by the tidal shoal deposit (Fig. 1.16), (Parsons and Swift 1995; Mixon 1985). After the deposition o f the Nassawadox Formation, sea level fell again, until approximately 18,000 years BP., when sea began to rise again. Sea level rose quickly (0.1 my'1), to about 7,000 years BP. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 48 H elen 20- OKrifaMScarp Mapps bar? scarp 1 0 - aea level - 10-* 20- 3o- 4o- 5o- 6 0 - Nassawadox Formation: Butlers Bluff and Occohannock Members, moderately sorted to well sorted, fine to coarse sand. Stumptown Member Unit C, muddy and shelly fine sand; Unit B, clay-silt; Unit A, gravelly sand and sandy gravel. Fig. 1.15.- Cross section showing the stratigraphic relationship of the members of the Nassawadox Formation (after Mixon 1985). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 49 Since about 4,000 years BP. sea level has men at a much slower rate. Presently, the sea has risen to the level at which it was during the deposition o f the Nassawadox Formation. A Holocene barrier lagoon system has moved in across the shelf as sea level rose, and is currently backed up against the Mappsburg Scarp, the shoreline of the Nassawadox high stand (Mixon 1985; Parsons and Swift 1995). The Oyster Site as a Natural Lab Oyster, Virginia has been selected by the Department of Energy to be the site where experiments in bacterial transport in heterogeneous porous media wDl be conducted. The Oyster Borrow Pit is an excellent location to study the heterogenic nature o f shallow marine aquifers because o f its accessibility, clean sands and truly heterogenic nature. The goal of this study is to relate scales of stratigraphic organization to the distribution of grain size, permeability and facies in shallow marine deposits. As pointed out earlier, one of the most significant problems in stratigraphy and sedimentology is that classical facies models and the use of borehole logs are inadequate in constructing the detailed anisotropy that exists in sedimentary deposits. Another problem that needs to be resolved is that very few studies have related reservoir characteristics to the depositional environment. The Oyster site is a suitable place to investigate these problems. The classical use of facies models and even sequence stratigraphic concepts require a considerable amount o f inference and can not resolve many uncertainties in the stratigraphic architecture. However, exposures at the Oyster site will allow us to resolve the relationship between scales o f stratigraphic architecture and its role in controlling the spatial distribution of important reservoir and aquifer characteristics such as grain size and permeability. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 50 ( a) transport pattern PROGRADING RECURVED SAND SPIT ______ PARABOLIC TIDAL SHOAL SUCCESSIVE POSITIONS OF © OUTER SPIT SHORELINE ZONE OF RAPID CO A STW ISE ADVANCE ZONE OF SLOW OSCILLATORY SEAW ARD ADVANCE © INTERNAL GEOMETRY OF SPIT SURFACES OF EQUAL TIME ARE CURVED WITHIN SPIT Fig. 1.16.- Evolution o f the Nassawadox Spit. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 51 Facies Erected in the Study Area The samples used in this program were collected during the field campaigns o f the subsurface science program (Department of Energy) in 1994 and 1996. In 1994, the Oyster borrow pit was exposed for the first time, and five measured sections were constructed. Grain size and permeability samples were collected in a preliminary investigation. In 1996, researchers returned to the Oyster pit in order to fully characterize the site. Three tiers were exposed that were twenty meters in length and two meters in height. Grain size and permeability samples were also collected, and the stratal geometry was mapped. All o f the beds in the Butlers Bluff member were deposited in a Shoreface setting (1-15 m water depth) and constitutes a shoreface facies. Mixon (1985) describes the Butlers Bluff Member as an 18 meter thick fine clean sand to coarse sand and gravel unit. This unit consists of cross-bedded deposits and it overlies the Stumptown Member. The most common feature o f this unit are the large scale trough cross beds and the ghost casts of Spisula solidissima as well as other bivalves. Mixon (1985) recognizes two distinct sediment types or facies within the Butlers Buff Member. The first type consists o f poorly sorted, medium to coarse pebbly sands composed mostly of quartz. This sediment type occurs mostly in the upper Butlers Bluff Member. In the Lower Butlers BlufE, the dominant sediment type or facies consists of well sorted, medium to fine sands with abundant black heavy minerals. During the first field campaign in 1994, three distinct sediment types or facies were recognized in the Oyster pit, based on the examination of feces excavated, photomosaics and on laboratory grain size analysis o f samples collected. The fecies recognized are, a Cross-Stratified Sand Facies, a Horizontally Stratified Sand Facies and a Shelly Gravelly Sand Facies. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 52 HYPOTHESIS TO BE TESTED I propose to investigate the sedimento logical sources o f variation of grain size, and permeability in shallow marine deposits by relating the small scale stratigraphic organization of the Oyster deposits to these properties. I propose to test the hypothesis that models of stratal architecture are more efficient predictors of grain size and permeability than are facies models in shallow marine sands. An important issue to be resolved by this study is the extent to which the permeability and grain size correlate with the distribution of set boundaries. THESIS LAYOUT Chapter I of this dissertation serves as an introduction to the study, and ends with the hypothesis to be tested. Chapter II describes the methods that will be used to address the hypothesis. Chapters HI and IV are the results section o f the dissertation. Chapter III focuses on the stratal architecture of the Oyster Pit, and Chapter IV is the results of the geo statistical analysis. Chapter V is the discussion and conclusions. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 53 CHAPTER II METHODS OF STUDY INTRODUCTION Approach The purpose of this study is to understand scales of physical heterogeneity that relate to grain size and permeability distributions within shallow marine deposits. In the undertaking of such a study, several important questions arise that help us to understand how scales of stratigraphic organization affect the distribution of grain size and permeability, as well as the development o f a better understanding of how primary textural properties affect secondary properties. These important questions that must be addressed are: (1) What are the predominant grain size and permeability correlation length scales? (2) What is the vertical distribution of grain size and permeability within and between sets? (3) What is the relationship between grain size and permeability? (4) What is the relationship between grain size and set thickness? (5) Is there more variability in the grain size and permeability distributions within sets or between sets? (6) Is there more variability in the grain size and permeability distributions within or between strata cosets? In order to answer these questions, I propose to use a combination of field, laboratory and geo statistical techniques. The remainder of this chapter is devoted to the explanation of these techniques and how they will help to construct the physical Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 54 heterogeneity of the Oyster site. Data Collected Field data collection and laboratory analysis were conducted between 1994 and 1996. Several field measurements and samples were collected by a number of investigators within the Department of Energy’s sub-surface science program. The data collected includes measured sections, geological maps, stratal geometry measurements, and permeability. Samples were collected in order to perform grain size and iron analysis. Table 2.1 illustrates the types o f data collected during the major field campaigns and the methods used. Table 2.1.- Data collected Year Data Collected Number of Method Used Samples 1994 measured sections 6 Jacob’s Staff permeability 1000 grain size 296 air-permeameter 60 gram vials 1996 measured sections 30 Jacob’s Staff geological maps 3 Photomosaics permeability 1092 air-permeameter grain size 444 60 gram sampler FIELD METHODS Opening of Pit Faces The Oyster sand pit was excavated for the first time in April of 1994. This initial investigation revealed a pit structure that was roughly equant, approximately 200 meters across and 15 meters deep. Six transects were carved out o f the margins o f the pit with Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 55 the aid o f a shovel, and a pace and compass map o f the area was constructed. In April of 1996, the Oyster pit was reopened for an intensive sampling and interpretation of the reservoir properties and stratal architecture o f this area. The initial 1994 study was not designed to determine the horizontal correlation structure or to take unbiased statistical measures o f the aquifer properties. The pit was excavated with the aid o f a backhoe, and three 20 meter long and 2 meter high outcrops or tiers were constructed. The tier feces were then smoothed with a shoveL Measured Sections Detailed measured sections were made for each transect using a Jacob’s staff. The Jacob’s staff is a pole that is one and a half meters in height and contains a clinometer and sighting bar. The Jacob’s staff is used to measure stratigraphic thicknesses accurately and quickly (Lewis 1984; Miall 1990). Visual estimates of grain size were taken with the aid o f a hand lens and a grain size comparator card. Paleocurrent measurements were also taken. In 1996, stratigraphic sections were constructed for each tier every 2 meters. Primary structures and facies type were identified in each. Visual estimates o f grain size were made, and paleocurrent measurements were also taken. Geological Mapping Detailed geological maps o f each o f the tiers were constructed. Horizontal distance of each tier was measured with a tape measure and painted on the face itself in one meter increments. Nails were put into the tops and bases o f each face at every meter and were then surveyed in order to create an accurate map in northings, eastings and elevation. Stratal set boundaries were also mapped on the geologic base map in order to Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 56 correlate the geometry of the deposits to the samples collected. Digital photographs of the outcrop and sampling locations were taken by professional photographers. Each photograph contains a scale and color chart. All photos were placed on CD, and used to construct photomosaics of the outcrop. After all o f the nails and samples were surveyed, a grid containing the nail locations and samples for each tier were created using ROCKBASE™, (Rockware 1991). The geological maps and the ROCKBASE™ maps were then scanned into Adobe Photoshop®. The ROCKBASE™ map was scaled to the geological maps and then put as a separate layer over the geological map for each tier. This gives an accurate placement for all samples taken. Sampling Procedures Sampling was conducted by using a staggered grid. The sample grids were two meters long and one meter high. Individual grid cells were 10 cm by 10 cm. Measurements of aquifer properties were made over several scales in order to construct the physical heterogeneity of the location, and to determine the scale controlling these properties. Each sample was then surveyed. Bias samples were also taken to insure that samples would cut across set boundaries. Samples were labeled such that they could be correlated to one another. This was done by using a unique eight digit sample number. The first two digits represent the year in which the sample was collected. The third and fourth digits represent the grid frame locations. The fifth, sixth and seventh numbers represent the grid box number. The last digit represents the sector o f the grid the sample was taken from. Each grid is divided into quarters, and the sectors are labeled in a clockwise manner (Fig. 2.1), (Mcling and Higgs 1996). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 57 10 cm ' 2 10 cm Y\ 3 *4 1 m 2 m Fig. 2 .1 Sample grid used to place samples on the outcrop face. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 58 Grain Size. Grain size samples were collected from the grids for detailed laboratory analysis. A 60 gram sampler was used to collect the sample, and each sample was labeled with a unique Sediment Dynamics Lab number (SDL#), for quality control purposes. A total o f596 grain size samples were collected from the pit over the two sampling campaigns. Permeability. Field measurements o f permeability in the Oyster pit were conducted by the use of a portable air-minipermeameter. The air-minipermeameter is an economical way to obtain several hundred measurements of hydraulic conductivity in a short period of time. This allows the investigator to determine the spatial distribution of permeability in an outcrop or petroleum reservoir. This instrument works by measuring the rate at which a glass syringe piston displaces a known volume o f air, which is injected through a tip seaL The permeability is calculated from the relation described below by Goggin et al. 1988. In equation 2-1, K is the hydraulic w , aG„(bD)(P]-Pl) <2' ° conductivity [m/s]; p. is the air viscosity [Pa.s]; q is equal to the volumetric flow rate [m3/s]; PI is the pressure at tip seal [Pa]; Po is equal to the atmospheric pressure [Pa]; a represents the inner radius o f tip seal [m]; b represents the outer tip seal radius [m]; bD is the dimensionless tip seal radius, and is equal to [b/a]; and Go(bD) is a dimensionless geometric factor (Davis et aL 1994). Permeability is determined from the Darcy equation. Stratal Geometry Measurements. Detailed measurements of the thickness and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 59 width o f individual strata, strata sets and cosets were made for each tier. Average values of these properties and the standard deviations were calculated for every set in each coset. Individual cosets are determined through the analysis of set thickness, lamina geometry and grain size characteristics. The stratal geometry statistics enables the construction of normative sets, as well as the relationship between mean grain size and set thickness. LABORATORY METHODS Grain Size Analysis Each sample was first labeled with a unique sediment Dynamics Laboratory Number for quality control purposes. Samples analyzed for grain size were first dried, then split down to approximately a 30 gram sample. Sediments in the range o f -2 to 2.75 phi were analyzed using standard methods of sieve analysis in quarter phi units (Folk 1974). Sediments that were finer than 2.75 phi were analyzed using an Electrozone particle size analyzer. The particle analyzer measures the volume o f the particles as they enter a particular size orifice tube. The sediments are suspended in an electrolyte and are drawn into the orifice tube where an electrical impedance is created across an electrode. The impedance is directly proportional to the volume o f the particle. The signal is magnified and the volume is recorded. This is a more accurate way o f measuring fine sands and muds than pipette analysis because it is not sensitive to shape or density effects (Milligan and Kranek 1991). Geostatistical Analysis T extu ra l P ro p erties. The first step in understanding the relationship between scales of stratigraphic organization and textural properties is to calculate basic moment Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 0 parameter statistics of the samples collected in order to determine if distinct patterns can be seen. Mean grain size, sorting (standard deviation), skewness, kurtosis and percent gravel were determined for all grain size samples. Standard box plots were also constructed for the permeability data. Bivariate plots of textural properties were constructed to investigate relationships between sedimentotogical parameters and to help construct the depositional environment Normalization o f Textural Properties to Set Geometry. As was pointed out earlier, measurements o f individual strata, and strata sets within each coset are used to define a normative set. In defining the set geometry, the Y axis represents the set thickness, X is the set width and Z is the set length. Individual lamina may act as grain size contours indicating a fining upward sequence within a set. In order to understand the vertical distribution o f grain size and permeability within strata sets, sample locations were assigned new coordinates based on their position relative to their height from the base o f the strata set. In this coordinate system, the y axis is the now the vertical distance from the base of the set to the top of the set, and samples were assigned values between 0 and 1, (Fig. 2.2). Variogram Construction. The basic tool for the analysis o f spatial structure is the semivariogram. Semivariogram analysis has been utilized by mining geologists for a number of years to characterize the correlation length scales of the particular property o f interest. The semivariogram, also called the variogram, is a measurement o f the mean- squared differences between individual sample values at user defined separation distances. The variogram is calculated with the following formula: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 61 Y(/7>=2 ^ ) E[Z(X' +/,)"Z(X/)]2 ( 2 " 2 ) In equation 2-2, y (A) is known as the variogram statistic, z (x,) is the observation at position (xy), /z is the distance between observations and n(h) is the number of data pairs separated by h (Hess et aL 1992; Davis 1973; Pannatier 1996). When the distance between observations is zero, every data point is being compared to itself therefore the semivariance is zero. When the distance between observations is small, the data points are usually very similar in magnitude and the semivariance is smalL As the distance between observation becomes larger, the observations are not as closely related to each other. In this case the semivariance increases. At some distance, the observations are no longer related to each other at all, the semivariance no longer increases and the semivariogram develops a flat region known as the silL This occurs because as the distance between the observations increases the squared differences will eventually equal the variance around the average value under stationary conditions. The distance where the semivariance approaches the variance is called the range of the variable. The range defines the distance over which observations are related to one another (Fig. 2-3), (Davis 1973). Semivariogram analysis was performed with the aid o f the commercial program VARIOWIN0, which is a collection o f programs designed for the analysis o f spatial data. Analysis o f Variance (ANOVA). One of the most universally used statistical techniques for analyzing data is analysis of variance. This technique has been used extensively in the biological and social sciences, and has found increasing applicability to Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 62 Y - SetTUekneaa X = Set Width 2 . Set Length dffdr * Mean Set Dimensions 0 y “ Vertical Distance from set trough (0-1) X “ Hastngs (meters) Fig. 2.2 Definition sketch for a normative set, and the normalization o f samples to set geometry. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 63 Sill ofeb •ca t Range Separation Distance Fig. 2.3.- Definition sketch of a typical variogram. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 64 This technique has been used extensively in the biological and social sciences, and has found increasing applicability to paleontological and sedimentological studies. The variance is defined as the variability of a particular group of data. In an analysis of variance, data are collected and organized such that the variability among the grouped data is compared to the variability between the groups. The variance is calculated as the sum of squared deviations o f the observations from the group mean divided by the degrees o f freedom. In equation 2-3, s2 is the variance, x is an individual observation, (2.3) A M ' ’ AT is the group arithmetic mean and N is the number of observations. The total variation is derived by calculating the average squared deviations of the observations from the grand mean (Dowdy and Wearden 1991; Krumbein and Miller 1953). E * £ -* •! 'S'J O' -yf (2-4) rta - 1 In equation 2-4, n represents the number of observations and a is the number of groups. Total variance is broken into two parts, the within-group variance and the among-group variance. The within-group variance is the average squared deviations of the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 65 observations from the group average (Eq 2-5). This is also known as the pooled variance. The among-group variance is calculated by taking the average E, E %-yf 2 a fn - l) squared deviations of the group averages from the grand average. This value is then multiplied by the number o f observations in each group (Eq 2-6). This type of analysis o f variance is known as a one-way completely randomized ANOVA. Y i . (y -y)2 ”[— V ] (2-6) a - l TheANOVA tests the hypothesis that the means between groups are equal This is known as the null hypothesis, and the alternative hypothesis is that at least one of the means o f the groups is not equaL The null hypothesis is tested by calculating an F ratio. The F ratio is defined as the ratio of the among-group variance to the within-group variance. This value is then compared to the critical F value for the particular degrees of freedom in the test and the desired a (confidence level). If the critical value is exceeded by the F ratio, then the null hypothesis is rejected, and one must conclude that at least one inequality between the group means exists. The analysis o f variance in this case will Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 66 be used to determine if significant variation exists within or between individual strata sets and cosets. There are three basic assumptions made when undergoing such an analysis. The three requirements for this test are the assumption of additivity, normality o f data groups and the homogeneity o f variance. The assumption of additivity requires that there is no significant interaction between individual observations. These three conditions will be explained and examined in detail in Chapter IV. Due to the large number of observations, the analysis o f variance tests were conducted with the aid of the statistical software package known as IMP®. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 67 CHAPTER EQ ARCHITECTURE OF THE OYSTER SITE INTRODUCTION Sediment o logical investigation o f the Oyster Pit sediments during the 1994 and 1996 field campaigns revealed very coarse, poorly sorted to fine grained well sorted sediments. Lenticular pebbly lag deposits occur in the upper two-thirds of the section exposed. Fig. 3.1 illustrates the dominant sedimentary feature o f cross-stratification which occur in cross-strata sets. Each cross-strata set is composed of trough shaped lamina. Pelecypod casts replaced by hydrous iron oxide, as well as vertical burrows of Spisula solidissima occur throughout the upper Butlers Bluff Member. Hydrous iron oxide staining o f the sedimentary deposits tend to outline individual cross strata sets. During the 1996 field campaign the pebbly lag deposits were found to occur generally at the base of cross strata sets. The lower third of the Butlers Bluff Member consists of parallel lamina that are nearly horizontal, and tend to have less iron oxide staining (Fig. 3.2). FACIES ARCHITECTURE During the initial examination o f the Oyster Site in 1994, three facies were recognized based on sedimentary structures and grain size gradients. The three facies identified are a Cross-stratified sand facies, a Shelly gravelly sand facies and a Horizontally stratified sand facies. The Spring 1996 field campaign opened three tiers measuring twenty meters across by 2 meters high. This gave the researcher a full view o f the facies relationships in the Butlers Bluff Member. Close inspection of Fig. 3.1 clearly demonstrates that the Shelly-gravelly sediments are generally located a the base of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 68 Fig. 3.1.- Photograph of trough cross-stratification at the Oyster Site. Note the basal gravel lags in cross strata sets (arrows). Fig. 3.2.- Photograph illustrating sediments from the lower Butlers Bluff Member. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 69 Cross-stratified sets. Therefore, the Shelly Gravelly sand facies and the Cross-stratified sand facies are more closely related to each other then they are to the Horizontally stratified sand facies and may be considered subfacies of a common cross stratified facies. A new facies was also recognized during the 1996 investigation. Sediments exposed near the base of Tier 3 (bottom of the section) contained coarse gravelly sediments with wavy bedding. This facies which I will call Micro cross stratified sand facies occurs beneath the Horizontally stratified sand facies. Unfortunately, due to pit instability, only a small portion o f this facies was exposed (Fig. 3.2). The distribution of facies within the Oyster Site can best be revealed by the construction of measured sections. Measured sections were constructed at every two meters horizontally for the entire Oyster Site. Fig. 3.3 through 3.6 illustrates the lateral and vertical facies distributions. From these measured sections it is clear that the upper two-thirds of the Oyster Site is dominated by the continuous Cross-stratified sand facies with lenticular pebbly deposits that make up the less continuous Shelly gravelly sand facies. The average grain size o f the Cross-stratified sand facies is 1.60 phi and the average sorting is 0.74. The average gravel content is 1.72%, and the samples were all very negatively skewed. The Lower third o f the Oyster Site consists mostly of the Horizontal stratified sand facies. The average grain size of the Horizontally stratified sand facies is 2.57 phi, and contains the best sorted deposits. The Micro cross stratified and the Shelly gravelly sand facies have sim ilar textural characteristics to those of the Cross-stratified sand facies (Table 3.1). The Cross-stratified sand facies makes up more than two-thirds of the entire Butlers Bluff Member, and the Horizontally stratified sand facies makes up 15 percent. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 70 Easting 958 960 962 964 Sod Profile Cross-Stratified Sand Facies I 2 Shelly-Gravelly Sand Fades Horizontally Stratified Sand Fa •3 1 Micro-cross stratified Sand Fades ? ° Horizontal (meters) Fig. 3.3.- Facies distribution between easting 958 and 964 (after Parsons 1998). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 71 Easting 966 97 0 964 96 8 □ Sod Profile □ Cross-Stratified Sand Facies I } Shefiy-CnveOy Saad Facia Horizontal (meters) □ Horizontally Stratified Sand Facies I I Micro-cross stratified Sand Facies Fig. 3.4.- Facies distribution between easting 964 and 970 (after Parsons 1998). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 72 Easting □ Sod Profile □ C ias-Stm ificd Sand Facies ~2n H Shetty-CnveOy Sand Facacs ^ 11 I - I Horizontally Stratified Sand Facies i^— - - Zi IH Micro-cross stratified Sand Facies Honamol (meters) Fig. 3.5.- Facies distribution between easting 970 and 976 (after Parsons 1998). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 73 Easting 976 978 / ,. 980 / / ' 982 \ - - 1 I V 7 \ < 1 ' ' N - - \ ^ ' ' v ------ 1 _____r1 - i l - v . — □ Soil Profile □ Cross-Stratified Sand Facies ■ Shelly-Gravelly Sand Facies 1*2 H s Horizontally Stratified Sand Facies ■ Micro-cross stratified Sand Facies i « 1 Fig. 3.6.- Facies distribution between easting 976 and 982 (after Parsons 1998). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 74 Table 3.1.- Textural properties o f each facies Facies Mean Grain Size Sorting (phi) Skewness % Gravel ______(phi)______Cross-strata. 1.60 0.74 -0.83 1.72 Shelty-grav. 1.52 0.82 -0.72 3.90 Micro-cross 1.65 0.68 0.26 1.85 strata. Horizontally- 2.57 0.46 -1J6 0.53 strata. Fig. 3.7 illustrates the percent distribution o f each facies type within the Butlers Bluff Member. Facies were also defined based on granulometric properties alone. This was done because it is often difficult to resolve stratal patterns in cores taken from sub-surface deposits o f aquifers. The goal for defining facies on the bases o f grain size data versus “classical” facies was to see if facies observed in the Oyster Pit Site could be projected into a nearby experimental aquifer in which the small width o f cores collected rendered facies identification difficult. In the granulometric facies scheme, samples that contain less than 10 % gravel and have a mean grain size that is coarser than 2 phi are assigned to the Cross-stratified sand facies. Those samples assigned to the Horizontally stratified sand facies had less than 10 % gravel and the mean grain size is 2 phi or finer. Samples that contain 10 % gravel or more are designated as Shelly gravelly sand facies (Table 3.2). Differentiation between Micro-cross stratified and Cross-stratified sand facies is not possible texturally, so only three facies are used for the comparison between petrographic facies and classical facies. Since the Micro-cross stratified sand facies Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 75 contains coarse deposits, they were counted as Shelly gravelly sand facies for this comparison. Table 3.2.- Petrographic facies classification ______% Gravel______Mean grain size Petrographic facies < 10% < 2.0 phi Cross-stratified sand facies < 10% > 2.0 phi Horizontally stratified sand facies 10% ------Shelly gravelly sand facies Samples collected for grain size in each of the three facies were compared to the predicted facies of the petrographic model. Comparison between classical facies identified and petrographic facies predicted resulted in a 77% match between predicted and actual facies. Twenty three samples did not match and are most likely due to the fact that the human eye can not distinguish between 8% and 10% gravel in a deposit (Fig. 3.8). STRATAL ARCHITECTURE General In the Oyster Site, all o f the sedimentary strata are less than one cm. thick, and are therefore classified as lamina. Lamina in the Oyster deposits organize to form cross lamina and lamina sets. Sets o f cross lamina and lamina further organize into genetically related cosets. The stratal architectural classification used to describe the Oyster sediments overlaps with the facies classification used in that cosets o f lamina sets Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 3.7.- Percentage o f facies within the Butlers Bluff Member. % discordant (23.00%) concordant (77.00%) Fig. 3.8.- Petrographic facies vs. classical facies. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 77 are typically analogous to facies volumes. This holds true in most cases for the Oyster deposits except for the Shelly-gravelly Sand Facies. As was pointed out earlier, this facies forms in the troughs of cross lamina sets and is therefore a sub-facies of the Cross- stratified Sand Facies. Therefore, the Shelly-Gravelly Sand facies, which is not continuous, occurs within strata sets (Fig. 3.9). Strata cosets were identified using the classification of McKee and Weir (1953) modified by Allen (1963). Criteria used to identify cosets include set grouping, set thickness, strata shape and the relationship between strata and the base of the sets. Also used to identify cosets is the shape of the lower bounding surface and the degree o f homogeneity o f sediments within individual strata sets. Based on these parameters, four cosets have been identified in the mapped exposure of the Butlers Bluff Member. Coset A Co set A is located within Tier 1, which is in the upper two meters of the Butlers Bluff Member. The most dominant feature is the large scale trough cross stratification formed by migrating dunes. Cross lamina thickness averages 2.58 mm, and has an average width of 24 cm. Table 3.3 summarizes the average stratal geometry measurements of Coset A. Individual sets are underlain by scoop shaped erosional surfaces. Sets comprising coset A are interfingering and grouped with erosional surfaces that plunge at one end. Cross strata within individual sets in the x plane are curved and symmetrical, whereas in the z plane they are sinuous. Average dip o f cross lamina is 20 degrees. In this case, the cross strata to base relationship is discordant (Fig. 3.10). The cross stratification patterns seen in Co set A most closely resemble Allen’s (1963) description of Pi-cross stratification, with one exception. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 78 Stntal Concepts Ficies Concepts Shelly Gravelly Faeie* Fig. 3.9.- Mesoscale architecture o f the Oyster Site. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 79 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 80 In this case, pebbly lag deposits are found in the troughs o f most sets making the degree o f lit ho logical uniformity heterogeneous rather than the homogeneous nature as described by Allen for Pi-cross stratification. Table 3.3.- Summary o f average stratal geometry measurements o f Coset A Lamina thickness Lamina width Set thickness (cm) Set width (mm) (cm) (m) Mean 2.58 23.89 10.95 4.49 Std. 0.76 8.10 3.48 3.12 Histograms of lamina thickness and lamina width indicate that these parameters are not normally distributed, and that lamina widths are considerably variable within Coset A (Fig. 3.11 and 3.12). Examination o f histograms for set thickness and width reveal that thickness is normally distributed but width is not (Figure 3.13 and 3.14). The mean and standard deviations for set properties also indicates that set width and thickness are quite variable as well. Grain size measurements within Co set A indicate that the average sediment is a medium sand, moderately sorted and negatively skewed. The average gravel content is 2.1%, but is quite variable within and between individual lamina sets (Table 3.4). Coset B Coset B which is contained within tier 2 is very similar to Coset A. Co set B is composed of large scale trough cross stratification with pebbly lag deposits in the troughs of individual sets. Sets are grouped and interfingering with erosional scooped Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. SI 12 -- 10 -- u>> os er3 S b . 6 - - 4 -- 2 -- 0.0 1.0 2.0 3.0 4.0 5.0 Lamina Thickness (mm) Fig. 3.11.- Histogram o f lamina thickness for Coset A. 12 ------ 10 -- 8 -- 4 ------ 2 -- 0 I- i —I | | | f f 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 Lamina Width (cm) Fig. 3.12.- Histogram o f lamina width for Coset A. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced . u 20 IS 0 5 Frequency 10 15 -- -- 5 -- 0.0 0.0 Fig. 3.13.- Histogram o f set thickness for Coset A. Coset for thickness f set o Histogram 3.13.- Fig. Fig. 3.14.- Histogram o f set width for Co Co A. for set width f set o Histogram 3.14.- Fig. 2.0 5.0 4.0 e hcns c ) (cm Thickness Set Set Width (m) Width Set 6.0 10.0 8.0 15.0 10.0 20.0 12.0 82 83 shaped surfaces similar to Coset A. Cross lamina dip at 20 degrees like that o f Coset A. Average set thickness and width for Coset B is not significantly different from Coset A. Table 3.4.- Textural properties o f Coset A Mean grain size Sorting (phi) Skewness % Gravel ______(phi)______Mean 1.43 0.84 -1.0 2.1 Std. 0 3 2 035 038 3.03 The cross strata to base relationship is also discordant and the degree of lithologic uniformity is heterogeneous (Fig. 3.15). What is significantly different are the average lamina thicknesses and widths. Table 3.5 shows that lamina are much more variable in thickness and width than in Coset A. Coset B probably begins between Tiers 1 and 2, however we can not see the actual location because tier construction obstructs it. Table 3.5.- Summary o f the average stratal geometry measurements o f Coset B Lamina thickness Lamina width Set thickness (cm) Set width (mm) (cm) (m) Mean 4.66 79.77 12.94 539 Std. 3.44 62.95 637 3.03 Histograms of lamina thickness and width indicate non normal distributions and are similar in shape to the distributions exhibited in Coset A (Fig. 3.16 and 3.17). Histograms of set thickness and width are also indicative o f non normal distributions (Fig. 3.18 and 3.19). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 3.15.- Photograph of the stratal geometry of Coset B. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 T-amina Thickness (mm) Fig. 3.16.- Histogram of lamina thickness for Coset B. 20 ------ 15 - 5 ■ - 0 * 0.0 60.0 120.0 180.0 240.0 Tairnna Width (cm) Fig. 3.17.- Histogram of lamina width for Coset B. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8 6 20 IS - - ! 10 - - 0 + 0 0 5.0 10.0 iss> 20.0 2S-0 3 0 j0 35.0 Set Tbiefciiea (era) Fig. 3.18.- Histogram o f set thickness for Co set B. s -- r b. 4 - - 2 - - 0.0 4 .0 6 .0 10.0 12.0 1 4 .0 16.0 18.0 Fig. 3.19.- Histogram o f set width for Co set B. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 87 Average values o f textural properties for Coset B are also significantly different from those o f Coset A. Grain size measurements indicate that on the average, deposits are a medium sand but the actual mean grain size o f 1.7 phi is significantly different than the mean grain size o f Coset A. Sediments in Coset B are better sorted than those in A, but are still classified as moderately sorted. The gravel content and distribution is quite similar to that o f Coset A. Table 3.6 summarizes the textural properties of Coset B. Table 3.6.- Summary o f textural properties for Coset B Mean grain size Sorting Skewness % Gravel ______(phO______Mean 1.70 0.69 -0.66 1.93 Std. 0.45 034 1.03 3.73 Coset C Coset C is extremely different from Cosets A and B, for it is composed entirely of parallel to nearly horizontally stratified sediments and thus contains the Horizontally stratified sand facies. Coset C is located in the lower part of the second tier exposed at the Oyster Site down to the middle section o f the third tier. This constitutes the lower part o f the butlers Bluff Member (Fig. 3.20). Individual lamina can barely be seen by heavy mineral contrasts, but could not be measured for thickness. Lamina widths are most likely continuous throughout the entire width o f individual sets. Sets of Coset C are differentiated by grain size and color contrasts. Sets are much thicker and wider for this coset than either Coset A or B, but show a significant amount o f variability (Table Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 3.20.- Photomosaic of Coset C, illustrating parallel laminations and set breaks. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 89 3.7). Lower bounding surfaces are non erosional, and fithology within a set is for the most part is homogeneous. The greater than sign for average set width must be inchided in the measurements because many sets of Coset C are continuous in width for the entire exposure. Table 3.7.- Summary o fstratal geometry measurements fo r Coset C Lamina thickness Lamina width Set thickness (cm) Set width (mm) (cm) (m) Mean N/A N/A 39.20 > 8.0 Std. N/A N/A 18.20 >7.0 Set thickness and set width histograms reveal non normal distributions. The primary set thickness mode is 45 cm, and the primary set width mode is 5 m (Fig. 3.21 and 3.22). Iron oxide staining also occurs throughout this coset. Grain size measurements within Coset C show that the sediments are fine grained sands with the best sorting in the entire Butlers Bluff Member. These well sorted sands are negatively skewed and have a patchy gravel distribution which is also not normally distributed (Table 3.8). Coset D Coset D is located in the bottom most section of the Butlers Bluff Member, and was the least exposed of the four cosets. Co set D contains the Micro-cross stratified sand facies, and is recognizable by its significant grain size change and color from the overlying horizontally stratified deposits o f Co set C. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.00 15.00 30.00 45.00 60.00 75.00 Set Thicknes (cm) Fig. 3.21.- Histogram of set thickness for Coset C. O oa s ocr 000 5.00 10.00 15.00 20.00 25.00 Set Width (m) Fig. 3.22.- Histogram of set width for Coset C. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 91 Coset D also contains the curious wavy bedding that is found in Tier 3 (Fig. 3.23). The bottom section of Coset D exposed in Tier 3 is very close to the water table, therefore the wavy pattern seen is most likely due to post depositional diagenic processes. Cross lamina occur throughout the entire coset but in many cases were difficult to see. Lamina that were measured for their stratal characteristics reveal similarities with cross lamina o f Coset B. Table 3.8.- Textural properties o f Coset C Mean grain size Sorting (phi) Skewness % Gravel Mean 235 0.46 -132 0.43 Std. 031 0.18 1.42 136 The average cross lamina thickness is 4.5 mm, and the average cross lamina width is 11.74 cm. Set thickness for Coset D does not appear to be significantly different from average set thicknesses o f Co sets A and B. However, average set width for this coset is significantly different from the other three cosets o f the Butlers Bluff Member (Table 3.9). Also, another difference between Cosets D and B are the average cross lamina dip angles of 10 degrees instead of 20. Examination o f histograms of set thickness and width indicate non normal distributions o f these stratal properties (Fig. 3.24 and 3.25). Histograms of lamina thickness and width were not constructed due to the low number o f samples taken. Textural properties measured in Coset D clearly illustrate the similarity of this coset with that of Coset B. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 3.23.- Photograph illustrating the break between Cosets C and D, and the general characteristics of Coset D. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced Frequency s u -- - J 0 L5-- 2 1 ------0.0 00 2. 00 60 8. 00 1.0 40 1.0 00 20. 00 .0 2 2 0 .0 0 2 0 .0 8 1 16.00 14.00 12.00 10.00 0 .0 8 6.00 0 .0 4 0 .0 2 0 .0 0 .0 2 Fig. 3.24.- Histogram o f set thickness for Coset D. Coset for thickness f set o Histogram 3.24.- Fig. Fig. 3.25.- Histogram o f set width for Coset D. Coset for width f set o Histogram 3.25.- Fig. 4.0 . 1. 1. 1. 1. 1. 20.0 18.0 16.0 14.0 12.0 10.0 2.0 Set Width (m) SetThidn>eg(cp) 00 .0 4 2 94 Table 3.9.- Summary o f stratal geometry measurements for Coset D Lamina thickness Lamina width Set thickness (cm) Set width (mm) (cm) (m) Mean 4.50 73.00 11.74 >14.10 Std. 0.50 6.00 4.84 > 7.35 Sediments in Coset D are generally medium grained, moderately sorted sands. The sediments appear to be positively skewed, but this may be due to the small sample size (n = 20) in this coset. The patchy gravel distribution is also similar to that o f Coset B (Table 3.10). Table 3.10.- Textural properties o f Coset D Mean grain size Sorting (phi) Skewness % Gravel ______(phj)______Mean 1.65 0.68 0.23 1.85 Std. 0.53 0.12 1.03 2.52 VERTICAL PATTERNS Set Thickness Set thickness within cosets tends to be quite variable, however there is an overall pattern that one can see from the Lower Butlers Bluff section upwards to the Upper Butlers Bluff section (Coset C to Coset A). Plots o f set thickness vs. elevation were constructed for various eastings across the Oyster Pit exposures. Close examination of these plots suggest that set thickness decreases from the Lower Butlers Bluff Member up Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 95 through the Upper Butlers Bluff Member (Fig. 3.26 through 3.30). This pattern does not hold true for Coset D, since it has very similar stratal patterns to that of Coset B. Coset D may actually represent an earlier stage of spit progradation across the Chesapeake Bay. Allen (1988) points out that as water depth increases, the height and wavelength of sandwaves increases. As a result, preserved cross strata sets also increase in scale. If this is true for sandwaves, then it must also hold true for dunes as well since the only difference between them is scale. In the Butlers Bluff Member, set thickness decreases upwards, indicating that the depth must be decreasing. This pattern supports the idea that the Butlers BluffMember represents the progradation of the Nassawadox Spit across the ancestral Chesapeake Bay. Grain Size The general textural pattern that exists within the Butlers Bluff member is that of a coarsening upwards sequence. This coarsening upwards sequence is indicative of a prograding shoreline, and can be seen in plots constructed of mean grain size vs. elevation for various easting along the Oyster Pit exposures (Fig. 3.31 through 3.33). Fig. 3.34 shows a weak but significant inverse linear relationship between elevation and mean grain size. This also illustrates the coarsening upward trend. The R2 is only .26, but the T ratio is 12.39 which is much higher than the critical T value (6.31) necessary for significance at the 95 % confidence interval. Close inspection of Fig. 3.31 through 3.33 also indicates that there is a weak but significant fining upwards pattern of grain size within individual sets. In order to test if this fining upward sequence occurs from the base o f the trough to the top o f individual sets, grain size data locations were given a new vertical position. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 96 58 65 56 53 68 55 **61 0) co 40 49 71 8 31 Coset Break 3 2 0 0.1 0.2 0.3 0 .4 0.5 0.6 Thickness (m) Fig. 3.26.- Vertical pattern of set thickness for easting 964. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced 68 S -- et#72 66 - 0 Fig. 3.27.- Vertical pattern of set thickness for easting 966. easting for thickness set of pattern Vertical 3.27.- Fig. 0.1 2 03 . 05 0.6 0.5 0.4 0.3 .2 0 Thickness (m) Thickness stBreak B oset C 97 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced 72 68 Set# 56 14 Fig. 3.28.- Vertical pattern of set thickness for easting 968. easting for thickness set of pattern Vertical 3.28.- Fig. 0 0.1 . 0. 4 05 0.6 0.5 .4 0 .3 0 0.2 oe reak B Coset Thickness (m) Thickness 98 99 25 22 59 64 56 61 =*71 0 0.1 0.2 0.3 0.4 0.5 0.6 Thickness (m) Coset Break Fig. 3.29.- Vertical pattern of set thickness for easting 970. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced 64 28 30 31 28 59 22 25 14 S et# 8 2 Fig. 3.30.- Vertical pattern of set thickness for easting 972. easting for thickness set of pattern Vertical 3.30.- Fig. 0 0.1 2 03 . 05 0.6 0.5 0.4 0.3 .2 0 Thickness (m) Thickness stBreak B oset C 100 101 Vertical positions assigned were based on height from the base of the trough for a particular set. All data points were assigned a value between zero and one. Data points assigned a value of zero lie at the base of set troughs, whereas those data points that were assigned a value of one are located at set tops. This new vertical position will be called set position. Only seven sets contained a sufficient amount o f grain size data points to test the hypothesis that grain size is correlated to set position. Table 3.11 summarizes the results of the Student’s T-test used for significance testing of this hypothesis. Table 3.11.- Results o f significance tests fo r correlation between set position and mean grain size Set# Student t Critical t Confidence P>t # Data Level Points 65 2.05 1.00 75 <0.048 36 61 39 1.00 75 0.698 36 59 134 1.00 75 0.199 17 56 239 1.00 75 <0.014 36 3 525 3.08 90 <0.0001 24 14 2.78 1.00 75 <0.0067 86 8 5.05 3.08 90 <0.007 6 From Table 3.11, it is clear that set position and mean grain size are correlated for sets 65, 59, 56, 3, 14 and 8. Most are only correlated at the 75 % confidence interval, and Set 61 does not indicate a significant correlation between grain size and set position at alL. O f the six sets that did show a significant correlation, three indicate a coarsening upwards pattern, and three show a fining upwards pattern. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 102 6.5 6 -- C oset A E, C oset B 1 5 .5 - CO LLi S e t B reak Coset C 4.5 -- Coset Break 0 0.5 1 1.5 2 2.5 3 Grain Size (phi) Fig. 3.31.- Vertical distribution of mean grain size for easting 965.3. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced Fig. 3.32.- Vertical distribution o f mean grain size for easting 966. easting for size grain f mean o distribution Vertical 3.32.- Fig. Elevation (m) 5.5 6.5 4.5 6 - - -- - 1 0 Grain Size (phi) Size Grain 1 C oset A oset C C oset C oset C Coset B Coset 2 3 C oset Break oset C S et Break et S 103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced Elevation (m) . - 6.5 4.5 - 5.5 Fig. 3.33.- Vertical distribution o f mean grain size for easting 968. easting for size grain f mean o distribution Vertical 3.33.- Fig. 6 - - 0 0.5 1 Grain Size (phi) Size Grain 1.5 Coset A Coset Coset B Coset C oset C oset C 2 . 3 2.5 e reak B set o C reak B t e S 104 105 Sets that contained coarsening upwards patterns all occur at the base o f coset breaks. Sets that showed a fining upwards pattern are all well preserved thick sets. 3.0 . r r s u : i 0.0- T ra tio = 1 2 J 9 Prob>t = 0.0001 - 1.0 2.8 3 J 4.8 S3 S.8 6 33.8 7 J Elevation (m) Fig. 3.34.- Elevation vs. mean grain size. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 106 CHAPTER IV GEOSTATISTICAL ANALYSIS OF THE OYSTER SITE INTRODUCTION The term geostatistics refers to a group of powerful techniques used to understand the nature o f spatial data. This chapter examines the spatial nature o f grain size and permeability in relation to the stratal architecture of the Oyster Site. This chapter also investigates the scales o f stratigraphic organization at which significant variation exists in grain size and permeability. The techniques used to interpret patterns of grain size and permeability within a stratal architectural framework include classical bi-variate plots used by sedimentologists and rigorous statistical one-way analysis of variance methods. Standardized variograms are constructed to determine correlation length scales and the Tukey-Kramer Means Comparisons Test is used to determine if there are significant differences between cosets as well as individual sets for grain size and permeability. Before any o f these techniques could be applied, it was necessary to construct detailed maps of the stratal architecture with the locations of grain size and permeability data points included. This allowed for the identification o f data points within cosets as well as individual sets of a particular coset. The methods used to construct the architectural maps are discussed in Chapter II. STRATAL ARCHITECTURAL MAPS Individual sets were mapped within each coset based on the identification o f erosional bounding surfaces and lamina geometry. In the case o f Coset C, individual sets were recognized by textural and color contrasts as stated earlier in Chapter HI. Often times, set boundaries were highlighted by iron oxide staining. Sets were numbered Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 107 sequentially from the base o f each coset bottom to top. Each set is designated with an S for surface followed by the number. Coset A This coset occurs at the top two meters of the Oyster Site, between 6 and 8 meters above sea level, and is completely contained within tier 1 o f the Oyster Site. A total o f 64 sets have been identified and mapped within Coset A. Although 20 meters horizontally were exposed within this coset, most samples were collected within an 8 meter distance concentrated mainly in the middle o f tier 1. Fig. 4.1 is an interpretation of the stratal architecture o f Co set A. Thick dark lines indicate set boundaries, and lamina within sets were drawn to illustrate lamina geometry. Each set contains a unique number as indicated on Fig. 4.1. Distribution o f Grain Size Samples. O f the 444 grain size samples collected at Oyster, 163 were contained in coset A. Table 4.1 is a tabulation of the grain size set statistics for oset A. Measurements of grain size were obtained from 15 sets in Co set A. Distribution o f Permeability Samples. A total of 1094 mini air-permeability samples were collected throughout the Oyster Site. Co set A contained 352 permeability samples, located within 19 sets. Table 4.2 is a compilation of averages and standard deviations of permeability measurements for each set. Coset B Coset B is located entirely within the upper two-thirds o f tier 2 in the Oyster Site. This coset is 20 meters long but is not as thick as Co set A. Co set B ranges from approximately 5.8 meters to 4.8 meters above sea leveL Since Coset B is not as thick as coset A, it is composed o f far less sets. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 108 e 8 architecture of the the Oyster Coset of A. architecture Site: 4 .1 Stratal Fig. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 109 Table 4.1.- Coset A: grain size set statistics Set# Mean Grain size Sotting Sotting Skewness Skewness % % Gravel grain deviation deviation deviation Gravel deviation sue S22 1.69 0 3 2 0.83 031 -1.43 0 3 4 2 3 6 231 S25 1.44 033 0.90 0 3 2 -1.44 0 3 9 3 3 2 3 3 ! S 3! 136 0.15 1.18 0.086 -0.922 0.17 5.03 1.98 S40 1.71 0.034 0.72 0.14 -132 0.40 135 031 S55 1.45 0.00 0.638 0.00 -030 0.00 0 3 8 0.00 S 36 1.61 0.15 0.66 0.15 -0.60 0.45 0 3 8 0 3 9 S 59 1-35 032 0.99 0 3 8 -0.81 0 3 5 4.00 5.02 S 61 132 032 0.91 0 3 4 -0.95 0 3 0 2.49 2.43 S 64 0.45 0.00 135 0.00 -0.08 0.00 16.74 0.00 S6S 1.45 035 0.84 0 3 2 -1.41 0.68 1.63 1.64 S 66 135 0.00 0.79 0.00 -0.95 0.00 0 3 4 0.00 S68 1.48 0.05 0.77 0 3 6 -0.89 0 3 3 1.01 0.76 S69 132 0.18 0.81 0.13 -0.94 0.08 1.40 0.82 S 71 135 032 0 3 4 0 3 0 -1.03 0 3 4 3 3 5 3.67 S 72 135 0.03 035 0.04 -0.78 0.17 236 0.76 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 110 Table 4.2.- Permeability set statistics: Coset A Set ft Mean Permeability Standard Deviation (darcys) S3 32.80 0.00 S22 37.48 11.05 S2S 53.79 19.16 S3I 1932 5.03 S35 4130 1.10 S40 26.80 10.14 S43 34.13 1230 SS3 38.40 0.00 S55 18.10 0.00 S56 32.71 11.42 S59 34.08 4.70 S6I 30.41 12.16 S64 33.88 11.67 S63 4139 1035 S66 17.70 0.00 S68 30.16 8.82 S69 1936 8.40 S7I 30.80 9.61 S72 27.00 13.85 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Ill A total of 28 sets were identified within this coset. Most of the samples collected form this coset occurred between eastings 964 and 972. Fig. 4.2 is an interpretation of the stratal architecture of Coset B and includes the upper part of Coset C. Distribution o f Grain Size Samples. The number o f grain size samples collected in Coset B equaled 198. Since there were less sets in Coset B, more sets were samples for grain size than in Coset A. A total o f 12 sets of the 28 identified in Coset B was sampled for grain size characteristics. Table 4.3 summarizes the textural characteristics of each set. Distribution o f Permeability Samples. A total o f 19 sets were sampled for permeability. Mini air-permeameter measurements are foster than grain size analysis since they are taken directly in the field, therefore many more o f these samples could be taken.. Almost every set was sampled for permeability with 487 individual measurements throughout this coset. Most sets in Coset B contained numerous measurements o f permeability. Table 4.4 is a tabulation o f the average perm eability and standard deviations for each set in Coset B. Coset C Coset C begins at the bottom o f tier 2, just below 5 meters above sea leveL Fig. 4.2 shows the stratal architecture o f the upper part o f Coset C, and Fig. 4.3 illustrates the architecture of the lower part. Since Coset C contains much thicker sets than A or B, for less sets comprise this coset. Only 6 sets exist within Coset C, all of which are composed of parallel laminations. Distribution o f Gram Size Samples. From coset C, a total of 73 grain size samples were collected. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CnaetD CoactC Fig. 4.3.- Stratal architecture of the Oyster Site: Coset C 4.3.- Fig. Stratal architecture of the Oyster Site: Coset D. and C a o 0 0 1 I I • • S3 2 S (u|N i)ag|pua Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 114 Table 4.3. - Coset B: grain size set statistics Set Mean Gram size Sorting Sorting Skewness Skewness % % Gravel * grain size deviation deviation deviation Gravel deviation S 3 1.73 0.63 1.03 0.48 -1.71 0.86 4.04 4.48 S 4 231 0.05 0 3 2 0.02 1.14 0.07 0.00 0.00 SS 221 0.03 0 3 9 0.00 0.80 0.18 0.00 0.00 S 6 0.80 0.13 138 0.16 -1.05 0.01 8.02 1.80 S8 1.17 0.78 0.94 0 3 6 -1.02 1.15 4.10 2.68 S 14 1.79 0 3 2 03 8 0 3 5 -032 0.98 131 3.64 S 17 1.06 0.00 1.09 0.00 -034 0.00 18.81 0.00 S 18 1.20 0.88 0.96 032 -030 0.10 5.96 0.41 S 21 0.86 0.63 0 3 7 0.42 -0.41 0 3 2 4.95 633 S 28 1.74 0.18 0 3 7 0 3 3 -0.91 0.61 0.60 0.63 S30 1.73 0.18 0.60 0.08 -0.67 0 3 8 1.13 1.12 S 31 1.55 0.24 0.68 0 3 2 -0.87 0.63 1.14 1.84 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 115 Table 4.4.- Permeability set statistics: Coset B Set# Mean Permeability (darcys) Standard Deviation S3 31.22 24.63 S 4 0.01 0.00 S 5 0.00 0.00 S 6 0.00 0.00 S 7 0.00 0.00 S 8 56.83 20.84 S 11 4623 9.01 S 12 60.82 33.99 S 13 46.10 0.00 S 14 46.51 17.69 S 15 31.18 15.06 S 16 3137 3.13 S 17 53.49 15.90 S 18 6320 15.02 S21 78.40 24.06 S 22 56.43 1328 S 28 38.87 7.81 S 30 48.15 9.00 S 31 4328 16.93 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 116 Grain size samples collected came from 4 o f the 6 sets that compose Coset C. Table 4.5 tabulates the grain size statistics for each set. Distribution o f Permeability Samples. Permeability samples collected from this coset equaled 234. Every set except for 2 were sampled, giving excellent coverage throughout this coset. Table 4.6 tabulates the permeability set statistics for Coset C. Table 4.5.- Coset C: grain size set statistics Set# M on Gam size Sating Sating Skewnes Skeuness % Gravel % Gravel p a n size deviation deviation deviatioi deviation SI 2.54 003 0.42 058 0.18 031 0.00 0.00 S2 262 0.15 0.43 0.15 -1.47 1.72 035 0.76 S5 243 0.29 0.54 0.22 -1.36 032 139 262 S 6 1.46 1.27 0.20 0.17 -0.65 0.65 031 0.48 Table 4.6.- Permeability set statistics: Coset C Set# Mean permeability (darcys) Standard deviation S 1 0.00 0.00 S 2 1836 734 S 5 2438 5.63 S 6 26.4 6.43 Coset D Coset D was the least exposed o f the 4 cosets as was pointed out in Chapter HI, therefore only a small number of samples were collected in this coset. Only four sets were identified within Coset D, with samples taken for grain size and permeability in 3 of the sets. Fig. 4.3 illustrates the architecture o f this coset. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 117 Distribution o f Grain Size Samples. Only 11 grain size samples were collected in this coset. Table 4.7 shows the grain size set statistics. Table 4.7.- Coset D: grain size set statistics S e t# M en G rain size S a tin g S a tn g Skew ness Skewness % Gravel % Gravel gam deviation d eviation deviation deviation size S 2 1.08 0.13 0.73 0 .07 1 2 0 0.14 3 3 7 321 S 3 1.42 a u 0.48 0.04 41.82 0 4 2 I3 S 132 S 4 219 0.21 0.72 0 .09 41.82 0.42 138 132 Distribution o f Permeability Samples. Of the 1094 permeability samples collected in the Oyster Site, only 20 are from coset D. Table 4.8 gives the permeability set statistics for coset D. Table 4.8. Permeability set statistics: Coset D B^^BSBBaaiB^BaaaBBBSaSSSaBaSBBSBnBBEB Set if _ Mean Permeability (darcys) Standard deviation S 2 90.53 20.69 S 3 62.03 3.88 S4 17.12 9.24 BIVARIATE STATISTICS General Bivariate plots have been used in sedimentology for several decades in order to discriminate between depositional environments. Several authors have attempted to use these techniques, most notably Folk and Ward (1957); Passega (1964, 1977); Friedman Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 1 8 (1967); Cronan (1972); and McCammon (1976) all of which have met with varying success. The idea behind the construction o f such plots is that clustering or trends in the data points are indicative of transport process and therefore depositional environments. Several bivariate plots were constructed in order to see if any such patterns exist in the Oyster Site, and if a physical process could be attributed to them. The plots constructed include mean grain size vs. sorting, skewness and % gravel, sorting vs. skewness, sorting vs. % gravel, mean grain size vs. permeability and sorting vs. permeability. The relationship between set thickness and mean grain size was also investigated. Textural Properties Mean Grain Size vs. Sorting. The first bivariate plot constructed was that of mean grain size vs. sorting. Fig. 4.4 clearly illustrates that a good, significant positive linear relationship exists between these two textural parameters for the Oyster Site. The R 2 is 0.56, and the t ratio is 23.75, which shows that the relationship is significant at the 99 % confidence level. Also evident is the segregation of the Horizontally stratified sand facies from the other facies. This is a strong indication that the progressive sorting process is at work in this depositional system. The plot also suggests that the Shelly gravelly sand facies is most likely a sub-facies o f the Cross-stratified sand facies. Mean Grain Size vs. Skewness. Mean grain size vs. skewness is shown in Fig. 4.5, and indicates that there is no clear pattern or relationship between these two variables at this site. Most samples are negatively skewed, although there is a small segregation of the Micro cross-stratified sand facies samples. Samples from this facies are positively skewed, however, as was pointed out in Chapter III, this is may be due to the small sample size rather than an indication o f a depositional environmental Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.00 Mean GralrfSize(phi) * Fig. Fig. 4.4.- Mean grain size vs. sorting. R square = 0.56 = square R * * = Micro cross stratified sand Facies Y Y gravelly sand Facies = Shelly X X = Cross stratified sand Facies =Z Horizontally stratified sand Facies Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 120 discriminator. Mean Grain Size vs. Percent GraveL The relationship between mean grain size and % gravel is illustrated in Fig. 4.6. The best curve fit for these two variables is a second order polynomial curve. A second order polynomial curve can also be fit to these variables. This plot demonstrates that the horizontally stratified sand fecks contains the least amount of gravel, whereas the gravel percentage is quite variable in the other three facies. Although the positive correlation suggested by Fig. 4.6 is moderate with an R2 o f 0.36, it is significant at the 95% confidence level (t ratio = 9.88). The relationship shown between grain size and % gravel is also indicative o f the progressive sorting process. Sorting vs. Percent GraveL The relationship between sorting and % gravel is strong with an R2 of 0.66 (Fig. 4.7). A second order polynomial curve can also be fit to this data, which shows that as sorting becomes poorer the gravel concentration increases. This feet will become very important to the understanding o f the permeability distribution within a stratal architectural framework. This plot also demonstrates the segregation of the horizontally stratified sand facies indicating progressive sorting down the shelf. Mean Grain Size vs. Permeability. The bivariate plot o f mean grain size vs. permeability reveals a weak positive linear relationship between these two variables (Fig. 4.8). The R2 is only .23, but the t-ratio is 11.44 indicating a significant relationship at the 95 % confidence leveL The plot also clearly illustrates the segregation of the horizontally stratified sand facies samples from the other fecks. The horizontally stratified sand fecies samples tend to have the grain sizes in the fine sand range and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced % % Gravel -3" ■4' -S' 10 -.0 0 50 10 150 5 1 1.00 0 5 .00 -0.50 -1.00 1 1 1 1 1— 1 ' 1 ■ 1 « 1 ' HoaoiyCrs rtfe tratified S rass C oraoouify H - Z Y - Shefly-GravettY S o d Facies Facies d o S Shefly-GravettY - Y x A * M icro C ross S tratified S a d Facies Facies d a S tratified S ross C icro M * A - C n n S tratified S aad Facies Facies aad S tratified S n n C - Fig. 4.5.- Mean grain size vs. skewness. vs. size grain Mean 4.5.- Fig. Fig. 4.6.- Mean grain size vs. vs. size grain Mean 4.6.- Fig. d m S F« Mean Grain Size (phi) % gravel. 2.00 0 5 2 i t 3.00 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced Permeability (darcys) 140.00 100 40.00* 60.00* 20 80.00* 0.00 . . 00 00 -1.00 * * 10* 0 2 25* 15* .25 * Fig.4.8.- Mean grain size vs. permeability. vs. size grain Mean Fig.4.8.- Fig. 4.7.- Sorting vs. % gravel. % vs. Sorting 4.7.- Fig. .00 JO Mean grain size (phi) size grain Mean Sotting (phi) Sotting 00 .0 1 j f ,? fc jr * * Vl & l V a ‘ 2 s * «sr ^ 9 i aly r ii and es ie c a F d n a d tifie tra s lly ta n o riz o H 9 Z Y “ S W Iy g re v e ffy sa n d F a c ie s s ie c a F d n sa ffy e v re s g ie Iy c a F W d S n a “ s d Y tifie tra s ss ra 11C X • “ M icro c ro s s s tra tifie d sa n d F a c ie s s ie c a F d n sa d tifie tra s s s ro c icro M “ • 1.75.75 00 .0 2 235 'X zi 3.00 122 123 Sorting vs. Permeability. Fig. 4.9 shows an extremely weak, almost no relationship between sorting and permeability. The R2 is 0.05, and the t-ratio is not significant at the 95% confidence level. This plot does show that the horizontally stratified sand facies has the best sorting and the lowest overall permeability. Mean Grain Size vs. Set Thickness. The relationship between mean grain size and set thickness was investigated at the Oyster Site. Fig. 4.10 indicates that a good parabolic relationship exists between these paired variables. The R2 is 0.52, and the correlation is significant at the 99 % confidence interval. The parabolic relationship suggests that the coarsest and the finest grain sizes tend to have the thickest sets preserved. An important feature to note is the minimum that exists at 1.5 phi (0.35 mm). ANALYSIS OF VARIANCE RESULTS General Analysis of variance tests ( ANOVA) are statistical tests that allow the total variation of a data set to be segregated into its parts. The analysis o f variance test is designed to compare the individual variances that make up the total variance. In doing this, one is able to test the statistical significance of the observations. The method in which one-way ANOVAS are calculated is discussed in Chapter II. However, as I mentioned earlier in Chapter II, I will discuss the assumptions o f the ANOVA tests in this section. I will also explain the Tukey-Kramer Means Comparison Test that was used after the analysis o f variance tests were performed (Krumbein and Miller 1953). Threemain assumptions should be met before undergoing such an analysis. The first assumption is that no significant interactions occur between observations. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 124 140 .0 0 ' 120.00 * X - Cross stratified sand Facies « = Micro cross stratified sand Facies Y ” Shefly gravelly sand F«cics 100.00 Z “ HotbBataOy stratified sand Facies *0.001 60.00 40.001 S 20.00 ^ w 0.00 —r~ 1—I t .25 .75 IJ 5 I.7S Z25 Sorting phi Fig. 4.9.- Sorting vs. permeability. 0.6 as* £ 2 0 3" I 02* ai* H -, ,-0.«902* Fig. 4.10.- Mean grain size vs. set thickness. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 125 This is also known as the assumption of additivity. For the type of data used in this study one can assume that there is no interaction between individual data points because grain size or permeability measurements in one location usually does not affect another. The second and third assumptions are much more important for most geological data. Assumption two is that o f normality. Each data group should theoretically be normally distributed, however it has been pointed out that the consequences of non normality are not serious since the f-ratio is quite robust for moderately skewed data. F-tests break down and are not valid only when the sample is extremely skewed (Cochran 1947). The third assumption is known as the homogeneity o f variance. The one-way ANOVA test generally assumes that the variances between each group are equal. This is probably the most important assumption because if this condition is not met the ordinary ANOVA test is invalid. The assumption o f normality and homogeneity of variances will be addressed for each ANOVA run (Krumbein and Miller 1953; Dowdy and Wearden 1991). An analysis o f variance test was conducted first using cosets as the data groups. This was done to test the null hypothesis that the mean grain size and permeability is not significantly different between individual cosets. Each coset is then tested for the hypothesis that individual set means o f grain size and permeability are not significantly different. These ANOVA tests will aid in the determination o f the stratigraphic scales at which grain size and permeability variability is most important. As an aid to the understanding of the ANOVA tests, box plots were constructed of the data groups so that visual comparisons could be made. Fig. 4.11 is an illustration o f a generic box plot used in this study. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 126 total mean total n mean 953: confidence jroupmean interval groip sample sees Fig. 4.11.- Example of box plots used in this study (after JMP Statistical Guide 1995). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 127 Tukey-Kramer Means Comparision Test The one-way analysis of variance test only determines if at least one of the group means is significantly different. If the null hypothesis is rejected, it would be advantageous to know which data group or groups were unequal. Several multiple comparisons test exist which are able to discern which groups are unequal. Some require the null hypothesis to be rejected first, while others do not. The multiple comparison test chosen for this study was the modified Tukey’s Honestly Significant Difference (Dowdy and Wearden 1991; Tukey 1949). All multiple comparison tests are based on what is known as “The Least Significant Difference.” This is basically a t test, therefore if all of the data groups are of equal size then two group means can be tested for a significant difference by the equation below. MS, 2 ------\y ry M * n (4-1) In this equation, Mse is the variance of the error or the mean square of the within set group. The confidence interval chosen for all tests was 95% (a = 0.05). This Least Squares Difference Test is also known as Fisher’s Test. Tukey’s Honestly Significant Difference Test was chosen over other tests because o f it’s conservative nature, and the feet that rejection of the null hypothesis is not required. In this test, the least squared difference is subtracted from the actual absolute difference in the means for all data pairs. This reduces the error rate to that o f the confidence interval chosen, and is one of the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 128 strictest means comparisons tests, for it uses a single critical difference unlike Fisher’s Test or others. MS' n (4-2) In the statistical equation above, q represents the quantile used to scale the least squared differences, and is similar to a Student’s t-test (Tukey 1949, 1991; Duncan 1955; Saville 1990; JMP Statistical Guide 1995). Kramer (1956) modified the Tukey Means Comparison test to include situations where data groups contain unequal sample sizes. The results of the multiple means comparison test is displayed in both tabular and graphic form. Once the analysis is run, a table is created that illustrates which data groups are significantly different from one another. All positive values in the table indicate significant differences in the means of those data groups. One can also visualize the results by constructing comparison circle plots. In the circle plot, group means are represented by a circle. A comparison o f individual group means is done by examining the intersection of the circles (Fig. 4.12). Group means whose circles intersect at a 90 degree angle or inscribed circles are not significantly different. If the intersection of two circles are less than 90 degrees or if they do not intersect at all, then the means are significantly different (JMP Statistical Guide 1995). Coset Variability Grain Size. An analysis o f variance test was performed first on individual cosets. The null hypothesis states that coset means are equal. The alternative hypothesis is that Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 129 angle greater than angle equal to angle less than 90 degrees 90 degrees 90 degrees not significantly border line significantly different significantly different different Fig. 4.12.- Definition sketch of means comparison circles (after JMP Statistical Guide 1995). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 130 at least one coset mean is unequal. As was stated earlier, the assumption o f normality should be tested for each data group. This was not conducted for grain size data groups because grain size is usually assumed to be log normality distributed. If this assumption is not made, then ordinary grain size statistics would be invalid, therefore for the purposes of grain size only log normality is assumed and the condition of normality for theANOVA is met. The F-ratio is also fairly robust for the homogeneity o f variances. In this case, variances are not very different so the conditions for the ordinary one-way ANOVA were met. Inspection o f the box plot for each coset reveals that the means for grain size are different (Fig. 4.13). The ANOVA test resulted in an F-Ratio o f 148.2, which far exceeds the critical F-value of 2.60 (Table 4.9). Since the F-Ratio exceeds the critical value, the null hypothesis must be rejected and the alternative hypothesis is accepted. The mean square values indicate that the variance among cosets is much greater than the variance within cosets. Table 4.9.- ANOVA results for grain size o f cosets Source Degrees o f Freedom Sum of squares Mean Square F-Rario Among Cosets 3 62.09 20.70 148.2 Within Cosets 440 61.46 0.14 ------ Total 443 123.57 ------ The Means comparison circles indicate that only coset D is indistinguishable by mean grain size (Fig. 4.13). Table 4.10 gives the results of the Tukey-Kramer HSD Test. Results from the Tukey-Kramer Test reveal that coset C has a significantly different mean grain size from all other cosets, and that the mean grain size of coset D is not Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 131 o o. _4J O C U)o *c Q.C3 £ o WJ eac V E 00 (njd) azjs ukiq oeafy Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 132 significantly different from cosets A and B. Table 4.10.- Means comparison results o f cosets: grain size COSET CB D A C -0.16 0.72 0.59 0.97 B 0.72 -0.10 -024 0.15 D 0.59 -0.24 -0.41 -0.09 A 0.97 0.15 -0.09 -0.11 2_58 Both theANOVA test and the Tukey-Kramer Means Comparison Test prove that statistically, the coset level exhibits significant control o f grain size variability. Permeability. An ANOVA test was performed to test the null hypothesis that coset means of permeability are equal Therefore, the alternative hypothesis is that coset permeability means are not equal First, the assumptions of normality and homogeneity of variances must be tested. In order to test if individual cosets pass the assumption of normality, quantile vs. quantile plots (Q-Q plots) were constructed. Plotted on the abscissa is the standard deviations from the mean, and the permeability values are on the ordinate. If a variable is normally distributed, then a diagonal line is plotted (Fig. 4.14). Q-Q plots for each coset illustrate that cosets closely fit the normal distribution and at the most are only moderately skewed (Fig. 4.15 through 4.18). Variances of each of the co sets were not extremely different, therefore the assumption of homogeneity of variances was met. Visual inspection of box plots constructed for mean permeability values for each coset suggests that a large amount o f variability exists between cosets (Fig. 4.19). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 133 180-f 160- 140- 120- 100- 80- 60- Normal QuantHe Fig. 4.14.- Example of the normal quantile plot (after JMP Statistical Guide 1995). JOS .K> SO .75 .90 .9505 .99 120 “ 100 “ 80“ 60“ 40“ 2 0 “ 0*1 -3 -2 I 0 I 2 3 Normal Quantile Fig. 4.15.- Q-Q plot: Coset A. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0 5 JO .7 5 9 0 9 5 120 * 100 * 60* o 40" 2 0 " 0*1 -2 -t-3 0 I 2 3 Normal Quantile Fig. 4.16.- Q-Q plot: Coset B. 01 0 5 .10 5 0 .7 5 9 5 9 9 40" 3 0 ' 2 0 " 10* 0"< ■3 -2 I 0 1 2 3 Normal Quantile Fig. 4.17.- Q-Q plot: Coset C. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 135 0 5 .10 .75 .90 9 5 .99 125" 100' 75" 50" 25" pOO •3 ■2 -1 0 1 2 3 Normal Quantile Fig 4.18.- Q-Q plot: Coset D. I«0" 120" 100" f l CL. 2 0 " C oset 0.05 Fig. 4.19.- Coset box plots and means comparison circles of permeability. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 136 The results o f theANOVA yielded an F-Ratio of 124.5, which exceeds the critical F- value. Therefore, the null hypothesis is rejected and the alternative hypothesis must be accepted (Table 4.11). The ANOVA also shows that the greatest amount o f variability in this test is at the coset scale (see mean square). Means comparisons circles indicate that three out of the four cosets have significantly different mean permeability values (Fig. 4.19). The Tukey-Kramer mean Comparison Test determined that mean permeability of coset C is significantly different from the other three cosets, and that cosets A and B are also significantly different. Co set D is not significantly different from A or B for permeability (Table 4.12). Table 4.11.- ANOVA results fo r permeability o f cosets Source Degrees of Freedom Sum of Squares Mean Square F-Ratio AmongCosets 3 123595.29 4II98.4 124.5 Within Cosets 1089 360383.59 330.9 ----- Total 1092 483978.88 ------ Table 4.12.- Means comparison test fo r permeability o f cosets C oset B DA c B -30 -9.97 764 23 96 D -997 -1480 -055 1607 A 764 -055 -353 1282 C 23 96 1607 12.82 -4 33 q = 2 J 7 Set Variability GeneraL In the previous section, it was shown that the coset scale exhibits a Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 137 large amount o f variability in both grain size and permeability, which distinguishes one coset from another. It was also shown that coset variability makes up more of the total variability than that o f set variability. In order to determine if set scale variability is statistically significantly important to grain size and permeability, ANOVAS and means comparison tests were performed for each coset. The data groups are now the individual sets, and the assumptions for the one-way ANOVA must be tested for each set group. Coset A . As was stated earlier, grain size data is assumed to be log normally distributed, therefore grain size is assumed to pass the assumption of normality. Permeability set groups were tested for normality by constructing Q-Q plots. Most groups were either closely normally distributed or only moderately skewed. A small number of set groups did not pass the normality test and were removed from the ANOVA test. This occurred in sets with only a few data points. As a general rule, sets that contained less than 4 data points were omitted from the analysis for both grain size and permeability. Grain size variances did not differ greatly, therefore the homogeneity of variances assumption was also met. The assumption of homogeneity o f variances also held true for permeability. Coset A: Grain Size Results. Set grain size means varied between 1.2 and 1.7 phi. Box plots o f set means indicate that more that one set group is most likely significantly different (Fig. 4.20). The ANOVA tested the null hypothesis that set grain size means are all equal. Results of the ANOVA Test yielded an F-Ratio o f 2.87, which exceeds the critical value o f 2.60. The null hypothesis is therefore rejected, and one must conclude that at least one o f the set means for grain size is significantly different. Table 4.13 shows that the set scale contains more than two-thirds of the total variation in Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 138 coset A. Means comparison circles indicate that at least three sets have significantly different grain size means (Fig. 4.20). The Tukey-Kramer Means Comparison Test reveals that several sets are indeed significantly different to one another with respect to grain size. Sets 40, 69, and 72 show no significant difference with any other set (Table 4.14). However, these three sets all have the minimum number o f observations allowed in this study. Table 4.13.- ANOVA results ofgrain size for Coset A K a^^nannaB nnB B B B aaB aaB aB ^^B staB B m ssss Source Degrees of freedom Sumof squares Mean square F-Ratio Among Sets 10 2 2 6 0 2 2 2.87 Within Sets 148 11.65 0.08 ------ Total 158 13.91 ------ All of the other sets are significantly different with more than one other set. The results of the means comparison test clearly indicate that sufficient variability exists between individual sets in a coset with respect to grain size. Sets that do not show a significant difference between mean grain size are typically very thin with significant truncation, as well as the small number of observations with the largest standard deviations. This result may be due to the severe truncation o f a set by the next set that causes no significant difference in grain size. Coset A: Permeability Results. Inspection of set box plots constructed for permeability indicate that several set means deviate from the grand mean (Fig. 4.21). The results of theANOVA test for permeability in this coset produced an F-Ratio of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 139 2f i I.S- I <5 21 1.0- 0 5 - 65 66 6S S e t * Fig. 4.20.- Box plots and means comparison circles o f grain size: Coset A. 130 120 no 100 90 3 60 40 64 All Pain Set* 0.05 Fig. 4.21.- Box plots and means comparison circle for permeability : Coset A. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 140 9.48. Since this F-Ratio exceeds the critical F-vahie, the null hypothesis is rejected and one is forced to conclude that at least one of the sets is significantly different from the grand mean (Table 4.15). Table 4.14.- Grain size means comparisons results: Coset A S e t# 40 22 56 6 9 68 65 25 59 71 61 72 40 -0.55 -0.46 -0.30 -031 -0.32 -0.14 -014 -005 -0.08 •0.01 -0.09 22 -0.46 -0.39 - 0 7 2 -0.25 -0 2 7 -0.06 -0 0 6 0.03 -0.0! 0.08 -0.03 56 -0 J 0 •0.22 •0.13 -0.24 -0.26 0.03 0.01 0.10 0.02 0.16 -0 0 3 69 -0 2 1 -0.25 -0.24 -045 -0.46 -027 •0 2 6 -.1 8 -0 2 1 -0 1 4 -0 2 3 68 -0.32 •0.27 -0.27 -0.46 -055 -028 -0 2 8 -0 2 9 -0 3 2 -0 2 5 -0 2 2 65 -0.15 -0.06 0.03 -0-27 -0.38 -0.13 -0 1 5 -0.06 -0.13 0.00 -0.19 25 -0.14 -0 0 6 0.01 -0.26 -0 3 8 -0.15 -020 -0.11 -0.17 -0.05 -0 2 2 59 -0.05 0.03 0.10 -0.18 -0 2 9 -0.06 -0.11 -0.19 -0 2 5 -0.13 -0 2 2 71 -0.08 -0.01 0 0 3 -0 2 1 -0 2 2 -0.13 -0.17 -0 2 5 -0 2 2 -0 2 2 -0 2 5 61 •0.01 0.08 0.16 -0.13 -025 0.00 -0.05 -0.13 -022 -0.13 -0.33 72 -0.09 -0.03 -0.03 -023 -022 -0.19 •022 -0 3 1 -0 2 5 -0 2 3 -0.55 Table 4.15.- ANOVA results for set permeability: Coset A Source Degrees of Freedom Sam of Squares Mean Square F-Ratio Among Sea II 17350.15 157729 9.48 Within Sets 331 5505621 16623 Total 342 72406.45 ------ Means comparison circles clearly signify that several sets are significantly different from one another with respect to permeability (Fig. 4.21). Results of the Tukey-Kramer Means comparison test can be found in Table 4.16. The Tukey-Kramer test not only Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 141 found that several sets are significantly different, but that the differences are much larger than those for grain size. Clearly the set level is a good predictor o f permeability since one can easily differentiate individual sets from one another with respect to permeability. Coset B. The assumption o f normality for the permeability data was met, since sets in this coset were closely normally distributed or only moderately skewed. The assumption of homogeneity of variances was also met for both grain size and permeability set groups, therefore the one-way analysis o f variance is valid for this coset. Coset B: Grain Size Results. Inspection of box plots constructed for each set indicates that possibly 5 sets are significantly different from the grand mean (Fig. 4.22). The analysis o f variance results yielded an F-Ratio o f 5.20, which is above the critical value o f 2.11. Therefore, the null hypothesis is rejected and the alternative hypothesis that at least one set mean for grain size is significantly different is accepted (Table 4.17). The ANOVA also indicates that over 90% of the total variability is at the set level in this coset. Means comparison circles also indicate that five sets are significantly different from one another with respect to grain size. The complete results of the Tukey-Kramer Means comparison test confirms that indeed 5 out of the 10 sets in coset B used in this analysis are significantly different from one another (Table 4.18). Coset B: Permeability Results. Several sets in coset B appear to be significantly different from the grand mean upon examination o f set box plots (Fig. 4.23). ANOVA results generated an F-Ratio that far exceeded the critical value of 1.81 (Table 4.19). Since the F-Ratio exceeded the critical value, the null hypothesis must be rejected. Therefore, we know that at least one set is significantly different from the others with respect to permeability. Means comparisons circles illustrate that many sets are Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced Table 4.16.- Means comparison results for permeability: Coset A Os 2.5" I s V) 10' i s3 00' S e tt 0.05 Fig. 4.22.- Box plots and means comparison circles of grain size: Coset B. 10 II 12 14 15 17 I t 21 22 2* 30 31 All Pnrs S c tf Fig. 4.23.- Box plots and means comparison circles of permeability: Coset B. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 144 Table 4.17.- ANOVA results fo r grain size: Coset B Source Degrees o f freedom Sum of Squares Men Square F-Ratio Among Sets 9 7.51 0.83 5.20 Within Sets 181 29.02 0.16 Total 190 36.53 Table 4.18.- Means comparison results for grain size: CosetB Set 7 14 3 28 30 31 21 8 18 17 # 7 47 4 404 407 417 419 014 404 042 018 4 1 6 14 404 419 4 2 7 4 4 6 4 4 8 4 0 0 441 0.16 4 1 6 4 5 6 3 407 4 27 4 3 6 4S 2 4 3 4 4 1 4 4 45 0.09 421 4 5 9 28 41 7 446 452 468 470 4 3 6 457 409 434 468 30 41 9 448 434 470 474 4.41 4 6 0 41 3 4 3 7 471 31 014 403 414 436 441 428 463 406 438 4 7 7 21 40 4 441 4 4 5 4 3 7 4.60 4 6 3 -128 491 -1.08 -134 8 042 016 009 409 413 4 0 6 491 4 5 7 4 8 4 -120 18 018 416 421 4 3 4 4 3 7 4 3 8 •1.08 4 8 4 -105 -134 17 41S 456 459 469 471 4 7 7 -134 -120 -134 -1.81 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 145 Table 4.19.- ANOVA results ofpermeability: Coset B Source Degrees of freedom Sum of Squares Mean Square F-Ratio Among Sets 14 63524.73 4537.48 12.56 Within Sets 461 166475.15 361.12 ------ Total 475 229999.88 ------ significantly different from one another (Fig. 4.23). Table 4.20 gives the full Tukey- Kramer results, indicating which sets are significantly different from one another. Coset C All the assumptions required for the one-way analysis o f variance for grain size were met This was also the case for the permeability data. Coset C contained a total of 72 observations organized into four sets. Coset C: Grain Size Results. Box plots constructed for each set indicate that at least one set group is different from the grand mean with respect to grain size (Fig. 4.24). ANOVA results produced an F-Ratio o f 3.27, which exceeds the critical value of 2.74 (Table 4.21). Results from the ANOVA test also show that variation is similar at both the set scale and lamina scale. The null hypothesis must therefore be rejected. This means that at least one set is significantly different from the other set with respect to grain size. Means comparison circles indicate that two of the four sets are significantly different from one another (Fig. 4.24). The full results o f the Tukey-Kramer Means comparison test can be found in Table 4.22. The Tukey-Kramer test revealed that set 2 and 5 are the only sets that are significantly different. These two sets have the most observations, whereas the other two have the minimum number o f observations. Set 1 has the smallest width, and set 6 is close to the top o f tier 3. Interestingly, set 2 is Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 146 located beneath coset B and set 5 is located just above coset D. Coset C: Permeability Results. Set # 1 was omitted from the analysis due to a low number o f observations. Careful examination of box plots reveals that set 2 mean permeability is different than set 5 and 6 (Fig. 4.25). ANOVA results indicate that the null hypothesis must be rejected, meaning that at least one set mean is statistically different than the other set with respect to permeability (Table 4.23). Means comparison circles indicate that two sets in coset C are significantly different with respect to permeability (Fig. 4.25). Table 4.24 gives the complete results o f the Tukey-Kramer Means comparison test for permeability in coset C. Coset D. All o f the required conditions for the one-way analysis o f variance were met for both grain size and permeability. Set 1 of this coset was omitted from both the ANOVA tests due to a low number of observation. A total of 11 observations located in 3 cosets were tested for the null hypothesis that all set means with respect to grain size and permeability are equal. Coset D: Grain Size Results. Box plots of the three sets in this coset indicate the possibility that more than one set is significantly different from the grand mean (Fig. 4.26). The analysis of variance test yielded a very significant F-Ratio, therefore the null hypothesis must be rejected (Table 4.25). Means comparison circles indicate that two of the thee sets are significantly different from each other with respect to grain size. Table 4.26 gives the results o f the Tukey-Kramer Means comparison test. This test revealed that set 4 is significantly different from sets 2 and 3, but that sets 2 and 3 are not significantly different from each other. Set 4 happens to be located just below coset C. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced Fig. 4.25.- Box plots and means comparison circles o f permeability : Coset C. Coset : f permeability o circles comparison means and plots Box 4.25.- Fig. Mean Grain Size (phi) Fig. 4.24.- Box plots and means comparison circles of grain size: Coset C. Coset size: grain of circles comparison means and plots Box 4.24.- Fig. - s u 2 2 ' 3 2 . . 4 1 - * t* e S HPm P AH 0.0S 147 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced Table 4.20.- Means comparison results of permeability: Coset B 148 149 Coset D: Permeability Results. The box plots o f permeability for this suggest that all three sets are significantly different (Fig. 4.27). Results of the ANOVA yielded a large F-Ratio, forcing the acceptance o f the alternative hypothesis that at feast one set mean is significantly different (Table 4.27). Means comparison circles also indicate that all three sets are significantly different with respect to permeability (Fig. 4.27). Table 4.21.- ANOVA results o fgrain size: Coset C Source Degrees o f freedom Sum o f Squares Mean Square F-Ratio Among Sets 3 0.43 0.14 3.27 Within Sets 68 2.99 0 0 4 ------ Total 71 3.43 ------ Table 4.22.- Means comparison results o f grain size: Coset C Set H 2 6 1 5 2 -0.12 -024 -023 0.03 6 -0.24 -029 -027 -0.18 I -0.22 •0 27 -029 -020 5 0.03 -0.18 -020 -0.17 Table 4.23.- ANOVA results o f permeability: Coset C Source Degrees o f freedom Sum o f Squares Mean Square F-Ratio Among Sets 2 133428 66729 1226 Within Sets 227 1205726 53.12 ------ Total 229 13391.84 ------ Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 150 2.5 2.0 " 1 V)3 c 1.5* 6 53 1.0 * Secf 0.05 Fig. 4.26.- Box plots and means comparison circles o f grain size: Coset D. ISO 125“ 100- s 3 «*§ a. JO- 25' Set* Fig. 4.27.- Box plots and means comparison circles of permeability: Coset D. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 151 Complete results o f the Tukey-Kramer Means Comparison Test is given in Table 4.28. Table 4.24.- Means comparison results ofpermeability fo r Coset C S et# 6 5 2 6 -10.02 -5.87 0.99 5 -5.87 -*.92 2.45 2 0.99 2.45 -1.91 Table 4.25.- ANOVA results o f grain size: Coset D Source Degrees of Stmt of Squares Mean Square F-Ratio freedom Among Sets 2 2.85 1.43 38.69 Within Sets 8 0.29 0.04 ------ Total 10 3.15 ------ Table 4.26.- Means comparison test results o f gram size: Coset D Set# 4 3 2 4 -035 0 3 2 0.74 3 0 3 2 -0 3 5 •0.14 2 0.74 -0.14 -039 Table 4.27.- ANOVA results o f permeability: Coset D Source Degrees of Sum of Squares Mean Square F-Ratio freedom Among Secs 2 21845.98 10923.00 5238 Within Sets 17 3552.14 208.90 Total 19 25398.11 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 152 The results show that indeed all three sets are significantly different with respect to permeability. Table 4.28.- Means comparison test results o f permeability: Coset D S et# 2 3 4 2 -21.41 12% 5459 3 2.28 -V i 2% 20.76 4 54.59 20.78 -15.81 VARIOGRAM RESULTS General Variograms were constructed in order to determine the horizontal and vertical correlation length scales of both grain size and permeability in the Oyster Site. The reason why such an analysis was done is that the correlation length scales provide detailed information regarding the spatial continuity o f the properties measured. Once the correlation length scales have been determined, they can then be compared to the scales of stratigraphic organization recognized in the Oyster Site sediments. This will aid in determination of the stratigraphic scales of organization that are most important to the distribution of grain size and permeability. Due to the nature of the data collected, variograms were constructed for both grain size and permeability for cosets A, B and C. Coset D data was not included in the variogram analysis because of the small number of observations and the lack of spatial coverage in this coset. The general theory behind the variogram can be found in Chapter II. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 153 Before the results of the variogram analysis are discussed, there are a few preliminary considerations about the construction of variograms that must be addressed. When constructing a variogram, there are several parameter values that must be chosen by the user in order to create the most confident variogram. The first parameters are the x and y coordinates. For this study, the x coordinate is the easting, and the y coordinate is the elevation. The next parameter is the direction angle. For the horizontal variogram, the angle is zero, and for the vertical direction the angle is 90 degrees. Because we know that most data pairs do not lie at exactly at zero or 90 degrees, we must choose an angular tolerance. This allows for the inclusion o f more data pairs in the analysis. For most of the variograms in this study, an angular tolerance of 20 degrees was used. Also important is the lag spacing, lag tolerance, and the number o f lags. The lag spacing is the distance over which the variogram samples the data set. A good lag spacing is typically the spacing used in the data acquisition (Isaaks and Srivastava 1989). In this study, the sampling spacing was approximately 0.2 meters, therefore, for each variogram the lag spacing was 0.2 or 0.1 meters. Since all the data points were not taken at exactly this spacing, a lag tolerance of half the lag spacing was chosen. The number of lags chosen for each variogram depends on the data itself One wants to get the most spatial coverage, but too many lags may obscure the structure (Fig. 4.28). AH of these parameters are carefully chosen to yield the most pairwise data points at the first lag distances and to produce the most structure. Generally, 20 or more pairwise data points in the first lag is considered optimal (Isaaks and Srivastava 1989; Davis 1986; Pannatier 1996). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 154 y-axis (north) maximum bandwidth lag lag 3 angular tolerance lagO direction x-axis (east) Fig. 4.28.- Definition sketch of parameters used to construct the directional variogram (after Pannatier 1996). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 155 Variogram Modeling Once an adequate variogram is obtained, one typically fits one of three common models in order to determine the correlation length scale. The three common models used are the exponential, spherical and gaussian. In this study, the spherical model and the exponential model were used because they fit the variograms welL The spherical model is defined by equation 4-3 (Pannatier 1986). In equation 4-3, a is the range and c is the sill value. T(|A|)=c*^A.(|A|)=c*[1.5-^-0.5M2l] (4 _3 ) a a The spherical model behaves linearly at the origin, until the sill is reached at the range. The exponential model is also commonly used to model variograms, and is defined by equation 4-4. r|A|=c»Sp.l*l=c*[l-« ‘ I ('M) Coset A Grain Size Results. The horizontal experimental variogram was calculated using an exponential model with a lag spacing o f 0.2 meters, and the number o f lags is 15. The exponential model for horizontal grain size produced a sill value o f 0.09 and a range o f 0.65 meters (Fig. 4.29). The variogram shows that the correlation length scale occurs at Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 156 a short distance (0.65 meters), which means that there is lack of extensive spatial correlation in this direction. Table 4.29 lists the number o f data pairs for each lag number. The vertical variogram o f grain size shows that there is no discemable range. This is a pure nugget model at the smallest lag, which suggests a correlation length scale that is small than the sampling distance (Fig. 4.30). Lag spacing for the variogram was 0.1 meters, and the number o f lags was 5. The resultant variograms indicate that grain size has a larger correlation length scale in the horizontal direction than in the vertical direction. Table 4.30 is a list o f the number of data pairs for each lag. Permeability Results. The horizontal variogram for permeability was calculated using an exponential model, and shows a similar structure to that o f grain size. The range occurs at 0.87 meters, indicating that both variables are highly variable at short spacial scales (Fig. 4.31). Table 4.31 gives the number o f data pairs for the horizontal permeability lags. The modeled variogram results show similar results to the vertical grain size variogram. The vertical variogram for permeability shows a pure nugget effect, indicating that the correlation length scale is below the scale of the smallest lag. This suggests that sampling should have taken place at a smaller spatial scale (Fig. 4.32). Table 4.32 tabulates the number of pairs for each lag for this variogram. Coset B Grain Size Results. For coset B, the lag spacing chosen for the horizontal variogram was 0.5 meters, and the number of lags is 20. The exponential model gave the most stable variogram with the largest amount of pairwise points for the first lag. The horizontal variogram for grain size shows a similar structure to coset A, however the range is much larger. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 157 7 (l>i|) Direction 0 0.1 0.08 0.06 0.04 0.02 0.4 0.8 1.6 2.4 2.8 IN Fig. 4.29.- Horizontal variogram of grain size: Coset A. Direction 90 0.12 0.1 0.08 0.06 0.04 0.02 J______I______1______1______I______I______I______L. 0 0.06 0.12 0.18 0.24 0.3 0.36 0.42 0.48 |h| Fig. 4.30.- Vertical variogram of grain size: Coset A. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 158 Direction 0 210 180 150 120 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 IN Fig. 4.31.- Horizontal variogram of permeability: Coset A. T(lh|) D irectio n 90 400' 360 320 280 240 200 160 120 80 40 J I 1_____ I------1------1------1------1------L 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 |b| Fig. 4.32.- Vertical variogram of permeability: Coset A. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 159 The correlation length scale is 2.0 meters, suggesting that grain size values are more continuous in the horizontal direction for Coset B than they are for Coset A (Fig. 4.33). This is an important result because Coset B contains larger cross-strata sets. Table 4.33 gives the number o f data pairs for each lag in this variogram. The vertical variogram for this coset was also modeled using an exponential model. Table 4.29.- Number o f data pairs for horizontal variogram: Coset A, grain size Lag# # of Pairs 0 43 1 209 2 259 3 515 4 418 5 408 6 437 7 436 8 664 9 442 10 587 11 615 12 440 13 556 14 362 15 375 The correlation length scale for the vertical variogram is 0.14 meters, which is in the order of the sampling distance (Fig. 4.34). This variogram is similar to the other vertical variograms in that correlation length scales are shorter vertically than they are Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 160 Table 4.30.- Number o f data pairs for vertical variogram: Coset A, grain size Lag # * of Pais 0 49 1 287 2 303 3 343 4 333 5 255 Table 4.31.- Number o f data pairs fo r horizontal variogram: Coset A, permeability Lag # U o f Pairs 0 36 1 282 2 393 3 448 4 559 5 565 6 822 7 656 8 678 9 672 10 672 II 779 12 857 13 797 14 868 15 915 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 161 Table 4.32.- Number of data pairs for vertical variogram: Coset A, permeability Lag# # ofPaira 0 36 1 282 2 393 3 448 4 559 5 565 horizontally. This suggested geometry o f grain size and permeability matches well with the stratal geometry o f the Oyster sediments. The lag spacing for this variogram was 0.1 meters, and the number of lags equaled 5 (Table 4.34). Permeability Results. The permeability correlation structure for coset B is similar to coset A in that a great amount o f variability exists at small spatial scales. The correlation length scale is 0.62 meters, which is smaller than the average set width for coset B (Fig. 4.35). The variogram statistic Y (h) is quite large for all of the permeability variograms compared to those o f grain size. Table 4.35 gives the number o f data pairs for each lag. Lag spacing is 0.2 meters, and the number o f lags is 15. The vertical variogram o f permeability for this coset was modeled using an exponential fit, and shows a small correlation length scale of 0.25 meters. The number o f lags for this variogram is 11, with a lag spacing o f 0.1 meters (Fig. 4.36). Table 4.36 shows the number o f data pairs for each lag. Coset C Grain Size Results. The horizontal variogram of grain size for coset C was modeled using an exponential fit Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. r (IN) Direction 0 0.32 0.28 0.24 0.16 0.12 0.08 0.04 -► 0 1 2 3 4 5 6 7 8 9 10 |h| Fig. 4.33.- Horizontal variogram o f grain size: Coset B. 7 (|h|) Direction 90 0274- 0 2 4 - 0 2 1 i 0.18 - 0.15 - 0.12 - 0.09 0.06 0.03 0 0.07 0.14 0.21 028 0.35 0,42 049 0.56 0u63 |h| Fig. 4.34- Vertical variogram o f grain size: Coset B. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Direction 0 1.2 1 m 0.8 0.6 0.4 0.2 0 0 0.5 1 1.52 2.5 3 3.5 4 IN Fig. 4.35.- Horizontal variogram of permeability: Coset B. / r(|h|) Direction 90 2000'L 1800 - 1600 1400 1200 1000 800 600 400 200 0 0.2 0.4 0.6 0.8 1 M Fig. 4.36.- Vertical variogram of permeability: Coset B. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 164 The exponential variogram revealed a correlation length scale of 0.97 meters, with a sill at 0.05. There are much less data points in this coset, therefore, an angular tolerance of 30 degrees was used. Also noticeable is the poorer modeling of the data in this coset due to the lower number of data points (Fig. 4.37). The lag spacing is at 0.2 meters and the number of lags is 9 (Table 4.37). Table 4.33.- Number o f data pairsfo r horizontal variogram: Coset B, grain size Lag# # o f Pairs 0 334 i 961 2 1232 3 1426 4 1SI6 S 1079 6 961 7 1387 8 1405 9 795 10 661 II 790 12 676 13 448 14 265 IS 600 16 398 17 264 18 4275 19 500 20 206 The vertical variogram of gram size yielded for coset C indicates a possible linear trend. This is important because coset C contains a finning upwards sequence. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 165 Table 4.34.- Number o f data pairs for vertical variogram: Coset B, grain size BEaBaBBEanHBBBaHHHBBBM BaM anB Lag I # of Pairs 0 76 1 164 2 133 3 (13 4 S7 5 82 Table 4.35.- Number o f data pairs for horizontal variogram: Coset Br permeability Lag# # of Pairs 0 337 1 1384 2 1963 3 2168 4 2062 S 2266 6 2209 7 2270 S 2325 9 2222 10 2178 11 1908 12 I6S3 13 1S48 14 1458 IS 1330 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 166 Table 4.36.- Number o f data pairs for vertical variogram: Coset B. permeability Lag * H o f Pans 0 439 1 676 2 1223 3 1346 4 1211 5 1082 6 978 7 872 8 360 9 170 10 9 11 5 Table 4.37.- Number o f data pairs fo r horizontal variogram: Coset C. grain size Lag U It o f Pain 0 34 I 37 2 72 3 33 4 50 5 53 6 35 7 27 8 16 9 48 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 167 The lag spacing is 0.1 meters, with six lags (Fig. 4.38). Again, due to the small sample size the variogram model is not as strong as it is for cosets A and B, and in this case a model was not fit to the variogram. Table 4.38 gives the number o f data pairs for this variogram. Permeability Results. The horizontal variogram for permeability of coset C was constructed using a spherical model, which reveals a correlation length scale of 1.9 meters, with a lag spacing of 0.1 meters and 12 lags. This is a larger correlation length scale for permeability than either coset A or B (Fig. 4.39). One should notice that the number of data pairs is significantly less than variograms o f the other cosets (Table 4.39). The vertical variogram of permeability for this for this coset was also modeled using a spherical fit. The spherical model for the vertical variogram for coset C revealed a similar correlation length scale to that o f coset B (Fig. 4.40). The correlation length scale is 0.23 meters, the lag spacing is 0.1 and the number of lags 5 (Table 4.40). Table 4.38.- Number o f data pairs fo r vertical variogram: Coset C, grain size Lag# # of Pans 0 19 1 56 2 37 3 28 4 40 5 19 6 7 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 168 Direction 0 0.081 0.072 0.063 0.054 0.045 0.036 0.027 0.018 0.009 ► 0 0.6 1.2 1.8 2.4 3 3.6 4.2 4.8 |h| Fig. 4.37.- Horizontal variogram of grain size: Co set C. y (IN) Direction 90 i 0.081 0.072 0.063 0.054 0.045 0.036 0.027 0.018 0.009 0 • I J ______I______I______I______l______L 0.07 0.14 0.21 0.28 0.35 0.42 0.49 0.56 IN Fig. 4.38.- Vertical variogram of grain size: Coset C. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 169 r (IN) Direction 0 / 1 210 180 150 120 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 IN Fig. 4-39.- Horizontal variogram o f permeability: Coset C Direction 90 420 360 300 240 180 120 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 IN Fig. 4.40.- Vertical variogram of permeability: Co set C. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 4.39.- Number o f data pairs for horizontal variogram: Coset C, permeability L ag# # ofPaws 0 22 i 215 2 2*5 3 259 4 283 S 281 6 330 7 305 8 314 9 360 10 375 11 460 12 396 Table 4.40.- Number o f data pairs fo r vertical variogram: Coset C, permeability Lag # # of Pairs 0 22 1 215 2 285 3 259 4 283 5 281 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 171 CHAPTER V CONCLUSIONS INTRODUCTION The problem of the study is introduced in Chapter I, and an extensive review of the subject is given. The hypothesis is formulated at the end o f this chapter as welL It is pointed out early in Chapter I that a fundamental concern o f the stratigrapher is to develop predictive models of stratigraphic organization. In sedimentology one of the most significant problems that has yet to be resolved is the feet that there is a lack of quantitative information regarding the relationship between geometry o f beds, thickness o f beds, grain size and sedimentary structures in sandy environments, especially shallow marine deposits. Scientists have also realized the need to correlate quantitative permeability data to sedimentary structures and scales of stratigraphic organization. In engineering this is called the physical heterogeneity o f a deposit The purpose of this study is to investigate the scales o f stratigraphic organization that control the variation of grain size and permeability in shallow marine deposits. A model of stralal architecture is constructed to relate scales of stratigraphic organization to these properties. Stratigraphers typically construct one-dimensional facies models to understand scales of stratigraphic organization. These facies models are used to define the large scale heterogeneity of sedimentary deposits and have recently been used to construct regional ground water models (Anderson 1989). Although fecies models are useful constructs rooted in the physics o f sedimentation, this approach usually requires considerable geologic interpolation, and is often unable to resolve the detailed spatial correlation of primary and secondary textural properties. The construction of fecies models does not Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. provide a means for representing uncertainties in the stratigraphic interpretation in more than one dimension (Johnson et al. 1989; Bridge 1993). Smaller spatial scales are almost entirety ignored in studies that relate reservoir and aquifer fluid properties to stratigraphic organization. I suggest that this practice is inferior to the information that can be obtained by constructing models of stratal architecture to understand the distribution of textural properties. A major goal of the study is to decide if stratigraphic scales smaller than fecies are statistically significant to the distribution of grain size and especially permeability. From the problem outlined above, the hypothesis found that models of stratal architecture are more efficient predictors of grain size and permeability than are fecies models in shallow marine sands. In Chapter II, important questions related to the hypothesis were outlined, and the methods used to test the hypothesis were described in detaiL One of the most important questions investigated in the study is to what extent, are permeability and grain size correlated to set boundaries? Several methods are used to test the hypothesis, including mapping of stratal geometry, measuring stratal characteristics, and the construction fecies distribution through measured sections. These techniques are used to build the stratal architecture of the Oyster Site deposits. Bivariate plots are produced to understand the depositional environment under which the Oyster Site deposits were formed. ANOVA, Tukey-Kramer Means comparison tests and experimental variograms are performed to test the statistical significance of mean grain size and permeability variability over multiple scales of stratigraphic organization. Two major statistical hypotheses are tested with theA N OVA tests. The statistical hypothesis formalized are: (1) Null hypothesis- Mean grain size and permeability o f cosets are equal. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 173 Alternative hypothesis- Mean grain size and permeability of cosets are not equaL (2) Null hypothesis- Mean grain size and permeability of individual sets within a coset are equaL Alternative hypothesis- Mean grain size and permeability of individual sets within a coset are not equaL The Tukey-Kramer Means Comparison Tests determined which cosets and sets are significantly different from one another with respect to grain size and permeability. Horizontal and vertical experimental variograms for each coset are constructed in order to decide the correlation length scales o f grain size and permeability. The correlation length scales are then compared with the scales o f stratigraphic organization as a separate technique from theANOVAS in determining the scale over which the distribution of grain size and permeability are most important. Chapters III and IV contained all o f the results from the study. Chapter III focused on the description of the architecture of the Oyster deposits, whereas Chapter IV summarizes the results o f the geo statistical analysis. In this chapter, I will relate the results from Chapters III and IV to the hypothesis formulated, and explain the significance o f the results. SIGNIFICANCE OF THE OYSTER SITE ARCHITECTURAL RESULTS Facies Architecture The 1996 field campaign revealed three fecies, and one sub-fecies. These fecies are a Cross-stratified sand fecies, a Horizontally stratified sand fecies, and Micro cross stratified sand fecies. The Shelly gravelly sand fecies originally identified during the 1994 field initiative is actually a sub-fecies o f the cross-stratified sand fecies. Facies Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. were identified using a binomial nomenclature based on both grain size and stratal architectural constructs (Fig. 3.9). Measured sections taken at every 2 meters horizontally show that the upper section of the Butlers Bluff member in this exposure consists of continuous Cross-stratified sand fecies and the less continuous Shelly gravelly sub-fecies. The lower section of the Butlers Bluff member contains the Horizontally stratified sand fecies and the Micro cross stratified sand fecies. When comparing the fecies distribution diagrams (Fig. 3.3 through Fig. 3.6) to the stratal architecture maps (Fig. 4.1, through Fig. 4.3), one can clearly see how much information is lost when constructing one-dimensional fecies models. Neither the sections nor the standard geological correlations between sections come close to predicting the actual geometry of the deposits. Certainty, the geometric information gained from erecting a stratal architectural model is fer superior to a one dimensional fecies model when attempting to understand the depositional environment. Also, measurements o f the stratal geometry can be used as parameters that define “real” sedimentary structures in quantitative models of aquifer and petroleum reservoirs. Stratal Architecture Chapter III showed that a modified McKee and Weir classification system can be used to describe the stratal architecture o f the Oyster deposits. In this system, individual lamina organizes to form lamina sets. Lamina sets organize to form genetically related cosets, which organize further to form a composite set (Fig. 1.3). Cosets are analogous to fecies volumes in the Oyster Site (Fig. 3.9). The significance o f this is that by constructing a model of stratal architecture in the Oyster Site, one can now relate the distribution and variability o f grain size and permeability to scales o f stratigraphic Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 175 organization and allow for the hypothesis to be tested. Using the modified classification system o f McKee and Weir, four cosets were recognized in the Oyster Site. Coset A is located in the uppermost section of the Oyster Site and contains the Cross-stratified sand fecies and Shelly gravelly sand sub-fecies. Beneath coset A, is coset B. This coset also contains the Cross-stratified sand fecies and the Shelly-gravelly sand sub-fecies. Coset B is located in tier 2 of the Oyster Site, and contains lamina thicknesses and widths that are generally larger than those in coset A. Again, this is the type of information that is often overlooked when creating one dimensional fecies models. The Shelly gravelly sand sub-fecies are the pebbly lag deposits that are found at the base of the trough shaped cross strata sets. The pebbly lag deposits are formed in scour pockets that contain the coarsest sediments. These scour pockets formed in front o f the linguoid dunes that migrated across the ancestral Chesapeake Bay, and are created by leeside eddies (Smith 1972; Fig. 5.1). Co set C, which is located in the lower part o f the Oyster Site contains the Horizontally stratified sand fecies. Sets are difficult to define in coset C, and are recognized by grain size and color contrasts. Lamina and set widths are very continuous throughout this co set, running wider than the exposure. Sets are also much thicker in Co set C than Cosets A or B. Coset D which is located in the bottom most section of tier 3 of the Oyster Site shows many similarities with cosets A and B. The main differences are that lamina tend to dip at a 10-degree angle rather than 20 degrees, and that a wavy bedding pattern is present. The wavy bedding is probably a diagenetic process, since the water table is close. Another difference is that set widths are much larger in Coset D than they are in A or B. In feet, set widths for this coset most closely resemble Co set C. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 176 Fig. 5.1.- The formation Fig. The 5.1.- formation cross of strata scour sets, notice the formed front in of the migrating dune. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 177 The ease at which the stratal architecture was constructed at this site shows that this method is a generic classification system that enables the researcher to obtain the maximum information from a sedimentary body. I contend that the construction of simple generic models o f stratal architecture are superior to not only one-dimensional fecies models, but to the architectural elements methods o f Miall and the bounding surface numbering o f Brookfield and Allen. The reason for this, is that the stratal architectural model used in this study can be used anywhere without the implication of the depositional environment. Miall’s architectural elements approach can only be used in fluvial systems, and locks the investigator into narrow interpretations (Fig. 1.11). This also holds true for Brookfield’s method, which is used mostly for aeolian deposits. Miall clams that a similar approach can be developed for shallow marine deposits, but why develop several models that can only be used in certain environments when a generic system can be used without imposing a predetermined interpretation. The stratal architectural approach can be applied uniformly to all environments unlike Miall’s or Brookfield’s approach (Bridge 1993; Miall 1988; Brookfield 1977). Vertical patterns of set thickness show a decrease upwards from the Lower Butlers Bluff Member (Co set C) to the Upper Butlers Bluff Member (Co set A). A vertical decrease in set thickness indicates that the water depth in which these sediments were deposited was decreasing from Co set C to Co set A, and supports the theory that the Butlers Bluff member represents the progradation of the Nassawadox Spit across an ancestral Chesapeake Bay (Allen 1988; Fig. 3.26 through Fig. 3.30). Co set C and D are the distal environment, whereas Co sets A and B represent the proximal environment along a dispersal path in the ancestral Chesapeake Bay. Vertical patterns of grain size Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 178 within the architectural framework of the Oyster Site suggests a complex two-fold nested trend. From the base of Coset C to the top of Coset A, (Lower Butlers Bluff to Upper Butlers Bluff Member) a coarsening upward sequence o f mean grain size exists. Coarsening upward sequences of grain size are also indicative o f a prograding shoreline (Fig. 3.34). Within individual cross strata sets, a weak fining upward sequence o f mean grain size exists (Fig. 3.31 through Fig. 3.33). This pattern is the result of grain sorting due the grains avalanching over ripple crests. As ripples or dunes migrate across the sea floor, sediment accumulates on the lee side building up the crest. The ripple actually migrates as sediment cascades down the stoss side of the bedform. During this process the coarser grains settle fester than the finer grains, therefore, the finer grains are deposited higher up in the avalanching lamina. Between successive avalanching episodes, grains settle out o f suspension on the stoss side of the ripple. This entire process creates the alternating coarse and fine lamina pattern exhibited in the Oyster Pit sediments (Jopling 1963; Allen 1984). Progressive Sorting on the Nassawadox Shoreface General. To understand the architectural results of the Oyster She fully, h is necessary to understand the processes in which fecies or cosets were formed. Facies are typically defined by horizontal grain size gradients in the order of meters to kilometers, and by vertical grain size variations on the scale o f millimeters to centimeters. Several authors describe “cook-book” rules for applying fecies models and erecting fecies schemes (Reading 1978; Walker 1989; Miall 1990). Articles addressing fecies and fecies models rarely show any insight as to the dynamics responsible for fecies differentiation. Swift et aL (1991a) has pointed out that in shallow marine settings, fecies are produced Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 179 during sediment dispersal by the combined processes of progressive sorting and stratal condensation. During the progressive sorting process, facies become differentiated as sediment moves down the dispersal pathway in response to episodic transport events such as storms. Russel (1939) recognized that in such settings the competence o f the transporting agent would decrease downstream as a result of the fluid power gradient. As a consequence of the decreasing competence, the coarsest particles are selectively deposited in the proximal environments. The coarsest particles entrained during episodic events are isolated in the sole of the bed formed as the current wanes. If the next event is less intense, then only the upper portion o f the bed will be re-suspended or re entrained. Therefore, over time, finer sediments are preferentially bypassed to downstream environments, and grain size will vary from proximal to distal locations along the dispersal pathway. Beds or lamina in the proximal environments retain the coarsest particles due to the energetic environment, whereas, finer grained beds and lamina are deposited in distal environments (Fig. 5.2). This process leads to stratal condensation (Swift et a l 1991a). In the proximal environments where fluid power is high, each resuspension event tends to strip o ff the fine caps o f the previous event. Therefore, only the truncated bases of the beds deposited by the rare intense events are preserved. This leads to a coarse stratally condensed deposit in which thick lam ina or beds are preserved. In proximal environments cross-stratified deposits are common due to the feet that most sediment in traveling as bedload. As the fluid power decreases down the dispersal path, bed successions become less condensed as the finer caps are preserved from each event. In the far distal environment sediment source becomes a factor. The coarse sands have been left behind, and only the finest sand, silt and clay is Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 180 Proxim al Distal S tation S tation T1 \ M T2 Fig. 5.2.- The progressive sorting mechanism acting through time steps T1-T3 (after Swift etal. 1991a). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 181 left. This causes another condensed section in the far distal environment because individual beds are difficult to differentiate. Lamina or beds in this environment are typically either laminated or bioturbated (Swift et aL 1991a). Swift et aL (1991b) illustrates the textures and structures that are the result of the progressive sorting process in shallow marine settings (Fig. 5.3). We see can the same processes working on the Nassawadox shelf. Sand moved along the oceanward side of the spit in a storm driven pulses in a narrow (100m wide) zone of shoaling and breaking waves. During peak flow events, rip currents expelled fluid and sand from the surf zone, and sand rained out on the shorefece. Washed residue retained by the surf zone was medium to coarse, pebbly sand, while the winnowed fraction deposited on the shoreface consisted o f fine sand (Fig. 5.4). This is an example of progressive sorting, and has led to the fecies differentiation and the stratal architecture o f the Oyster Site. Progressive sorting has induced further effects. Medium and coarse sand travels as bed load, and bed load transport is accomplished entirely by migrating bedforms (ripples, dunes). These migrating bedforms deposit sediment into a characteristic cross stratification patten (Collison and Thompson 1982; Fig. 5.1), therefore the medium sand fecies is a cross stratified fecies (Coset A and B). The fine sand rains out of suspension in the distal environment to form horizontally layered strata sets as the current wanes. Therefore, the fine sand fecies is a horizontally stratified fecies (Coset C). In our case, small bodies of the Cross Stratified, medium Sand fecies, and the Shelly-gravelly coarse Sand fecies are intimately admixed. In feet, the Shelly-gravelly sand facies are analagous to Swift’s lag strata from the Mesaverde Sandstone (see Fig. 5.3). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced Fig. S.3.- Textures and structures o f depositional systems that have undergone undergone have that systems f depositional o structures and S.3.- Textures Fig. rgesv otn atrSite l 1991b). al. et Swift (after sorting progressive PHI OIAMETER 7 0.0 2.0 (.0 - i - ^ 1.0 CROSS-STRATA a Beds Lag + Cr s— r a ta tra —S ss ro C ■ GRADED STRATA GRADED ts e S G rad ed and and ed rad G umcy ds ed B Hummocky SETS * H SADR OEVIATION STANDARD PHI / . •*ve-'O*.- 0.5 _ PROGRESSIVE INITIAL SORTING TREND Y K C O M M U H STRATA IGE EVENT, SINGLE ROO / GRAOEO STRATA HUMMOCKY STRATA STRATA -*'7 .0 0 /CROSS-STRATA/ l I 9 I SETS SETS I , PROGRESSIVE SECONOARY SORTING TREND MULTLEVENT STRATA STRATA G A L t i STRATA t LAG 182 Shelly Gravelly Facies A Cross-Stratified Facies Coarse Horizontally Stratified Facies B AtSdbpopulallone SafcaHon Deposit (Sand) BisubpopdaUon: SuspersionDepost (sand) CSUbpopdaHon; Traction Depost (Gravel) Fig. 5.4.- Progressive sorting on the Nassawadox shoreface. 184 The progressive sorting process is distinctly illustrated in the bivariate plots constructed o f textual properties. A significant linear relationship exists between mean grain size and sorting, which shows the segregation of the Horizontally stratified sand facies from the other three (Fig. 4.4). Notice how closely Fig. 4.4 resembles Fig. 5.3. Bivariate plots of mean grain size vs. % gravel, sorting vs. % gravel, and even grain size vs. permeability is indicative of the progressive sorting process at work on the Nassawadox shoreface (Fig. 4.6 and Fig. 4.9). Mean grain size shows a weak but significant linear relationship to permeability. This indicates that other factors control permeability and grain size. Interestingly, sorting shows almost no relationship to permeability. Grain packing most likely has the most significant effect permeability. However, this is beyond the scope o f the research. One of the most significant results from the bivariate plots is the relationship between set thickness and mean grain size. Mean Grain Size vs. Set Thickness. The relationship between set thickness and grain size was investigated at the Oyster Site. Previous work by Schwarzacher (1953) suggests that a positive linear relationship between bed thickness and median grain size exists. The R2 of this relationship is 0.34. This demonstrates a weak but significant relationship between the two variables. In a paper by Scheidegger and Potter (1967), the same data are used and a log-log plot is created. The coefficient of correlation was not reported, but it is obviously the same as the previous study. The authors of this study claim that larger sand wave heights are associated with greater turbulence, therefore allowing coarser grains to be transported. On the surface this idea may sound good, but some problems exist. The idea that as ripple or dune height increases, the turbulence increases causing a more competent flow suggests that dune height directly affects the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 185 grain size o f a deposit. If turbulence is so great, then a significant amount o f scouring must be occurring, so how can thick deposits be formed? Since grain size directly affects the transporting mode of a sediment, does Scheidegger and Potter’s statement realty make sense? It seems more likely that grain size would affect dune height, not the other way around. The relationship between set thickness and mean grain size was studied further at the Oyster Site. Both cross-bedded deposits and horizontally stratified deposits were used in the study. Figure 4.10 shows that a non linear relationship exists between these two variables. In fact, the relationship is parabolic and the R2 is considerably higher (0.5) then that of Schwarzacher. The parabolic relationship found between grain size and set thickness is significant at the 99% confidence level One could probably fit the same parabolic curve to Schwarzacher’s data and produce similar results as was found at the Oyster Site. The relationship also shows that aminimum occurs at 1.5 phi or 0.35mm. The parabolic relationship recognized between mean grain size and set thickness has a familiar shape to sedimentologists. The curve is sim ilar to the well- known HjOlstrom curve that relates current velocity necessary for erosion and grain size (Fig.5.5). The HjOlstrom curve illustrates that the coarsest and finest grain sizes are the most difficult to erode. The minimum point on this diagram occurs at 0.35mm or 1.5 phi. Sand grains whose size is between 0.1mm and 0.2mm are the most mobile, and usually only require a velocity of about 0.3 m/s to be transported (Seibold and Berger 1982). In comparison, the relationship between set thickness and mean grain size shows that the minimum occurs at about the same grain size. This suggests that the coarsest and finest sands produce the thickest deposits. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced Velocity, in centimeter* per second 2000 Ooo999 00 q p o o o 0 0o Op Oo O o op O OOp o o O v o - . - «o" e cv r Clay C - (after Seiboki and Berger 1982). Berger and Seiboki (after Fig. 5.5.- Hjulstrom curve, relating grain size to velocity velocity to size grain relating curve, Hjulstrom 5.5.- Fig. e e a r n « coeoo o o pop o o ooo o o 000 o o ooo o o pop o coeoo o « n r a e e Gram sue. in millimetersin sue. Gram ...... EROSION 0 _ o 0 0 - n e eiaio o o 000 o o 000 o o 000 o o eiaio e n - 0 0 o DO O O OOO O O O O However, unlike the HjQlstrom, the relationship found between set thickness and mean grain size is not caused by electrostatic forces. Instead, the parabolic relationship found between set thickness and mean grain size is the result o f the coupled processes of progressive sorting and stratal condensation. This makes more sense than a linear relationship because o f the Hjtilstrom relationship. In the proximal environment of a dispersal system, the coarsest sediment moves as bedload forming ripples and dunes as well as coarse lag deposits. Therefore thick deposits are preserved, since the coarse particles are difficult to erode. The finer sediments are carried down the dispersal system, following the fluid power gradient. Since grain sizes between 0.1 and 0.2 mm are the easiest to erode, only thin deposits are preserved with these grain sizes. At the distal end of the dispersal system, the finest sands are deposited as the current wanes. Once these grains are deposited they are much more difficult to suspend then they were to carry. Thus, thick deposits are also preserved. This suggests that the relationship between mean grain size and set thickness is the evolutionary consequence o f the progressive sorting and stratal condensation processes. In feet, the process o f progressive sorting necessitates the parabolic relationship found between grain size and set thickness, not a linear one. SIGNIFICANCE OF ANOVA RESULTS Results o f the ANOVA test and the Tukey-Kramer Mean Comparison test indicate that Cosets are significantly different from one another with respect to grain size and permeability (Fig. 4.13 and Fig. 4.19). This comes as no surprise because Co sets are analogous to fecies volumes we should expect to see significant differences between fecies. More importantly, the ANOVA results clearly show that individual sets can be Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. distinguished from one another with respect to grain size and permeability as well (Fig. 4.20 through Fig. 4.27). In fact, the mean comparisons test show that more than one set is significantly different from one another within each Co set, indicating that set grain size and permeability is an important stratigraphic scale and mappable. The ANOVA tests prove that grain size and permeability variability is significant over multiple scales of stratigraphic organization. Also, another important result from the means comparisons tests are the recognizable patterns o f sets in a coset that are significantly different. Those sets that are significantly different from one another with respect grain size are usually significantly different with respect to permeability. Careful examination of the means comparisons results for each coset reveals that in general, sets occurring at the top of a particular coset are significantly different from sets occurring in the middle of the coset but not to each other. Also, sets occurring at the base o f a coset are significantly different from those at the middle, but not to each other. Finally, sets at the base may or may not be significantly different from those at the tops o f a coset (Table 4.14; Fig. 4.1). This pattern occurs in all four cosets, and suggests that yet another scale o f stratigraphic organization is operating here that is also important to grain size and permeability variations. For historical purposes I will can this the bed scale. Therefore, in the Oyster Site of the Butlers Bhiff Member the stratal architecture containslamina that build lamina sets. Lamina sets build beds, and beds build cosets. One should recognize immediately that the stratigraphic organization described above actually more closely resembles Campbell’s classification system (Table 1.7). Therefore, the mean comparisons test proved that not only are individual sets significant with respect to grain size and permeability distributions, but that the preferred stratal architectural Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 189 classification system may be Campbell's instead o f McKee and Weir. SIGNIFICANCE OF VARIOGRAM RESULTS Variograms are constructed as an independent test of the scale of stratigraphic organization at which grain size and permeability demonstrate the most variability. Results from the variograms indicate that for both grain size and permeability the correlation length scales were always smaller than set widths or thicknesses. This held true for each coset tested. The horizontal correlation length scale for grain size was typically around 0.6 meters except for Coset B. Coset B has a correlation length scale for grain size o f 2.0 meters (Fig. 4.33). Average set widths for Co sets A and B is 5 meters. Vertical correlation length scales for grain size and permeability were always less than set thicknesses. The variogram results indicate that grain size and permeability exhibit a high degree o f spatial variability. Since correlation length scales were always less than set widths and thicknesses, one can infer that the lamina scale is also significant with respect to the spatial variability o f grain size and permeability. Actually, the lamina scale is probably the most significant stratigraphic scale for understanding the distribution of grain size and permeability because o f the small correlation length scales. GENERAL CONCLUSIONS TheANOVA test, means comparisons test and the variograms all prove that multiple levels o f stratigraphic organization are statistically significant with respect to the spatial variability o f grain size and permeability, and the one-dimensional facies models are clearly unable to resolve these important stratigraphic scales. This study clearly shows that models o f stratal architecture are more efficient predictors of grain size and permeability than are fecies models in shallow marine deposits. Traditional methods Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 190 such as coring and log studies can only develop lithofacies models that can not duplicate the complexities of the geologic framework. The stratal architectural model is more than just a nomenclature for stratigraphic organization, for it actually defines the shape and scale o f sedimentary deposits at multiple scales. Knowledge of the shape and scale o f the sedimentary structures over several stratigraphic scales will aid in the prediction local deviations from regional groundwater and petrophysical models because the geological complexity can be built into the models. The study also suggests that a simple generic model of stratal architecture is a better approach to the understanding of sedimentary deposits and their associated textural properties than environment specific complex architectural element or bounding surface numbering approaches, because it does not require one to approach the outcrop with a predefined genetic interpretation for each bounding surface. Bivariate plots o f textural properties indicate that progressive sorting shaped the stratal architecture of the Oyster Site in the Butlers Bluff Member. A parabolic relationship was discovered to exist between mean grain size and set thickness, and is thought to be the evolutionary consequence of the progressive sorting process. FUTURE RESEARCH Suggestions for future research on this subject include a detailed investigation of grain size and permeability on the lamina scale by using small box cores. Also, the third dimension (set length) should be fully measured and mapped in order to fully describe the three-dimensional architecture of shallow marine deposits. Unfortunately this was not possible during this study. I also suggest measuring the spatial variation of permeability in two directions (width and length) to determine how much the internal geometry o f sedimentary deposits control the permeability structure. Finally, the relationship between Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 191 set thickness and mean grain size should be investigated to see if it really is a universal relationship to all sedimentary environments. Reproduced with permission of the copyright owner. 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V a n W a g o n e r J .C ., P o s am e n t ie r J L W., M ttchum J L M , V a il J ’.R ., Sa r g J.F., Loimr,T.S., H a rd en B o l J . , 1988, An Overview of the Fundamentals of Sequence Stratigraphy and Key Definitions: in Seal-Level Changes - An Intergrated Approaches, SEPM Special Publication n. 42. W a l k e r , R.W., 1989, General Introduction: Facies, Facies Sequences and Facies Models: in, Roger W. Walker, ed Facies Models, Second Edition, Geoscience Canada Reprint Series 1, p. 1-9. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 198 VITA Andrew C. Muller 2052 East 37 Street Brooklyn, NY 11234 EDUCATION Ph.D., Oceanography, May 1999 Old Dominion University, Department of Ocean, Earth and Atmospheric Sciences, Norfolk, VA 23529 M.S., Oceanography, August 1992 Old Dominion University, Department of Oceanography, Norfolk, VA 23529 B.S., Earth Science, May 1989 Adelphi University, Department o f Earth Science, Garden City, NY 11530 TEACHING EXPERIENCE Visiting Assistant Professor, August 1998 to August 1999 Millersville University, Department of Earth Sciences, Millersville, PA 17603 Co-Instructor, Coastal Oceanography of Virginia I and n , 1992 to 1997 Old Dominion University, Department of Oceanography, Norfolk, VA 23529 Graduate Teaching Assistant, Introduction to Oceanography, 1991 to 1994 Old Dominion University, Department of Oceanography, Norfolk, VA 23529 RESEARCH EXPERIENCE Graduate Research Assistant, August 1989 to July 1998 Old Dominion University, Department of Oceanography, Norfolk, VA 23529 Visiting Researcher, June 1993 to August 1993 Bedford Institute o f Oceanography, Dartmouth, Nova Scotia, Canada B2 Y 4A8 Reproduced with permission of the copyright owner. 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