1. Elements of Map-Scale Structure ............................. 1
1.1. Introduction .............................................. 1
1.2. Representation of a Structure in Three Dimensions ......... 1
1.2.1. Structure Contour Map ............................. 3
1.2.2. Triangulated Irregular Network .................... 3
1.2.3. Cross Section ..................................... 3
1.3. Map Units and Contact Types ............................... 4
1.3.1. Depositional Contacts ............................. 5
1.3.2. Unconformities .................................... 6
1.3.3. Time-Equivalent Boundaries ........................ 6
1.3.4. Welds ............................................. 7
1.3.5. Intrusive Contacts and Veins ...................... 7
1.3.6. Other Boundaries .................................. 8
1.4. Thickness ................................................. 8
1.5. Folds ..................................................... 9
1.5.1. Styles ............................................ 9
1.5.2. Three-Dimensional Geometry ....................... 13
1.5.3. Mechanical Origins ............................... 15
1.6. Faults ................................................... 18
1.6.1. Slip ............................................. 19
1.6.2. Separation ....................................... 20
1.6.3. Geometrical Classifications ...................... 20
1.6.4. Mechanical Origins ............................... 22
1.6.5. Fault-Fold Relationships ......................... 24
1.7. Sources of Structural Data and Related Uncertainties ..... 26
1.7.1. Direct Observations .............................. 26
1.7.2. Wells ............................................ 27
1.7.3. Seismic Reflection Profiles ...................... 30
2. Location and Attitude ...................................... 33
2.1. Introduction ............................................. 33
2.2. Location ................................................. 33
2.2.1. Map Coordinate Systems, Scale, Accuracy .......... 33
2.2.2. Geologic Mapping in 3-D .......................... 36
2.2.3. Wells ............................................ 37
2.3. Orientations of Lines and Planes ......................... 41
2.3.1. Stereogram ....................................... 44
2.3.2. Natural Variation of Dip and Measurement
Error ............................................ 46
2.3.3. Tangent Diagram .................................. 47
2.4. Finding the Orientations of Planes ....................... 49
2.4.1. Graphical Three-Point Problem .................... 50
2.4.2. Analytical Three-Point Problem ................... 52
2.5. Apparent Dip ............................................. 53
2.6. Structure Contours ....................................... 54
2.6.1. Structure Contours from Point Elevations ......... 54
2.6.2. Structure Contours from Attitude ................. 55
2.6.3. Dip from Structure Contours ...................... 55
2.7. Intersecting Contoured Surfaces .......................... 55
2.8. Derivation: Tangent Diagram on a Spreadsheet ............. 57
2.9. Exercises ................................................ 57
2.9.1. Interpretation of Data from an Oil Well .......... 57
2.9.2. Attitude ......................................... 58
2.9.3. Attitude from Map ................................ 59
3. Structure Contouring ....................................... 63
3.1. Introduction ............................................. 63
3.2. Structure Contouring ..................................... 63
3.3. Structural Style in Contouring ........................... 65
3.3.1. Equal Spacing .................................... 66
3.3.2. Parallel ......................................... 66
3.3.3. Interpretive ..................................... 66
3.3.4. Smooth vs. Angular ............................... 67
3.4. Contouring Techniques .................................... 68
3.4.1. Choosing the Neighboring Points: TIN or Grid? .... 69
3.4.2. Triangulated Irregular Networks .................. 70
3.4.3. Interpolation .................................... 72
3.4.4. Adjusting the Surface Shape ...................... 75
3.5. Mapping from Profiles .................................... 76
3.6. Adding Information to the Data Base ...................... 78
3.6.1. Bedding Attitude ................................. 78
3.6.2. Projected and Composite Surfaces ................. 79
3.6.3. Fluid-Flow Barriers .............................. 84
3.7. Exercises ................................................ 85
3.7.1. Contouring Styles ................................ 85
3.7.2. Contour Map from Dip and Elevation ............... 86
3.7.3. Depth to Contact ................................. 86
3.7.4. Projected-Surface Map ............................ 87
4. Thickness Measurements and Thickness Maps .................. 89
4.1. Thickness of Plane Beds .................................. 89
4.1.1. Universal Thickness Equation ..................... 89
4.1.2. Thickness between Structure Contours ............. 92
4.1.3. Map-Angle Thickness Equations .................... 94
4.1.4. Effect of Measurement and Mapping Errors ......... 95
4.2. Thickness of Folded Beds ................................. 98
4.2.1. Circular-Arc Fold ................................ 98
4.2.2. Dip-Domain Fold ................................. 100
4.3. Thickness Maps .......................................... 100
4.3.1. Isopach Maps .................................... 101
4.3.2. Isocore Maps .................................... 102
4.4. Derivation: Map-Angle Thickness Equations ............... 104
4.5. Exercises ............................................... 106
4.5.1. Interpretation of Thickness in a Well ........... 106
4.5.2. Thickness ....................................... 106
4.5.3. Thickness from Map .............................. 106
4.5.4. Isopach Map ..................................... 106
5. Fold Geometry ............................................. 109
5.1. Introduction ............................................ 109
5.2. Trend from Bedding Attitudes ............................ 109
5.2.1. Cylindrical Folds ............................... 109
5.2.2. Conical Folds ................................... 111
5.2.3. Tangent Diagram on a Spreadsheet ................ 114
5.2.4. Example Using a Tangent Diagram ................. 115
5.2.5. Crest and Trough on a Map ....................... 116
5.3. Dip Domain Fold Geometry ................................ 117
5.4. Axial Surfaces .......................................... 119
5.4.1. Characteristics ................................. 119
5.4.2. Orientation ..................................... 122
5.4.3. Location in 3-D ................................. 124
5.5. Using the Trend in Mapping .............................. 125
5.6. Minor Folds ............................................. 126
5.7. Growth Folds ............................................ 129
5.8. Exercises ............................................... 130
5.8.1. Geometry of the Sequatchie Anticline ............ 130
5.8.2. Geometry of the Greasy Cove Anticline ........... 130
5.8.3. Structure of a Selected Map Area ................ 131
6. Cross Sections, Data Projection and Dip-Domain Mapping .... 133
6.1. Introduction ............................................ 133
6.2. Cross-Section Preliminaries ............................. 133
6.2.1. Choosing the Line of Section .................... 133
6.2.2. Choosing the Section Dip ........................ 136
6.2.3. Vertical and Horizontal Exaggeration ............ 137
6.3. Illustrative Cross Sections ............................. 142
6.3.1. Construction by Hand or with Drafting
Software ........................................ 142
6.3.2. Slicing ......................................... 144
6.4. Predictive Cross-Section Construction ................... 145
6.4.1. Dip-Domain Style ................................ 146
6.4.2. Circular Arcs ................................... 153
6.5. Changing the Dip of the Section Plane ................... 159
6.6. Data Projection ......................................... 160
6.6.1. Projection Along Plunge ......................... 162
6.6.2. Projection by Structure Contouring .............. 168
6.7. Dip-Domain Mapping from Cross Sections .................. 169
6.8. Derivations ............................................. 172
6.8.1. Vertical and Horizontal Exaggeration ............ 172
6.8.2. Analytical Projection along Plunge Lines ........ 173
6.9. Exercises ............................................... 176
6.9.1. Vertical and Horizontal Exaggeration ............ 176
6.9.2. Cross Section and Map Trace of a Fault .......... 176
6.9.3. Illustrative Cross Section from a Structure
Contour Map 1 ................................... 176
6.9.4. Illustrative Cross Section from a Structure
Contour Map 2 ................................... 177
6.9.5. Illustrative Cross Section from a Structure
Contour Map 3 ................................... 177
6.9.6. Predictive Dip-Domain Section ................... 177
6.9.7. Predictive Cross Sections from Bedding
Attitudes and Tops .............................. 179
6.9.8. Fold and Thrust Fault Interpretation ............ 179
6.9.9. Projection ...................................... 179
7. Properties of Faults ...................................... 181
7.1. Introduction ............................................ 181
7.2. Recognition of Faults ................................... 181
7.2.1. Discontinuities in Geological Map Pattern ....... 181
7.2.2. Discontinuities on Reflection Profile ........... 182
7.2.3. Discontinuities on Structure Contour Map ........ 186
7.2.4. Stratigraphic Thickness Anomaly ................. 187
7.2.5. Discontinuity in Stratigraphic Sequence ......... 188
7.2.6. Rock Type ....................................... 190
7.2.7. Fault Drag ...................................... 191
7.3. Unconformities .......................................... 191
7.4. Displacement ............................................ 193
7.4.1. Slip ............................................ 194
7.4.2. Separation ...................................... 196
7.4.3. Heave and Throw from Stratigraphic Separation ... 198
7.5. Geometric Properties of Faults .......................... 200
7.5.1. Surface Shape ................................... 200
7.5.2. Displacement Distribution ....................... 200
7.6. Growth Faults ........................................... 204
7.6.1. Effect on Heave and Throw ....................... 204
7.6.2. Expansion Index ................................. 205
7.7. Fault-Cut Correlation Criteria .......................... 206
7.7.1. Trend and Sense of Throw ........................ 207
7.7.2. Shape ........................................... 208
7.7.3. Stratigraphic Separation ........................ 209
7.7.4. Growth History .................................. 211
7.8. Exercises ............................................... 212
7.8.1. Fault Recognition on a Map ...................... 212
7.8.2. Fault Recognition on a Seismic Line 1 ........... 213
7.8.3. Fault Recognition on a Seismic Line 2 ........... 213
7.8.4. Finding Fault Cuts .............................. 213
7.8.5. Correlating Fault Cuts .......................... 213
7.8.6. Estimating Fault Offset ......................... 214
7.8.7. Fault Offset .................................... 216
7.8.8. Growth Faults ................................... 216
8. Faulted Surfaces .......................................... 219
8.1. Introduction ............................................ 219
8.2. Geometry of a Faulted Surface ........................... 219
8.2.1. Heave and Throw on a Structure Contour Map ...... 219
8.2.2. Stratigraphic Separation from a Structure
Contour Map ..................................... 221
8.3. Constructing a Faulted Marker Horizon ................... 222
8.3.1. Locating the Fault .............................. 223
8.3.2. Joining Offset Marker Surfaces to a Fault ....... 225
8.4. Fault Cutoff Maps and Allan Diagrams .................... 229
8.4.1. Construction .................................... 229
8.4.2. Determination of Fluid Migration Pathways ....... 232
8.4.3. Determination of Fault Slip ..................... 233
8.5. Faults on Isopach Maps .................................. 235
8.6. Displacement Transfer ................................... 237
8.6.1. Relay Overlap ................................... 239
8.6.2. Branching Fault ................................. 240
8.6.3. Splay Fault ..................................... 241
8.6.4. Fault Horse ..................................... 243
8.7. Crossing Faults ......................................... 243
8.7.1. Sequential Faults ............................... 243
8.7.2. Contemporaneous Faults .......................... 251
8.8. Exercises ............................................... 252
8.8.1. Heave and Throw from a Map ...................... 252
8.8.2. Construct the Fault Trace ....................... 252
8.8.3. Construct the Fault Trace ....................... 254
8.8.4. Reservoir Structure ............................. 254
8.8.5. Normal Fault .................................... 255
8.8.6. Reverse Fault ................................... 257
8.8.7. Faults on an Isopach Map ........................ 258
8.8.8. Cutoff Map of Normal Fault ...................... 258
8.8.9. Cutoff Map of Reverse Fault ..................... 258
8.8.10. Fluid Migration across a Fault .................. 258
8.8.11. Thrust-Faulted Fold ............................. 258
8.8.12. Relay Zone ...................................... 258
8.8.13. Branching Fault ................................. 262
8.8.14. Splay Faults .................................... 262
8.8.15. Sequential Faults 1 ............................. 263
8.8.16. Sequential Faults 2 ............................. 263
9. Dip-Sequence Analysis ..................................... 265
9.1. Introduction ............................................ 265
9.2. Curvature Models ........................................ 267
9.3. Dip Components .......................................... 268
9.4. Analysis of Uniform Dip ................................. 270
9.5. Analysis of Folds ....................................... 270
9.6. Analysis of Faults ...................................... 276
9.7. Exercises ............................................... 282
9.7.1. SCAT Analysis of the Sequatchie Anticline ....... 282
9.7.2. SCAT Analysis of Bald Hill Structure ............ 282
9.7.3. SCAT Analysis of Greasy Cove Anticline .......... 282
10. Quality Control ........................................... 285
10.1. Introduction ............................................ 285
10.2. Data Errors and Contouring Artifacts .................... 285
10.2.1. Data Errors ..................................... 285
10.2.2. Edge Effects .................................... 287
10.2.3. Excessive Detail ................................ 288
10.3. Trend Incompatibilities ................................. 289
10.4. Bed Thickness Anomalies ................................. 292
10.4.1. Compatibility between Structure Contour Maps .... 292
10.4.2. Compatibility of Thicknesses on Cross
Sections ........................................ 294
10.4.3. Realistic Growth History ........................ 296
10.5. Unlikely or Impossible Fault Geometries ................. 298
10.5.1. Fault Shape ..................................... 298
10.5.2. Fault Separation ................................ 299
10.5.3. Fault Cutoff Geometry ........................... 301
10.6. Exercises ............................................... 302
10.6.1. Cross-Section Quality ........................... 302
10.6.2. Map Validation .................................. 303
10.6.3. Map and Fault Cut Validation .................... 304
11. Structural Validation, Restoration, and Prediction ........ 305
11.1. Introduction ............................................ 305
11.2. Restoration and Balance ................................. 308
11.2.1. Boundaries ...................................... 308
11.2.2. Palinspastic vs. Geometric Restoration .......... 309
11.2.3. Sequential Restoration .......................... 311
11.3. Strain and Strain Partitioning .......................... 314
11.4. Area-Balance Methods .................................... 316
11.4.1. Area Restoration ................................ 316
11.4.2. Depth to Detachment and Layer-Parallel Strain ... 317
11.4.3. Area-Depth Relationship of Locally Balanced
Structures ...................................... 319
11.4.4. Area-Depth Relationships of Regionally
Balanced Structures ............................. 322
11.4.5. Applications .................................... 325
11.5. Rigid-Body Displacement ................................. 328
11.5.1. Restoration ..................................... 328
11.5.2. Domino-Block Predictive Model ................... 329
11.5.3. Circular-Fault Predictive Model ................. 331
11.6. Flexural-Slip Deformation ............................... 334
11.6.1. Restoration ..................................... 335
11.6.2. Fault Shape Prediction .......................... 340
11.6.3. Flexural-Slip Kinematic Models .................. 341
11.7. Simple-Shear Deformation ................................ 344
11.7.1. Restoration ..................................... 344
11.7.2. Fault Shape Prediction Techniques ............... 350
11.7.3. Sensitivity of Prediction ....................... 353
11.7.4. Layer-Parallel Strain in Hangingwall ............ 353
11.7.5. Choosing the Best Shear Angle ................... 355
11.8. Fault-Parallel Simple Shear ............................. 360
11.8.1. Restoration ..................................... 360
11.8.2. Fault-Shape Prediction .......................... 360
11.9. Pure Shear Deformation .................................. 362
11.9.1. Vertical-Sided Graben Model ..................... 362
11.9.2. Normal-Fault Bounded Graben Model ............... 362
11.10.Exercises ............................................... 365
11.10.1.Cross-Section Validation and
Interpretation 1 ................................ 365
11.10.2.Cross-Section Validation and
Interpretation 2 ................................ 365
11.10.3.Rigid-Body Restoration .......................... 366
11.10.4.Restoration of the Rhine Graben ................. 366
11.10.5.Flexural-Slip Restoration 1 ..................... 368
11.10.6.Flexural-Slip Restoration 2 ..................... 368
11.10.7.Flexural-Slip Restoration 3 ..................... 368
11.10.8.Balance and Restoration ......................... 368
11.10.9.Predict Fault Geometry .......................... 371
11.10.10.Simple-Shear Restoration ....................... 371
11.10.11.Restoration and Prediction ..................... 371
12. Direction Cosines and Vector Geometry ..................... 373
12.1. Introduction ............................................ 373
12.2. Direction Cosines of Lines .............................. 373
12.2.1. Direction Cosines of a Line from Azimuth
and Plunge ...................................... 374
12.2.2. Azimuth and Plunge from Direction Cosines ....... 374
12.2.3. Direction Cosines of a Line on a Map ............ 375
12.2.4. Azimuth and Plunge of a Line from the
End Points ...................................... 376
12.2.5. Pole to a Plane ................................. 376
12.3. Attitude of a Plane from Three Points ................... 376
12.4. Vector Geometry of Lines and Planes ..................... 377
12.4.1. Angle between Two Lines or Planes ............... 378
12.4.2. Line Perpendicular to Two Vectors ............... 378
12.4.3. Line of Intersection between Two Planes ......... 379
12.4.4. Plane Bisecting Two Planes ...................... 380
References Cited .............................................. 383
Index ......................................................... 393
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