Acknowledgements xvii
Website xix
1 A Framework for Structural Geology 1
1.1 Introduction 1
1.1.1 Deformation 1
1.1.2 Empirical vs. Theoretical Approaches 1
1.1.3 Continuum Mechanics and its Applicability to Structural Geology 6
1.1.4 How to use this Book 6
References 8
2 Structures Produced by Deformation 10
2.1 Geological Structures 10
2.1.1 Structural Fabrics 10
2.1.2 Folds and Boudinage 12
2.1.3 Fractures and Stylolites 15
2.1.4 Faults and Fault Zones 17
2.1.5 Shear Zones 22
2.2 Additional Considerations 25
3 Microstructures 26
3.1 Introduction 26
3.1.1 Overview 26
3.1.2 Framework 27
3.1.3 Imaging of Microstructures 27
3.2 Fractures 28
3.3 Fault Rocks 30
3.4 Overgrowths, Pressure Shadows and Fringes, and Veins 33
3.5 Indenting, Truncating and Interpenetrating Grain Contacts, Strain Caps, and Stylolites 37
3.6 Aligned Grain Boundaries, T Grain Boundaries, and Foam Texture 38
3.7 Undulose Extinction, Subgrains, Deformation and Kink Bands, Deformation Lamellae, Grain Boundary Bulges, and Core-and-Mantle Microstructure 40
3.8 Deformation Twins 43
3.9 Grain Shape Fabrics, Ribbon Grains, and Gneissic Banding 43
3.10 Porphyroblasts 47
3.11 Crystallographic Fabrics (Crystallographic Preferred Orientations) 49
3.12 Shear Sense Indicators, Mylonites, and Porphyroclasts 49
3.12.1 Asymmetric Pressure Shadows and Fringes 53
3.12.2 Foliation Obliquity and Curvature 55
3.12.3 SC, SC′, and SCC′ Fabrics 55
3.12.4 Porphyroclast Systems 56
3.12.5 Precautions with Shear Sense Determination 59
3.13 Collecting Oriented Samples and Relating Sample to Geographic Frames of Reference 60
References 65
4 Displacements 66
4.1 Overview 66
4.2 Chapter Organization 66
4A Displacements: Conceptual Foundation 67
4A.1 Specifying Displacements or Individual Particles 67
4A.1.1 Basic Ideas 67
4A.1.2 Geological Example 69
4A.2 Particle Paths and Velocities 70
4A.2.1 Particle Paths 70
4A.2.2 Velocities 71
4A.3 Displacements of Collections of Particles – Displacement Fields 74
4A.3.1 Displacement Fields 74
4A.3.2 Uniform vs. Nonuniform and Distributed vs. Discrete Displacement Fields 76
4A.3.3 Classes of Displacement Fields 77
4A.4 Components of Displacement Fields: Translation, Rotation, and Pure Strain 79
4A.5 Idealized, Two-Dimensional Displacement Fields 85
4A.5.1 Simple Shear 87
4A.5.2 Pure Shear 88
4A.6 Idealized, Three-Dimensional Displacement Fields 89
4A.7 Summary 90
4B Displacements: Comprehensive Treatment 90
4B.1 Specifying Displacements for Individual Particles 90
4B.1.1 Defining Vector Quantities 90
4B.1.2 Types of Vectors 92
4B.1.3 Relating Position and Displacement Vectors 94
4B.1.4 Characterizing Vector Quantities 95
4B.2 Particle Paths and Velocities 97
4B.2.1 Incremental Displacements for Particles 97
4B.2.2 Particle Paths and Movement Histories 98
4b.2.3 Dated Particle Paths, Instantaneous Movement Directions, and Velocities 99
4B.3 Displacements of Collections of Particles – Displacement Fields 101
4B.3.1 Concept of a Displacement Field 101
4B.3.2 Field Quantities 103
4b.3.3 Gradients of the Displacement Field: Discrete and Distributed Deformation 103
4B.3.4 Idealized Versus True Gradients of the Displacement Field 104
4B.4 The Displacement Gradient Tensor – Relating Position and Displacement Vectors 106
4b.4.1 Components of Displacement Fields: Translation, Rotation, and Pure Strain 107
4B.4.2 Translation Displacement Fields 107
4B.4.3 Rigid Rotation Displacement Fields 107
4B.4.4 Pure Strain Displacement Fields 109
4B.4.5 Total Displacement Fields 110
4b.4.6 Using Displacement Gradient Matrices to Represent Displacement Fields 110
4B.5 Idealized, Two- dimensional Displacement Fields 111
4B.5.1 Simple Shear Displacement Fields 111
4B.5.2 Uniaxial Convergence or Uniaxial Divergence Displacement Fields 113
4B.5.3 Pure Shear Displacement Fields 115
4B.5.4 General Shear Displacement Fields 117
4B.6 Idealized, Three-Dimensional Displacement Fields 117
4B.6.1 Three-Dimensional Simple Shear Displacement Fields 119
4b.6.2 Three-Dimensional Orthogonal Convergence and Divergence Displacement Fields 121
4B.6.3 Pure Shearing Displacement Fields 121
4B.6.4 Constrictional Displacement Fields 122
4B.6.5 Flattening Displacement Fields 123
4B.6.6 Three-Dimensional General Shearing Displacement Fields 124
4B.7 Summary 124
Appendix 4-I: Vectors 124
4-I.1 Simple Mathematical Operations with Vectors 124
4-I.2 Vector Magnitudes 126
4-I.3 Properties of Vector Quantities 126
4-I.4 Relating Magnitude and Orientation to Cartesian Coordinates 127
4-I.5 Vector Products 129
Appendix 4-II: Matrix Operations 130
4-II.1 Defining Matrices 130
4-II.2 Matrix Addition and Subtraction 130
4-II.3 Matrix Multiplication 131
4-II.3.1 Multiplying Two “2 × 2” Matrices 132
4-II.3.2 Multiplying Two “3 × 3” Matrices 132
4-II.3.3 Multiplying a 2 × 2 Matrix Times a 2 × 1 Matrix 133
4-II.3.4 Multiplying a 3 × 3 Matrix Times a 3 × 1 Matrix 133
4-II.3.5 Scalar Multiplication 134
4-II.4 Transpose of a Matrix 134
4-II.5 Determinant of a Square Matrix 135
4-II.6 Inverse of a Square Matrix 135
4-II.7 Rotation Matrices 136
References 137
5 Strain 138
5.1 Overview 138
5.2 Chapter Organization 139
5A Strain: Conceptual Foundation 139
5A.1 Specifying Strain in Deformed Rocks 139
5A.2 One-dimensional Manifestations of Strain 141
5A.2.1 Basic Ideas 141
5A.2.2 Geological Example 142
5A.3 Two-dimensional Manifestations of Strain 143
5A.3.1 Longitudinal Strains in Different Directions 143
5A.3.2 Shear Strain 147
5A.4 Relating Strain to Displacements 151
5A.5 Homogeneous and Inhomogeneous Strain 153
5A.6 Finite Strain Ellipse and Finite Strain Ellipsoid 154
5A.6.1 Finite Strain Ellipse 154
5A.6.2 Finite Strain Ellipsoid 159
5A.7 States of Strain and Strain Paths 163
5A.7.1 States of Strain 163
5A.7.2 Strain Paths and Dated Strain Paths 163
5A.7.3 Coaxial Versus Non-Coaxial Strain Paths 164
5A.8 Instantaneous Strains and Strain Rates 166
5A.9 Infinitesimal Strains 166
5A.10 Summary 167
5A.11 Practical Methods for Measuring Strain 167
5A.11.1 Using Fabrics to Estimate Strain Ellipsoid Shape 167
5A.11.2 Types of Methods for Measuring Strain in Two Dimensions 168
5A.11.3 Measuring Strain in Two Dimensions Using Deformed Markers 169
5B Strain: Comprehensive Treatment 176
5B.4 Relating Strain to Displacements 176
5B.4.1 Longitudinal Strains and Displacement Gradients 177
5B.4.2 Longitudinal Strains and Position Gradients 179
5B.4.3 Relating Displacement Gradients and Position Gradients 179
5B.4.4 Longitudinal Strain in Continuous Deformation 179
5B.4.5 Consequences of Longitudinal Strains 181
5B.4.6 Displacement Gradients and Longitudinal Strains in Different Directions 182
5B.4.7 Position Gradients and Longitudinal Strains in Different Directions 184
5B.4.8 Relating Displacement Gradients and Position Gradients in Two Dimensions 185
5B.4.9 Area Ratios in Two-Dimensional Deformation 186
5B.4.10 Discontinuous Deformation in Two Dimensions 186
5B.4.11 Displacement Gradients and Shear Strains 187
5B.4.12 Shear Strains and Position Gradients 188
5B.4.13 Applying Matrix Algebra to Two-dimensional Deformation 188
5B.4.14 Applying Matrix Algebra to Three-dimensional Deformation 195
5B.5 Homogeneous and Inhomogeneous Deformation 197
5B.5.1 Homogeneous Deformation 197
5B.5.2 Inhomogeneous Deformation 198
5B.6 Finite Strain Ellipse and Finite Strain Ellipsoid 200
5B.6.1 Homogeneous Deformations and the Finite Strain Ellipse 200
5B.6.2 Working with Strain Markers 200
5B.6.3 Finite Strain Ellipsoid 205
5B.7 States of Strain and Strain Paths 205
5B.7.1 States of Strain 205
5B.7.2 Strain Paths 206
5B.7.3 Velocity Gradient Tensor and Decomposition 207
5B.8 Vorticity 210
5B.8.1 Vorticity Vector 211
5B.8.2 Kinematic Vorticity Number 213
5B.9 Summary 213
Appendix 5-I 214
References 216
6 Stress 217
6.1 Overview 217
6A Stress: Conceptual Foundation 218
6A.1 Forces, Tractions, and Stress 220
6A.1.1 Accelerations and the Forces that Act on Objects 220
6A.1.2 Forces Transmitted Through Objects 221
6A.1.3 Traction – A Measure of “Force Intensity” within Objects 221
6A.1.4 Stress 223
6A.2 Characteristics of Stress in Two Dimensions 225
6A.2.1 Normal and Tangential Stress Components 225
6A.2.2 Stresses on Planes with Different Orientations 227
6A.2.3 Principal Stresses and Differential Stress 227
6A.2.4 The Fundamental Stress Equations 231
6A.3 State of Stress in Two Dimensions 233
6A.3.1 The Stress Matrix 233
6A.3.2 The Stress Ellipse 234
6A.3.3 The Mohr circle 235
6A.3.4 Hydrostatic vs. Non-hydrostatic Stress 246
6A.3.5 Homogeneous vs. Inhomogeneous Stress 248
6A.4 Stress in Three Dimensions 248
6A.4.1 The Stress Ellipsoid 251
6A.4.2 Hydrostatic, Lithostatic, and Deviatoric Stresses 251
6A.5 Pore-fluid Pressure and Effective Stress 253
6A.6 Three-dimensional States of Stress 254
6A.7 The State of Stress in Earth 255
6A.8 Change of Stress: Paleostress, Path, and History 256
6A.9 Comparison of Displacements, Strain and Stress 257
6A.10 Summary 259
6A.11 Practical Methods for Measuring Stress 261
6A.11.1 In situ Stress Measurements 261
6A.11.2 Paleostress 268
6B Stress: Comprehensive Treatment 272
6B.1 Force, Traction, and Stress Vectors 272
6B.1.1 Accelerations and Forces 272
6B.1.2 Traction or Stress Vectors 273
6b.1.3 Relating Traction or Stress Vector Components in Different Coordinate Frames 274
6B.1.4 Stress Transformation Law in Two Dimensions and the Mohr Circle 277
6b.1.5 Stress Transformation Law in Three Dimensions and the Mohr Diagram 279
6B.1.6 An Alternative Way to Define Traction or Stress Vectors 281
6B.1.7 Determining Stress Principal Directions and Magnitudes 282
6B.1.8 Stress Invariants 284
6B.1.9 Spatial Variation in Stress 285
Appendix 6-I 289
References 291
7 Rheology 292
7.1 Overview 292
7A Rheology: Conceptual Foundation 293
7A.1 Moving Beyond Equilibrium 293
7A.1.1 Conducting and Interpreting Deformation Experiments 294
7A.1.2 Recoverable Deformation versus Material Failure 297
7A.1.3 Moving from Deformation Experiments to Mathematical Relations 301
7A.2 Models of Rock Deformation 303
7A.2.1 Elastic Behavior 303
7A.2.2 Criteria for Fracture or Fault Formation 308
7A.2.3 Yield and Creep 321
7A.2.4 Viscous Behavior 322
7A.2.5 Plastic Behavior 322
7A.2.6 Constitutive Equations for Viscous Creep and Plastic Yield 324
7A.3 Summary 327
7B Rheology: Comprehensive Treatment 328
7B.1 Combining Deformation Models to Describe Rock Properties 328
7B.2 Rock Deformation Modes 332
7B.2.1 Elasticity 332
7B.2.2 Fracture or Fault Formation 337
7B.2.3 Differential Stress, Pore Fluid Pressure, and Failure Mode 356
7B.2.4 Yield and Creep 359
7B.2.5 Viscous Behavior 360
7B.2.6 Plastic Behavior 363
7B.2.7 Lithospheric Strength Profiles 363
References 364
8 Deformation Mechanisms 367
8.1 Overview 367
8A Deformation Mechanisms: Conceptual Foundation 370
8A.1 Elastic Distortion 371
8A.2 Cataclastic Deformation Mechanisms 373
8A.2.1 Fracture of Geological Materials 373
8A.2.2 Frictional Sliding 376
8A.2.3 Microstructures Associated with Cataclasis and Frictional Sliding 380
8A.2.4 Cataclasis and Frictional Sliding as a Deformation Mechanism 380
8A.3 Diffusional Deformation Mechanisms 380
8A.3.1 Diffusion 380
8A.3.2 Grain Shape Change by Diffusion 385
8A.3.3 Microstructures Associated with Diffusional Mass Transfer 387
8A.3.4 Diffusional Mass Transfer as a Deformation Mechanism 390
8a.3.5 Flow Laws for Three Diffusional Mass Transfer Deformation Mechanisms 391
8A.4 Dislocational Deformation Mechanisms 393
8A.4.1 Dislocations as Elements of Lattice Distortion 393
8A.4.2 Dislocation Interactions 403
8A.4.3 Recovery and Recrystallization 405
8a.4.4 Microstructures Indicative of Dislocation- Accommodated Deformation 409
8A.4.5 Dislocation Glide: A Deformation Mechanism 414
8A.4.6 Flow Law for Dislocation Glide 415
8A.4.7 Dislocation Creep: A Deformation Mechanism 415
8A.4.8 Flow Law for Dislocation Creep 415
8A.4.9 Other Lattice Deformation Processes – Twinning and Kinking 416
8A.5 Diffusion- and/or Dislocation-Accommodated Grain Boundary Sliding 418
8A.6 Deformation Mechanism Maps 419
8A.7 Summary 422
8B Deformation Mechanisms: Comprehensive Treatment 423
8B.1 Cataclastic Deformation Mechanisms 423
8B.1.1 Joints, Fractures, and Mesoscopic Faults 423
8B1.2 Fault Zones 431
8B.2 Diffusional Deformation Mechanisms 448
8B.2.1 Diffusional Mass Transfer Structures 448
8B.2.2 Understanding Diffusion Through Crystalline Materials 453
8B.2.3 The Effect of Differential Stress 455
8B.2.4 Flow Laws for Diffusional Deformation Mechanisms 456
8B.2.5 Paths of Rapid Diffusion – Dislocations and Grain Boundaries 458
8B.2.6 The Effect of Fluid Phases Along Grain Boundaries 459
8B.3 Dislocational Deformation Mechanisms 460
8B.3.1 Origin of Dislocations 460
8B.3.2 Dislocation Movement 461
8B.3.3 Dislocation Interactions 467
8B.3.4 Stresses Associated with Dislocations 470
8B.3.5 Strains Accommodated by the Glide of Dislocations 470
8B.3.6 Constitutive Equations for Dislocation Creep 473
8B.3.7 Recovery, Recrystallization, and Dislocation Creep Regimes 475
8B.3.8 Twinning and Kinking 477
8B.4 Grain Boundary Sliding and Superplasticity 482
Appendix 8-I 484
Appendix 8-II 486
References 487
9 Case Studies of Deformation and Rheology 496
9.1 Overview 496
9.2 Integrating Structural Geology and Geochronology: Ruby Gap Duplex, Redbank Thrust Zone, Australia 497
9.2.1 Geological Setting and Deformation Character 497
9.2.2 Microstructures and Deformation Mechanisms 502
9.2.3 Rheological Analysis Using Microstructures by Comparison to Experimental Deformation 508
9.2.4 Geochronology 508
9.2.5 Evaluating Displacement Through Time 510
9.2.6 Orogenic Development Through Time 512
9.2.7 Summarizing Deformation in the Ruby Gap Duplex 512
9.3 The Interplay of Deformation Mechanisms and Rheologies in the Mid-Crust: Copper Creek Thrust Sheet, Appalachian Valley and Ridge, Tennessee, United States 514
9.3.1 Introduction 514
9.3.2 General Characteristics of the Southern Appalachian Fold-Thrust Belt 514
9.3.3 Deformation of the Copper Creek Thrust Sheet 518
9.3.4 Summarizing Deformation of the Copper Creek Thrust Sheet 534
9.4 Induced Seismicity 535
9.4.1 Overview of Induced Seismicity 535
9.4.2 Earthquakes in the Witwatersrand Basin, South Africa 536
9.4.3 Basel, Switzerland 539
9.4.4 Blackpool, United Kingdom 540
9.4.5 Oklahoma, United States 543
9.4.6 Koyna and Warna, India 545
9.4.7 A Framework for Understanding Induced Seismicity 549
9.5 Using Case Studies to Assess Lithospheric Strength Profiles 556
9.5.1 Lithospheric Strength Profiles 556
9.5.2 Comparing Stress Magnitudes Inferred from the Case Studies to Lithospheric Strength Profiles 562
9.5.3 Recap 564
9.6 Broader Horizons 565
References 566
Index 573
