AN INTEGRATED FRAMEWORK FOR STRUCTURAL GEOLOGY

A modern and practice-oriented approach to structural geology

An Integrated Framework for Structural Geology: Kinematics, Dynamics, and Rheology of Deformed Rocks builds a framework for structural geology from geometrical description, kinematic analysis, dynamic evolution, and rheological investigation of deformed rocks. The unique approach taken by the book is to integrate these principles of continuum mechanics with the description of rock microstructures and inferences about deformation mechanisms. Field, theoretical and laboratory approaches to structural geology are all considered, including the application of rock mechanics experiments to nature.

Readers will also find:

• Three case studies that illustrate how the framework can be applied to deformation at different levels in the crust and in an applied structural geology context
• Hundreds of detailed, two-color illustrations of exceptional clarity, as well as many microstructural and field photographs
• The quantitative basis of structural geology delivered through clear mathematics

Written for advanced undergraduate and graduate students in geology, An Integrated Framework for Structural Geology will also earn a place in the libraries of practicing geologists with an interest in a one-stop resource on structural geology.

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