An Integrated Framework for Structural Geology: Kinematics, Dynamics, and Rheology of Deformed Rocks

ISBN-13: 9781405106849 / Angielski / Miękka / 2022 / 608 str.

Tom Blenkinsop

Spis treści

Acknowledgements xviiWebsite xix1 A Framework for Structural Geology 11.1 Introduction 11.1.1 Deformation 11.1.2 Empirical vs. Theoretical Approaches 11.1.3 Continuum Mechanics and its Applicability to Structural Geology 61.1.4 How to use this Book 6References 82 Structures Produced by Deformation 102.1 Geological Structures 102.1.1 Structural Fabrics 102.1.2 Folds and Boudinage 122.1.3 Fractures and Stylolites 152.1.4 Faults and Fault Zones 172.1.5 Shear Zones 222.2 Additional Considerations 253 Microstructures 263.1 Introduction 263.1.1 Overview 263.1.2 Framework 273.1.3 Imaging of Microstructures 273.2 Fractures 283.3 Fault Rocks 303.4 Overgrowths, Pressure Shadows and Fringes, and Veins 333.5 Indenting, Truncating and Interpenetrating Grain Contacts, Strain Caps, and Stylolites 373.6 Aligned Grain Boundaries, T Grain Boundaries, and Foam Texture 383.7 Undulose Extinction, Subgrains, Deformation and Kink Bands, Deformation Lamellae, Grain Boundary Bulges, and Core-and-Mantle Microstructure 403.8 Deformation Twins 433.9 Grain Shape Fabrics, Ribbon Grains, and Gneissic Banding 433.10 Porphyroblasts 473.11 Crystallographic Fabrics (Crystallographic Preferred Orientations) 493.12 Shear Sense Indicators, Mylonites, and Porphyroclasts 493.12.1 Asymmetric Pressure Shadows and Fringes 533.12.2 Foliation Obliquity and Curvature 553.12.3 SC, SC', and SCC' Fabrics 553.12.4 Porphyroclast Systems 563.12.5 Precautions with Shear Sense Determination 593.13 Collecting Oriented Samples and Relating Sample to Geographic Frames of Reference 60References 654 Displacements 664.1 Overview 664.2 Chapter Organization 664A Displacements: Conceptual Foundation 674A.1 Specifying Displacements or Individual Particles 674A.1.1 Basic Ideas 674A.1.2 Geological Example 694A.2 Particle Paths and Velocities 704A.2.1 Particle Paths 704A.2.2 Velocities 714A.3 Displacements of Collections of Particles - Displacement Fields 744A.3.1 Displacement Fields 744A.3.2 Uniform vs. Nonuniform and Distributed vs. Discrete Displacement Fields 764A.3.3 Classes of Displacement Fields 774A.4 Components of Displacement Fields: Translation, Rotation, and Pure Strain 794A.5 Idealized, Two-Dimensional Displacement Fields 854A.5.1 Simple Shear 874A.5.2 Pure Shear 884A.6 Idealized, Three-Dimensional Displacement Fields 894A.7 Summary 904B Displacements: Comprehensive Treatment 904B.1 Specifying Displacements for Individual Particles 904B.1.1 Defining Vector Quantities 904B.1.2 Types of Vectors 924B.1.3 Relating Position and Displacement Vectors 944B.1.4 Characterizing Vector Quantities 954B.2 Particle Paths and Velocities 974B.2.1 Incremental Displacements for Particles 974B.2.2 Particle Paths and Movement Histories 984b.2.3 Dated Particle Paths, Instantaneous Movement Directions, and Velocities 994B.3 Displacements of Collections of Particles - Displacement Fields 1014B.3.1 Concept of a Displacement Field 1014B.3.2 Field Quantities 1034b.3.3 Gradients of the Displacement Field: Discrete and Distributed Deformation 1034B.3.4 Idealized Versus True Gradients of the Displacement Field 1044B.4 The Displacement Gradient Tensor - Relating Position and Displacement Vectors 1064b.4.1 Components of Displacement Fields: Translation, Rotation, and Pure Strain 1074B.4.2 Translation Displacement Fields 1074B.4.3 Rigid Rotation Displacement Fields 1074B.4.4 Pure Strain Displacement Fields 1094B.4.5 Total Displacement Fields 1104b.4.6 Using Displacement Gradient Matrices to Represent Displacement Fields 1104B.5 Idealized, Two- dimensional Displacement Fields 1114B.5.1 Simple Shear Displacement Fields 1114B.5.2 Uniaxial Convergence or Uniaxial Divergence Displacement Fields 1134B.5.3 Pure Shear Displacement Fields 1154B.5.4 General Shear Displacement Fields 1174B.6 Idealized, Three-Dimensional Displacement Fields 1174B.6.1 Three-Dimensional Simple Shear Displacement Fields 1194b.6.2 Three-Dimensional Orthogonal Convergence and Divergence Displacement Fields 1214B.6.3 Pure Shearing Displacement Fields 1214B.6.4 Constrictional Displacement Fields 1224B.6.5 Flattening Displacement Fields 1234B.6.6 Three-Dimensional General Shearing Displacement Fields 1244B.7 Summary 124Appendix 4-I: Vectors 1244-I.1 Simple Mathematical Operations with Vectors 1244-I.2 Vector Magnitudes 1264-I.3 Properties of Vector Quantities 1264-I.4 Relating Magnitude and Orientation to Cartesian Coordinates 1274-I.5 Vector Products 129Appendix 4-II: Matrix Operations 1304-II.1 Defining Matrices 1304-II.2 Matrix Addition and Subtraction 1304-II.3 Matrix Multiplication 1314-II.3.1 Multiplying Two "2 × 2" Matrices 1324-II.3.2 Multiplying Two "3 × 3" Matrices 1324-II.3.3 Multiplying a 2 × 2 Matrix Times a 2 × 1 Matrix 1334-II.3.4 Multiplying a 3 × 3 Matrix Times a 3 × 1 Matrix 1334-II.3.5 Scalar Multiplication 1344-II.4 Transpose of a Matrix 1344-II.5 Determinant of a Square Matrix 1354-II.6 Inverse of a Square Matrix 1354-II.7 Rotation Matrices 136References 1375 Strain 1385.1 Overview 1385.2 Chapter Organization 1395A Strain: Conceptual Foundation 1395A.1 Specifying Strain in Deformed Rocks 1395A.2 One-dimensional Manifestations of Strain 1415A.2.1 Basic Ideas 1415A.2.2 Geological Example 1425A.3 Two-dimensional Manifestations of Strain 1435A.3.1 Longitudinal Strains in Different Directions 1435A.3.2 Shear Strain 1475A.4 Relating Strain to Displacements 1515A.5 Homogeneous and Inhomogeneous Strain 1535A.6 Finite Strain Ellipse and Finite Strain Ellipsoid 1545A.6.1 Finite Strain Ellipse 1545A.6.2 Finite Strain Ellipsoid 1595A.7 States of Strain and Strain Paths 1635A.7.1 States of Strain 1635A.7.2 Strain Paths and Dated Strain Paths 1635A.7.3 Coaxial Versus Non-Coaxial Strain Paths 1645A.8 Instantaneous Strains and Strain Rates 1665A.9 Infinitesimal Strains 1665A.10 Summary 1675A.11 Practical Methods for Measuring Strain 1675A.11.1 Using Fabrics to Estimate Strain Ellipsoid Shape 1675A.11.2 Types of Methods for Measuring Strain in Two Dimensions 1685A.11.3 Measuring Strain in Two Dimensions Using Deformed Markers 1695B Strain: Comprehensive Treatment 1765B.4 Relating Strain to Displacements 1765B.4.1 Longitudinal Strains and Displacement Gradients 1775B.4.2 Longitudinal Strains and Position Gradients 1795B.4.3 Relating Displacement Gradients and Position Gradients 1795B.4.4 Longitudinal Strain in Continuous Deformation 1795B.4.5 Consequences of Longitudinal Strains 1815B.4.6 Displacement Gradients and Longitudinal Strains in Different Directions 1825B.4.7 Position Gradients and Longitudinal Strains in Different Directions 1845B.4.8 Relating Displacement Gradients and Position Gradients in Two Dimensions 1855B.4.9 Area Ratios in Two-Dimensional Deformation 1865B.4.10 Discontinuous Deformation in Two Dimensions 1865B.4.11 Displacement Gradients and Shear Strains 1875B.4.12 Shear Strains and Position Gradients 1885B.4.13 Applying Matrix Algebra to Two-dimensional Deformation 1885B.4.14 Applying Matrix Algebra to Three-dimensional Deformation 1955B.5 Homogeneous and Inhomogeneous Deformation 1975B.5.1 Homogeneous Deformation 1975B.5.2 Inhomogeneous Deformation 1985B.6 Finite Strain Ellipse and Finite Strain Ellipsoid 2005B.6.1 Homogeneous Deformations and the Finite Strain Ellipse 2005B.6.2 Working with Strain Markers 2005B.6.3 Finite Strain Ellipsoid 2055B.7 States of Strain and Strain Paths 2055B.7.1 States of Strain 2055B.7.2 Strain Paths 2065B.7.3 Velocity Gradient Tensor and Decomposition 2075B.8 Vorticity 2105B.8.1 Vorticity Vector 2115B.8.2 Kinematic Vorticity Number 2135B.9 Summary 213Appendix 5-I 214References 2166 Stress 2176.1 Overview 2176A Stress: Conceptual Foundation 2186A.1 Forces, Tractions, and Stress 2206A.1.1 Accelerations and the Forces that Act on Objects 2206A.1.2 Forces Transmitted Through Objects 2216A.1.3 Traction - A Measure of "Force Intensity" within Objects 2216A.1.4 Stress 2236A.2 Characteristics of Stress in Two Dimensions 2256A.2.1 Normal and Tangential Stress Components 2256A.2.2 Stresses on Planes with Different Orientations 2276A.2.3 Principal Stresses and Differential Stress 2276A.2.4 The Fundamental Stress Equations 2316A.3 State of Stress in Two Dimensions 2336A.3.1 The Stress Matrix 2336A.3.2 The Stress Ellipse 2346A.3.3 The Mohr circle 2356A.3.4 Hydrostatic vs. Non-hydrostatic Stress 2466A.3.5 Homogeneous vs. Inhomogeneous Stress 2486A.4 Stress in Three Dimensions 2486A.4.1 The Stress Ellipsoid 2516A.4.2 Hydrostatic, Lithostatic, and Deviatoric Stresses 2516A.5 Pore-fluid Pressure and Effective Stress 2536A.6 Three-dimensional States of Stress 2546A.7 The State of Stress in Earth 2556A.8 Change of Stress: Paleostress, Path, and History 2566A.9 Comparison of Displacements, Strain and Stress 2576A.10 Summary 2596A.11 Practical Methods for Measuring Stress 2616A.11.1 In situ Stress Measurements 2616A.11.2 Paleostress 2686B Stress: Comprehensive Treatment 2726B.1 Force, Traction, and Stress Vectors 2726B.1.1 Accelerations and Forces 2726B.1.2 Traction or Stress Vectors 2736b.1.3 Relating Traction or Stress Vector Components in Different Coordinate Frames 2746B.1.4 Stress Transformation Law in Two Dimensions and the Mohr Circle 2776b.1.5 Stress Transformation Law in Three Dimensions and the Mohr Diagram 2796B.1.6 An Alternative Way to Define Traction or Stress Vectors 2816B.1.7 Determining Stress Principal Directions and Magnitudes 2826B.1.8 Stress Invariants 2846B.1.9 Spatial Variation in Stress 285Appendix 6-I 289References 2917 Rheology 2927.1 Overview 2927A Rheology: Conceptual Foundation 2937A.1 Moving Beyond Equilibrium 2937A.1.1 Conducting and Interpreting Deformation Experiments 2947A.1.2 Recoverable Deformation versus Material Failure 2977A.1.3 Moving from Deformation Experiments to Mathematical Relations 3017A.2 Models of Rock Deformation 3037A.2.1 Elastic Behavior 3037A.2.2 Criteria for Fracture or Fault Formation 3087A.2.3 Yield and Creep 3217A.2.4 Viscous Behavior 3227A.2.5 Plastic Behavior 3227A.2.6 Constitutive Equations for Viscous Creep and Plastic Yield 3247A.3 Summary 3277B Rheology: Comprehensive Treatment 3287B.1 Combining Deformation Models to Describe Rock Properties 3287B.2 Rock Deformation Modes 3327B.2.1 Elasticity 3327B.2.2 Fracture or Fault Formation 3377B.2.3 Differential Stress, Pore Fluid Pressure, and Failure Mode 3567B.2.4 Yield and Creep 3597B.2.5 Viscous Behavior 3607B.2.6 Plastic Behavior 3637B.2.7 Lithospheric Strength Profiles 363References 3648 Deformation Mechanisms 3678.1 Overview 3678A Deformation Mechanisms: Conceptual Foundation 3708A.1 Elastic Distortion 3718A.2 Cataclastic Deformation Mechanisms 3738A.2.1 Fracture of Geological Materials 3738A.2.2 Frictional Sliding 3768A.2.3 Microstructures Associated with Cataclasis and Frictional Sliding 3808A.2.4 Cataclasis and Frictional Sliding as a Deformation Mechanism 3808A.3 Diffusional Deformation Mechanisms 3808A.3.1 Diffusion 3808A.3.2 Grain Shape Change by Diffusion 3858A.3.3 Microstructures Associated with Diffusional Mass Transfer 3878A.3.4 Diffusional Mass Transfer as a Deformation Mechanism 3908a.3.5 Flow Laws for Three Diffusional Mass Transfer Deformation Mechanisms 3918A.4 Dislocational Deformation Mechanisms 3938A.4.1 Dislocations as Elements of Lattice Distortion 3938A.4.2 Dislocation Interactions 4038A.4.3 Recovery and Recrystallization 4058a.4.4 Microstructures Indicative of Dislocation- Accommodated Deformation 4098A.4.5 Dislocation Glide: A Deformation Mechanism 4148A.4.6 Flow Law for Dislocation Glide 4158A.4.7 Dislocation Creep: A Deformation Mechanism 4158A.4.8 Flow Law for Dislocation Creep 4158A.4.9 Other Lattice Deformation Processes - Twinning and Kinking 4168A.5 Diffusion- and/or Dislocation-Accommodated Grain Boundary Sliding 4188A.6 Deformation Mechanism Maps 4198A.7 Summary 4228B Deformation Mechanisms: Comprehensive Treatment 4238B.1 Cataclastic Deformation Mechanisms 4238B.1.1 Joints, Fractures, and Mesoscopic Faults 4238B1.2 Fault Zones 4318B.2 Diffusional Deformation Mechanisms 4488B.2.1 Diffusional Mass Transfer Structures 4488B.2.2 Understanding Diffusion Through Crystalline Materials 4538B.2.3 The Effect of Differential Stress 4558B.2.4 Flow Laws for Diffusional Deformation Mechanisms 4568B.2.5 Paths of Rapid Diffusion - Dislocations and Grain Boundaries 4588B.2.6 The Effect of Fluid Phases Along Grain Boundaries 4598B.3 Dislocational Deformation Mechanisms 4608B.3.1 Origin of Dislocations 4608B.3.2 Dislocation Movement 4618B.3.3 Dislocation Interactions 4678B.3.4 Stresses Associated with Dislocations 4708B.3.5 Strains Accommodated by the Glide of Dislocations 4708B.3.6 Constitutive Equations for Dislocation Creep 4738B.3.7 Recovery, Recrystallization, and Dislocation Creep Regimes 4758B.3.8 Twinning and Kinking 4778B.4 Grain Boundary Sliding and Superplasticity 482Appendix 8-I 484Appendix 8-II 486References 4879 Case Studies of Deformation and Rheology 4969.1 Overview 4969.2 Integrating Structural Geology and Geochronology: Ruby Gap Duplex, Redbank Thrust Zone, Australia 4979.2.1 Geological Setting and Deformation Character 4979.2.2 Microstructures and Deformation Mechanisms 5029.2.3 Rheological Analysis Using Microstructures by Comparison to Experimental Deformation 5089.2.4 Geochronology 5089.2.5 Evaluating Displacement Through Time 5109.2.6 Orogenic Development Through Time 5129.2.7 Summarizing Deformation in the Ruby Gap Duplex 5129.3 The Interplay of Deformation Mechanisms and Rheologies in the Mid-Crust: Copper Creek Thrust Sheet, Appalachian Valley and Ridge, Tennessee, United States 5149.3.1 Introduction 5149.3.2 General Characteristics of the Southern Appalachian Fold-Thrust Belt 5149.3.3 Deformation of the Copper Creek Thrust Sheet 5189.3.4 Summarizing Deformation of the Copper Creek Thrust Sheet 5349.4 Induced Seismicity 5359.4.1 Overview of Induced Seismicity 5359.4.2 Earthquakes in the Witwatersrand Basin, South Africa 5369.4.3 Basel, Switzerland 5399.4.4 Blackpool, United Kingdom 5409.4.5 Oklahoma, United States 5439.4.6 Koyna and Warna, India 5459.4.7 A Framework for Understanding Induced Seismicity 5499.5 Using Case Studies to Assess Lithospheric Strength Profiles 5569.5.1 Lithospheric Strength Profiles 5569.5.2 Comparing Stress Magnitudes Inferred from the Case Studies to Lithospheric Strength Profiles 5629.5.3 Recap 5649.6 Broader Horizons 565References 566Index 573

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Steven Wojtal is Professor of Geoscience at Oberlin College in Oberlin, Ohio, United States.Tom Blenkinsop is Professor in Earth Science at Cardiff University, United Kingdom.Basil Tikoff is Professor of Geoscience at the University of Wisconsin-Madison, United States.