Introduction to Structural Geology

Contents i

GEOL 326

Cornell University

Spring 1999

Richard W. Allmendinger Department of Geological Sciences Snee Hall Cornell University, Ithaca, NY 14853-1504 USA

Contents

Lecture 1—Introduction, Scale, & Basic Terminology...... 1 1.1 Introduction...... 1 1.2 Levels of Structural Study...... 2 1.3 Types of Structural Study...... 2 1.4 Importance of Scale...... 3 1.4.1 Scale Terms...... 3 1.4.2 Scale Invariance, Fractals...... 4

Lecture 2 —Coordinate Systems, etc...... 8 2.1 Introduction...... 8 2.2 Three types of physical entities...... 8 2.3 Coordinate Systems...... 9 2.3.1 Spherical versus Cartesian Coordinate Systems...... 10 2.3.2 Right-handed and Left-handed Coordinate Systems...... 10 2.3.3 Cartesian Coordinate Systems in Geology...... 11 2.4 Vectors...... 12 2.4.1 Vectors vs. Axes ...... 12 2.4.2 Basic Properties of Vectors...... 12 2.4.3 Geologic Features as Vectors...... 14 2.4.4 Simple Vector Operations...... 17 2.4.5 Dot Product and Cross Product ...... 18

Lecture 3 — Descriptive Geometry: Seismic Reflection...... 21 3.1 Echo Sounding...... 21 3.2 Common Depth Point (CDP) Method...... 23 3.3 Migration ...... 25 3.4 Resolution of Seismic Reflection Data...... 26 3.4.1 Vertical Resolution ...... 26 3.4.2 Horizontal Resolution...... 27 3.5 Diffractions...... 28 3.6 Artifacts...... 29 Contents iii

3.6.1 Velocity Pullup/pulldown ...... 29 3.6.2 Multiples...... 29 3.6.3 Sideswipe...... 30 3.6.4 Buried Focus...... 31 3.6.5 Others ...... 32

Lecture 4 — Introduction to Deformation & Strain...... 33 4.1 Introduction...... 33 4.2 Kinematics ...... 33 4.2.1 Rigid Body Deformations ...... 33 4.2.2 Strain (Non-rigid Body Deformation)...... 34 4.2.3 Continuum Mechanics...... 36 4.2.4 Four Aspects of a Deforming Rock System: ...... 37 4.3 Measurement of Strain...... 38 4.3.1 Change in Line Length:...... 39 4.3.2 Changes in Angles:...... 40 4.3.3 Changes in Volume (Dilation): ...... 41

Lecture 5 — Strain II: The Strain Ellipsoid ...... 42 5.1 Motivation for General 3-D Strain Relations ...... 42 5.2 Equations for Finite Strain...... 43 5.3 Extension of a Line ...... 43 5.4 Shear Strain...... 45

Lecture 6 — Strain III: Mohr on the Strain Ellipsoid...... 47 6.1 Introduction...... 47 6.2 Mohr’s Circle For Finite Strain ...... 47 6.3 Principal Axes of Strain...... 48 6.4 Maximum Angular Shear ...... 49 6.5 Ellipticity...... 50 6.6 Rotation of Any Line During Deformation ...... 50 6.7 Lines of No Finite Elongation...... 51

Lecture 7 — Strain IV: Finite vs. Infinitesimal Strain...... 53 7.1 Coaxial and Non-coaxial Deformation ...... 54 Contents iv

7.2 Two Types of Rotation...... 55 7.3 Deformation Paths ...... 55 7.4 Superposed Strains & Non-commutability ...... 58 7.5 Plane Strain & 3-D Strain...... 58

Lecture 8—Stress I: Introduction ...... 60 8.1 Force and Stress...... 60 8.2 Units Of Stress...... 61 8.3 Sign Conventions:...... 61 8.4 Stress on a Plane; Stress at a Point ...... 62 8.5 Principal Stresses ...... 63 8.6 The Stress Tensor ...... 64 8.7 Mean Stress...... 64 8.8 Deviatoric Stress...... 64 8.9 Special States of Stress...... 65

Lecture 9—Vectors & Tensors...... 66 9.1 Scalars & Vectors ...... 67 9.2 Tensors...... 68 9.3 Einstein Summation Convention...... 69 9.4 Coordinate Systems and Tensor Transformations ...... 70 9.5 Symmetric, Asymmetric, & Antisymmetric Tensors...... 71 9.6 Finding the Principal Axes of a Symmetric Tensor ...... 73

Lecture 10—Stress II: Mohr’s Circle...... 74 10.1 Stresses on a Plane of Any Orientation from Cauchy’s law...... 74 10.2 A more “Traditional” Way to Derive the above Equations...... 75 10.2.1 Balance of Forces...... 76 10.2.2 Normal and Shear Stresses on Any Plane...... 77 10.3 Mohr’s Circle for Stress...... 78 10.4 Alternative Way of Plotting Mohr’s Circle...... 80 10.5 Another Way to Derive Mohr’s Circle Using Tensor Transformations ...... 81 10.5.1 Transformation of Axes...... 81 10.5.2 Tensor Transformations...... 82 10.5.3 Mohr Circle Construction...... 82 Contents v

Lecture 11—Stress III: Stress-Strain Relations 11.1 More on the Mohr’s Circle...... 85 11.1.1 Mohr’s Circle in Three Dimensions ...... 86 11.2 Stress Fields and Stress Trajectories ...... 86 11.3 Stress-strain Relations...... 87 11.4 Elasticity...... 88 11.4.1 The Elasticity Tensor...... 88 11.4.2 The Common Material Parameters of Elasticity...... 89 11.5 Deformation Beyond the Elastic Limit...... 90

Lecture 12—Plastic & Viscous Deformation...... 92 12.1 Strain Rate...... 92 12.2 Viscosity...... 93 12.3 Creep ...... 94 12.4 Environmental Factors Affecting Material Response to Stress...... 95 12.4.1 Variation in Stress...... 95 12.4.2 Effect of Confining Pressure (Mean Stress)...... 95 12.4.3 Effect of Temperature ...... 96 12.4.4 Effect of Fluids ...... 96 12.4.5 The Effect of Strain Rate...... 97 12.5 Brittle, Ductile, Cataclastic, Crystal Plastic ...... 97

Lecture 13—Deformation Mechanisms I: Elasticity, Compaction...... 100 13.1 Elastic Deformation...... 100 13.2 Thermal Effects and Elasticity...... 102 13.3 Compaction...... 103 13.4 Role of Fluid Pressure ...... 104 13.4.1 Effective Stress...... 105

Lecture 14—Deformation Mechanisms II: Fracture...... 106 14.1 Effect of Pore Pressure...... 111 14.2 Effect of Pre-existing Fractures...... 112 14.3 Friction...... 113

Lecture 15—Deformation Mechanisms III: Pressure Solution & Crystal Plasticity 114 Contents vi

15.1 Pressure Solution...... 114 15.1.1 Observational Aspects ...... 114 15.1.2 Environmental constrains on Pressure Solution ...... 117 15.2 Mechanisms of Crystal Plasticity ...... 117 15.2.1 Point Defects...... 118 15.2.2 Diffusion ...... 118 15.2.3 Planar Defects...... 119

Lecture 16—Deformation Mechanisms IV: Dislocations ...... 121 16.1 Basic Concepts and Terms...... 121 16.2 Dislocation (“Translation”) Glide ...... 123 16.3 Dislocations and Strain Hardening...... 123 16.4 Dislocation Glide and Climb...... 125 16.5 Review of Deformation Mechanisms ...... 126

Lecture 17—Flow Laws & State of Stress in the Lithosphere ...... 127 17.1 Power Law Creep ...... 127 17.2 Diffusion Creep...... 129 17.3 Deformation Maps...... 129 17.4 State of Stress in the Lithosphere...... 130

Lecture 18—Joints & Veins ...... 133 18.1 Faults and Joints as Cracks...... 133 18.2 Joints ...... 133 18.2.1 Terminology ...... 134 18.2.2 Surface morphology of the joint face:...... 135 18.2.3 Special Types of Joints and Joint-related Features ...... 136 18.2.4 Maximum Depth of True Tensile Joints...... 136 18.3 Veins ...... 137 18.3.1 Fibrous Veins in Structural Analysis...... 138 18.3.2 En Echelon Sigmoidal Veins...... 139 18.4 Relationship of Joints and Veins to other Structures ...... 140

Lecture 19—Faults I: Basic Terminology...... 141 19.1 Descriptive Fault Geometry ...... 141 Contents vii

19.2 Apparent and Real Displacement...... 142 19.3 Basic Fault Types ...... 143 19.3.1 Dip Slip...... 143 19.3.2 Strike-Slip...... 143 19.3.3 Rotational fault ...... 144 19.4 Fault Rocks...... 144 19.4.1 Sibson’s Classification ...... 144 19.4.2 The Mylonite Controversy ...... 146

Lecture 20—Faults II: Slip Sense & Surface Effects...... 147 20.1 Surface Effects of Faulting...... 147 20.1.1 Emergent Faults...... 147 20.1.2 Blind Faults ...... 149 20.2 How a Fault Starts: Riedel Shears...... 149 20.2.1 Pre-rupture Structures...... 150 20.2.2 Rupture & Post-Rupture Structures ...... 151 20.3 Determination of Sense of Slip ...... 151

Lecture 21—Faults III: Dynamics & Kinematics...... 157 21.1 Introduction ...... 157 21.2 Anderson’s Theory of Faulting...... 158 21.3 Strain from Fault Populations...... 161 21.3.1 Sense of Shear ...... 161 21.3.2 Kinematic Analysis of Fault Populations ...... 161 21.3.3 The P & T Dihedra ...... 162 21.4 Stress From Fault Populations1...... 164 21.4.1 Assumptions...... 164 21.4.2 Coordinate Systems & Geometric Basis...... 165 21.4.3 Inversion Of Fault Data For Stress...... 167 21.5 Scaling Laws for Fault Populations...... 169

Lecture 22—Faults IV: Mechanics of Thrust Faults...... 170 22.1 The Paradox of Low-angle Thrust Faults...... 170 22.2 Hubbert & Rubey Analysis...... 170 22.3 Alternative Solutions...... 174 Contents viii

Lecture 23—Folds I: Geometry...... 178 23.1 Two-dimensional Fold Terminology...... 178 23.2 Geometric Description of Folds...... 180 23.2.1 Two-dimensional (Profile) View:...... 180 23.2.2 Three-dimensional View:...... 181 23.3 Fold Names Based on Orientation...... 182 23.4 Fold Tightness ...... 183

Lecture 24 — Folds II: Geometry & Kinematics...... 184 24.1 Fold Shapes...... 184 24.2 Classification Based on Shapes of Folded Layers...... 185 24.3 Geometric-kinematic Classification:...... 186 24.3.1 Cylindrical Folds...... 186 24.3.2 Non-Cylindrical Folds...... 188 24.4 Summary Outline ...... 189 24.5 Superposed Folds...... 189

Lecture 25—Folds III: Kinematics...... 191 25.1 Overview...... 191 25.2 Gaussian Curvature...... 191 25.3 Buckling ...... 192 25.4 Shear Parallel to Layers...... 193 25.4.1 Kink folds...... 195 25.4.2 Simple Shear during flexural slip...... 196 25.5 Shear Oblique To Layers...... 196 25.6 Pure Shear Passive Flow...... 197

Lecture 26—Folds IV: Dynamics...... 198 26.1 Basic Aspects ...... 199 26.2 Common Rock Types Ranked According to “Competence”...... 199 26.3 Theoretical Analyses of Folding...... 199 26.3.1 Nucleation of Folds ...... 200 26.3.2 Growth of Folds...... 201 26.3.3 Results for Kink Folds ...... 202 Contents ix

Lecture 27—Linear Minor Structures...... 203 27.1 Introduction to Minor Structures...... 203 27.2 Lineations...... 203 27.2.1 Mineral Lineations...... 203 27.2.2 Deformed Detrital Grains (and related features)...... 204 27.2.3 Rods and Mullions...... 205 27.3 Boudins...... 205 27.4 Lineations Due to Intersecting Foliations...... 206

Lecture 28—Planar Minor Structures I...... 207 28.1 Introduction to Foliations...... 207 28.2 Cleavage...... 207 28.2.1 Cleavage and Folds ...... 208 28.3 Cleavage Terminology...... 209 28.3.1 Problems with Cleavage Terminology...... 210 28.3.2 Descriptive Terms...... 210 28.4 Domainal Nature of Cleavage...... 211 28.4.1 Scale of Typical Cleavage Domains ...... 212

Lecture 29—Planar Minor Structures II: Cleavage & Strain ...... 213 29.1 Processes of Foliation Development ...... 213 29.2 Rotation of Grains...... 213 29.2.1 March model ...... 214 29.2.2 Jeffery Model...... 214 29.2.3 A Special Case of Mechanical Grain Rotation ...... 214 29.3 Pressure Solution and Cleavage ...... 215 29.4 Crenulation Cleavage ...... 216 29.5 Cleavage and Strain ...... 217

Lecture 30—Shear Zones & Transposition...... 219 30.1 Shear Zone Foliations and Sense of Shear...... 219 30.1.1 S-C Fabrics ...... 219 30.1.2 Mica “Fish” in Type II S-C Fabrics...... 219 30.1.3 Fractured and Rotated Mineral Grains...... 220 Contents x

30.1.4 Asymmetric Porphyroclasts...... 220 30.2 Use of Foliation to Determine Displacement in a Shear Zone...... 221 30.3 Transposition of Foliations...... 222

Lecture 31—Thrust Systems I: Overview & Tectonic Setting...... 225 31.1 Basic Thrust System Terminology ...... 225 31.2 Tectonic Setting of Thin-skinned Fold & Thrust Belts...... 226 31.2.1 Andean Type:...... 227 31.2.2 Himalayan Type: ...... 227 31.3 Basic Characteristics of Fold-thrust Belts...... 228 31.4 Relative and Absolute Timing in Fold-thrust Belts...... 229 31.5 Foreland Basins...... 229

Lecture 32—Thrust Systems II: Basic Geometries ...... 231 32.1 Dahlstrom’s Rules and the Ramp-flat (Rich Model) Geometry...... 231 32.2 Assumptions of the Basic Rules ...... 232 32.3 Types of Folds in Thrust Belts ...... 233 32.4 Geometries with Multiple Thrusts...... 234 32.4.1 Folded thrusts ...... 234 32.4.2 Duplexes ...... 235 32.4.3 Imbrication...... 237 32.4.4 Triangle Zones ...... 237

Lecture 33—Thrust Systems III: Thick-Skinned Faulting...... 239 33.1 Plate-tectonic Setting...... 239 33.2 Basic Characteristics ...... 240 33.3 Cross-sectional Geometry ...... 240 “Upthrust” Hypothesis ...... 240 33.3.1 Overthrust Hypothesis...... 240 33.3.2 Deep Crustal Geometry ...... 241 33.4 Folding in Thick-skinned Provinces ...... 242 33.4.1 Subsidiary Structures...... 242 33.5 Late Stage Collapse of Uplifts...... 243 33.6 Regional Mechanics...... 244 Contents xi

Lecture 34—Extensional Systems I...... 245 34.1 Basic Categories of Extensional Structures...... 245 34.2 Gravity Slides...... 245 34.2.1 The Heart Mountain Fault...... 246 34.2.2 Subaqueous Slides...... 246 34.3 Growth Faulting on a Subsiding Passive Margin...... 247 34.4 Tectonic Rift Provinces...... 248 34.4.1 Oceanic Spreading Centers...... 248 34.4.2 Introduction to Intracontinental Rift Provinces...... 249

Lecture 35—Extensional Systems II...... 250 35.1 Basic Categories of Extensional Structures...... 250 35.2 Rotated Planar Faults...... 250 35.3 Listric Normal Faults...... 252 35.4 Low-angle Normal Faults...... 253 35.5 Review of Structural Geometries...... 254 35.6 Thrust Belt Concepts Applied to Extensional Terranes...... 254 35.6.1 Ramps, Flats, & Hanging Wall Anticlines:...... 254 35.6.2 Extensional Duplexes:...... 254 35.7 Models of Intracontinental Extension...... 255 35.7.1 Horst & Graben:...... 255 35.7.2 “Brittle-ductile” Transition & Sub-horizontal Decoupling:...... 255 35.7.3 Lenses or Anastomosing Shear Zones:...... 255 35.7.4 Crustal-Penetrating Low-Angle Normal Fault:...... 256 35.7.5 Hybrid Model of Intracontinental Extension...... 256

Lecture 36—Strike-slip Fault Systems ...... 257 36.1 Tectonic setting of Strike-slip Faults...... 257 36.1.1 Transform faults...... 257 36.2 Transcurrent Faults and Tear Faults...... 258 36.3 Features Associated with Major Strike-slip Faults...... 259 36.3.1 Parallel Strike-slip...... 259 36.3.2 Convergent-Type...... 262 36.3.3 Divergent Type...... 262 36.4 Restraining and Releasing bends, duplexes...... 263 Contents xii

36.5 Terminations of Strike-slip Faults...... 264

Lecture 37—Deformation of the Lithosphere ...... 265 37.1 Mechanisms of Uplift...... 265 37.1.1 Isostasy & Crust-lithosphere thickening...... 265 37.1.2 Differential Isostasy...... 266 37.1.3 Flexural Isostasy ...... 267 37.2 Geological Processes of Lithospheric Thickening ...... 269 37.2.1 Distributed Shortening:...... 269 37.2.2 “Underthrusting”: ...... 269 37.2.3 Magmatic Intrusion:...... 269 37.3 Thermal Uplift...... 270 37.4 Evolution of Uplifted Continental Crust...... 270