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# Earthquake and Volcano DeformationPaul Segall

 TABLE OF CONTENTS: Preface xi Acknowledgments xv Origins xvii Chapter 1: Deformation, Stress, and Conservation Laws 1 1.1 Strain 2 1.1.1 Strains in Curvilinear Coordinates 7 1.2 Rotation 9 1.3 Stress 13 1.4 Coordinate Transformations 16 1.5 Principal Strains and Stresses 18 1.6 Compatibility Equations 21 1.7 Conservation Laws 21 1.7.1 Equilibrium Equations in Curvilinear Coordinates 24 1.8 Constitutive Laws 24 1.9 Reciprocal Theorem 27 1.10 Problems 28 1.11 References 30 Chapter 2: Dislocation Models of Strike-Slip Faults 32 2.1 Full-Space Solution 32 2.2 Half-Space Solution 37 2.2.1 Coseismic Faulting 38 2.2.2 Interseismic Deformation 39 2.2.3 Postseismic Slip 42 2.3 Distributed Slip 43 2.4 Application to the San Andreas and Other Strike-Slip Faults 44 2.5 Displacement at Depth 47 2.6 Summary and Perspective 49 2.7 Problems 50 2.8 References 50 Chapter 3: Dip-Slip Faults and Dislocations in Three Dimensions 51 3.1 Volterra's Formula 52 3.1.1 Body Force Equivalents andMoment Tensors 54 3.2 Screw Dislocations 59 3.3 Two-Dimensional Edge Dislocations 60 3.3.1 Dipping Fault 63 3.4 Coseismic Deformation Associated with Dipping Faults 67 3.5 Displacements and Stresses Due to Edge Dislocation at Depth 71 3.6 Dislocations in Three Dimensions 75 3.6.1 Full-Space Green's Functions 75 3.6.2 Half-Space Green's Functions 77 3.6.3 Point-Source Dislocations 78 3.6.4 Finite Rectangular Dislocations 80 3.6.5 Examples 82 3.6.6 Distributed Slip 84 3.7 Strain Energy Change Due to Faulting 86 3.8 Summary and Perspective 87 3.9 Problems 87 3.10 References 90 Chapter 4: Crack Models of Faults 92 4.1 Boundary Integral Method 92 4.1.1 Inversion of the Integral Equation 97 4.2 Displacement on the Earth's Surface 98 4.3 A Brief Introduction to Fracture Mechanics 99 4.4 Nonsingular Stress Distributions 105 4.5 Comparison of Slip Distributions and Surface Displacements 107 4.6 Boundary ElementMethods 110 4.7 Fourier TransformMethods 111 4.8 Some Three-Dimensional Crack Results 113 4.9 Summary and Perspective 114 4.10 Problems 115 4.11 References 117 Chapter 5: Elastic Heterogeneity 118 5.1 Long Strike-Slip Fault Bounding Two Media 118 5.2 Strike-Slip Fault within a Compliant Fault Zone 120 5.3 Strike-Slip Fault beneath a Layer 125 5.4 Strike-Slip within a Layer over Half-Space 129 5.5 Propagator Matrix Methods 131 5.5.1 The Propagator Matrix for Antiplane Deformation 135 5.5.2 Vertical Fault in a Homogeneous Half-Space 136 5.5.3 Vertical Fault within Half-Space beneath a Layer 138 5.5.4 Vertical Fault in Layer over Half-Space 139 5.5.5 General Solution for an Arbitrary Number of Layers 141 5.5.6 Displacements and Stresses at Depth 143 5.5.7 PropagatorMethods for Plane Strain 143 5.6 Propagator Solutions in Three Dimensions 150 5.7 Approximate Solutions for Arbitrary Variations in Properties 154 5.7.1 Variations in Shear Modulus 157 5.7.2 Screw Dislocation 158 5.7.3 Edge Dislocation 159 5.8 Summary and Perspective 159 5.9 Problems 162 5.10 References 164 Chapter 6: Postseismic Relaxation 166 6.1 Elastic Layer over Viscous Channel 169 6.2 Viscoelasticity 172 6.2.1 Correspondence Principle 175 6.3 Strike-Slip Fault in an Elastic Plate Overlying a Viscoelastic Half-Space 176 6.3.1 Stress in Plate and Half-Space 181 6.4 Strike-Slip Fault in Elastic Layer Overlying a Viscoelastic Channel 182 6.5 Dip-Slip Faulting 187 6.5.1 Examples 190 6.6 Three-Dimensional Calculations 191 6.7 Summary and Perspective 193 6.8 Problems 197 6.9 References 198 Chapter 7: Volcano Deformation 200 7.1 Spherical Magma Chamber 203 7.1.1 Center of Dilatation 208 7.1.2 Volume of the Uplift, Magma Chamber, and Magma 212 7.2 EllipsoidalMagma Chambers 214 7.3 Magmatic Pipes and Conduits 225 7.4 Dikes and Sills 229 7.4.1 Crack Models of Dikes and Sills 231 7.4.2 Surface Fracturing and Dike Intrusion 236 7.5 Other Magma Chamber Geometries 237 7.6 Viscoelastic Relaxation around Magma Chambers 240 7.7 Summary and Perspective 248 7.8 Problems 249 7.9 References 252 Chapter 8: Topography and Earth Curvature 255 8.1 Scaling Considerations 259 8.2 Implementation Considerations 260 8.3 Center of Dilatation beneath a Volcano 260 8.4 Earth's Sphericity 261 8.5 Summary and Perspective 263 8.6 Problems 265 8.7 References 265 Chapter 9: Gravitational Effects 267 9.1 Nondimensional Formof Equilibrium Equations 270 9.2 Inclusion in Propagator Matrix Formulation 273 9.3 Surface Gravity Approximation 275 9.4 Gravitational Effects in Viscoelastic Solutions 276 9.4.1 Incompressible Half-Space 277 9.4.2 No-Buoyancy Approximation 278 9.4.3 Wang Approach 279 9.4.4 Comparison of Different Viscoelastic Models 280 9.4.5 Relaxed Viscoelastic Response 282 9.5 Changes in Gravity Induced by Deformation 283 9.5.1 Gravity Changes and Volcano Deformation 289 9.5.2 An Example from Long Valley Caldera, California 292 9.6 Summary and Perspective 292 9.7 Problems 294 9.8 References 295 Chapter 10: Poroelastic Effects 297 10.1 Constitutive Laws 300 10.1.1 Macroscopic Description 300 10.1.2 Micromechanical Description 303 10.2 Field Equations 305 10.3 Analogy to Thermoelasticity 308 10.4 One-Dimensional Deformation 309 10.4.1 Step Load on the Free Surface 310 10.4.2 Time-Varying Fluid Load on the Free Surface 312 10.5 Dislocations in Two Dimensions 313 10.6 Inflating Magma Chamber in a Poroelastic Half-Plane 315 10.7 Cumulative Poroelastic Deformation in Three Dimensions 321 10.8 Specified Pore Pressure Change 324 10.9 Summary and Perspective 328 10.10 Problems 329 10.11 References 330 Chapter 11: Fault Friction 332 11.1 Slip-Weakening Friction 333 11.2 Velocity-Weakening Friction 335 11.3 Rate and State Friction 336 11.3.1 Linearized Stability Analysis 344 11.4 Implications for Earthquake Nucleation 347 11.5 Nonlinear Stability Analysis 357 11.6 Afterslip 360 11.7 Transient Slip Events 366 11.8 Summary and Perspective 367 11.9 Problems 368 11.10 References 369 Chapter 12: Interseismic Deformation and Plate Boundary Cycle Models 372 12.1 Elastic Dislocation Models 372 12.1.1 Dip-Slip Faults 373 12.2 Plate Motions 376 12.3 Elastic BlockModels 378 12.4 Viscoelastic CycleModels 380 12.4.1 Viscoelastic Strike-Slip Earthquake Cycle Models 380 12.4.2 Comparison to Data from San Andreas Fault 386 12.4.3 Viscoelastic Models with Stress-Driven Deep-Fault Creep 389 12.4.4 Viscoelastic CycleModels for Dipping Faults 394 12.5 Rate-State Friction Earthquake CycleModels 407 12.6 Summary and Perspective 409 12.7 Problems 412 12.8 References 413 APPENDIX A: Integral Transforms 415 A.1 Fourier Transforms 415 A.2 Laplace Transforms 416 A.3 References 419 APPENDIX B: A Solution of the Diffusion Equation 420 APPENDIX C: Displacements Due to Crack Model of Strike-Slip Fault by Contour Integration 423 Index 425 Return to Book DescriptionFile created: 4/21/2017 Questions and comments to: webmaster@press.princeton.eduPrinceton University Press