内容

目次

Preface xi Acknowledgments xv Origins xvii Chapter 1:Deformation, Stress, and Conservation Laws 1 1.1 Strain 2 1.1.1 Strains inCurvilinear Coordinates 7 1.2 Rotation 9 1.3 Stress 13 1.4 CoordinateTransformations 16 1.5 Principal Strains and Stresses 18 1.6 CompatibilityEquations 21 1.7 Conservation Laws 21 1.7.1 Equilibrium Equations inCurvilinear Coordinates 24 1.8 Constitutive Laws 24 1.9 Reciprocal Theorem27 1.10 Problems 28 1.11 References 30 Chapter 2: Dislocation Modelsof Strike-Slip Faults 32 2.1 Full-Space Solution 32 2.2 Half-Space Solution37 2.2.1 Coseismic Faulting 38 2.2.2 Interseismic Deformation 39 2.2.3Postseismic Slip 42 2.3 Distributed Slip 43 2.4 Application to the SanAndreas and Other Strike-Slip Faults 44 2.5 Displacement at Depth 47 2.6Summary and Perspective 49 2.7 Problems 50 2.8 References 50 Chapter3: Dip-Slip Faults and Dislocations in Three Dimensions 51 3.1 Volterra'sFormula 52 3.1.1 Body Force Equivalents andMoment Tensors 54 3.2 ScrewDislocations 59 3.3 Two-Dimensional Edge Dislocations 60 3.3.1 DippingFault 63 3.4 Coseismic Deformation Associated with Dipping Faults 67 3.5Displacements and Stresses Due to Edge Dislocation at Depth 71 3.6Dislocations in Three Dimensions 75 3.6.1 Full-Space Green's Functions 753.6.2 Half-Space Green's Functions 77 3.6.3 Point-Source Dislocations 783.6.4 Finite Rectangular Dislocations 80 3.6.5 Examples 82 3.6.6Distributed Slip 84 3.7 Strain Energy Change Due to Faulting 86 3.8 Summaryand Perspective 87 3.9 Problems 87 3.10 References 90 Chapter 4: CrackModels of Faults 92 4.1 Boundary Integral Method 92 4.1.1 Inversion of theIntegral Equation 97 4.2 Displacement on the Earth's Surface 98 4.3 A BriefIntroduction to Fracture Mechanics 99 4.4 Nonsingular Stress Distributions105 4.5 Comparison of Slip Distributions and Surface Displacements 107 4.6Boundary ElementMethods 110 4.7 Fourier TransformMethods 111 4.8 SomeThree-Dimensional Crack Results 113 4.9 Summary and Perspective 114 4.10Problems 115 4.11 References 117 Chapter 5: Elastic Heterogeneity 1185.1 Long Strike-Slip Fault Bounding Two Media 118 5.2 Strike-Slip Faultwithin a Compliant Fault Zone 120 5.3 Strike-Slip Fault beneath a Layer 1255.4 Strike-Slip within a Layer over Half-Space 129 5.5 Propagator MatrixMethods 131 5.5.1 The Propagator Matrix for Antiplane Deformation 135 5.5.2Vertical Fault in a Homogeneous Half-Space 136 5.5.3 Vertical Fault withinHalf-Space beneath a Layer 138 5.5.4 Vertical Fault in Layer over Half-Space139 5.5.5 General Solution for an Arbitrary Number of Layers 141 5.5.6Displacements and Stresses at Depth 143 5.5.7 PropagatorMethods for PlaneStrain 143 5.6 Propagator Solutions in Three Dimensions 150 5.7 ApproximateSolutions for Arbitrary Variations in Properties 154 5.7.1 Variations inShear Modulus 157 5.7.2 Screw Dislocation 158 5.7.3 Edge Dislocation 1595.8 Summary and Perspective 159 5.9 Problems 162 5.10 References 164Chapter 6: Postseismic Relaxation 166 6.1 Elastic Layer over Viscous Channel169 6.2 Viscoelasticity 172 6.2.1 Correspondence Principle 175 6.3Strike-Slip Fault in an Elastic Plate Overlying a Viscoelastic Half-Space 1766.3.1 Stress in Plate and Half-Space 181 6.4 Strike-Slip Fault in ElasticLayer Overlying a Viscoelastic Channel 182 6.5 Dip-Slip Faulting 187 6.5.1Examples 190 6.6 Three-Dimensional Calculations 191 6.7 Summary andPerspective 193 6.8 Problems 197 6.9 References 198 Chapter 7: VolcanoDeformation 200 7.1 Spherical Magma Chamber 203 7.1.1 Center of Dilatation208 7.1.2 Volume of the Uplift, Magma Chamber, and Magma 212 7.2EllipsoidalMagma Chambers 214 7.3 Magmatic Pipes and Conduits 225 7.4 Dikesand Sills 229 7.4.1 Crack Models of Dikes and Sills 231 7.4.2 SurfaceFracturing and Dike Intrusion 236 7.5 Other Magma Chamber Geometries 2377.6 Viscoelastic Relaxation around Magma Chambers 240 7.7 Summary andPerspective 248 7.8 Problems 249 7.9 References 252 Chapter 8:Topography and Earth Curvature 255 8.1 Scaling Considerations 259 8.2Implementation Considerations 260 8.3 Center of Dilatation beneath a Volcano260 8.4 Earth's Sphericity 261 8.5 Summary and Perspective 263 8.6Problems 265 8.7 References 265 Chapter 9: Gravitational Effects 2679.1 Nondimensional Formof Equilibrium Equations 270 9.2 Inclusion inPropagator Matrix Formulation 273 9.3 Surface Gravity Approximation 275 9.4Gravitational Effects in Viscoelastic Solutions 276 9.4.1 IncompressibleHalf-Space 277 9.4.2 No-Buoyancy Approximation 278 9.4.3 Wang Approach 2799.4.4 Comparison of Different Viscoelastic Models 280 9.4.5 RelaxedViscoelastic Response 282 9.5 Changes in Gravity Induced by Deformation 2839.5.1 Gravity Changes and Volcano Deformation 289 9.5.2 An Example from LongValley Caldera, California 292 9.6 Summary and Perspective 292 9.7 Problems294 9.8 References 295 Chapter 10: Poroelastic Effects 297 10.1Constitutive Laws 300 10.1.1 Macroscopic Description 300 10.1.2Micromechanical Description 303 10.2 Field Equations 305 10.3 Analogy toThermoelasticity 308 10.4 One-Dimensional Deformation 309 10.4.1 Step Loadon the Free Surface 310 10.4.2 Time-Varying Fluid Load on the Free Surface312 10.5 Dislocations in Two Dimensions 313 10.6 Inflating Magma Chamber ina Poroelastic Half-Plane 315 10.7 Cumulative Poroelastic Deformation inThree Dimensions 321 10.8 Specified Pore Pressure Change 324 10.9 Summaryand Perspective 328 10.10 Problems 329 10.11 References 330 Chapter11: Fault Friction 332 11.1 Slip-Weakening Friction 333 11.2Velocity-Weakening Friction 335 11.3 Rate and State Friction 336 11.3.1Linearized Stability Analysis 344 11.4 Implications for EarthquakeNucleation 347 11.5 Nonlinear Stability Analysis 357 11.6 Afterslip 36011.7 Transient Slip Events 366 11.8 Summary and Perspective 367 11.9Problems 368 11.10 References 369 Chapter 12: Interseismic Deformationand Plate Boundary Cycle Models 372 12.1 Elastic Dislocation Models 37212.1.1 Dip-Slip Faults 373 12.2 Plate Motions 376 12.3 Elastic BlockModels378 12.4 Viscoelastic CycleModels 380 12.4.1 Viscoelastic Strike-SlipEarthquake Cycle Models 380 12.4.2 Comparison to Data from San Andreas Fault386 12.4.3 Viscoelastic Models with Stress-Driven Deep-Fault Creep 38912.4.4 Viscoelastic CycleModels for Dipping Faults 394 12.5 Rate-StateFriction Earthquake CycleModels 407 12.6 Summary and Perspective 409 12.7Problems 412 12.8 References 413 APPENDIX A: Integral Transforms 415A.1 Fourier Transforms 415 A.2 Laplace Transforms 416 A.3 References 419APPENDIX B: A Solution of the Diffusion Equation 420 APPENDIX C:Displacements Due to Crack Model of Strike-Slip Fault by Contour Integration423 Index 425