Earthquake and volcano deformation

Earthquake and Volcano Deformation is the first textbook to present the mechanical models of earthquake and volcanic processes, emphasizing earth-surface deformations that can be compared with observations from Global Positioning System (GPS) receivers, Interferometric Radar (InSAR), and borehole strain- and tiltmeters. Paul Segall provides the physical and mathematical fundamentals for the models used to interpret deformation measurements near active faults and volcanic centers.

Segall highlights analytical methods of continuum mechanics applied to problems of active crustal deformation. Topics include elastic dislocation theory in homogeneous and layered half-spaces, crack models of faults and planar intrusions, elastic fields due to pressurized spherical and ellipsoidal magma chambers, time-dependent deformation resulting from faulting in an elastic layer overlying a viscoelastic half-space and related earthquake cycle models, poroelastic effects due to faulting and magma chamber inflation in a fluid-saturated crust, and the effects of gravity on deformation. He also explains changes in the gravitational field due to faulting and magmatic intrusion, effects of irregular surface topography and earth curvature, and modern concepts in rate- and state-dependent fault friction. This textbook presents sample calculations and compares model predictions against field data from seismic and volcanic settings from around the world.

Earthquake and Volcano Deformation requires working knowledge of stress and strain, and advanced calculus. It is appropriate for advanced undergraduates and graduate students in geophysics, geology, and engineering.

Professors: A supplementary Instructor's Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: https://press.princeton.edu/class_use/solutions.html

Author Notes

Paul Segall is professor of geophysics at Stanford University.

Reviews 1

Choice Review

An understanding and modeling of Earth's crustal deformation connected with earthquakes and volcanic activity has enabled significantly improved precision in the application of space-based geodetic systems. Segall (geophysics, Stanford Univ.) provides this first work on the topic that highlights, from a thorough mathematical basis, new insights into the basic theory of mechanical models and applications of GPS and InSAR to improve understanding of Earth's deformation processes. The 12-chapter work begins with "Deformation, Stress, and Conservation Laws." The next two chapters cover strike-slip and dip-slip fault dislocation models. The remaining chapters are titled "Crack Models of Faults," "Elastic Heterogeneity," "Postseismic Relaxation," "Volcano Deformation," "Topography and Earth Curvature," "Gravitational Effects," "Poroelastic Effects," "Fault Friction," and "Interseismic Deformation and Plate Boundary Cycle Models." Each chapter is reinforced with an extensive bibliography. This excellent advanced textbook will most positively impact graduate education and basic and applied research into the science of crustal deformation. Summing Up: Highly recommended. Graduate students through professionals/practitioners in geophysics, geology, and rock mechanics engineering. T. L. T. Grose emeritus, Colorado School of Mines

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

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