This book provides an approachable and concise introduction to seismic theory, designed as a first course for undergraduate students. It clearly explains the fundamental concepts, emphasizing intuitive understanding over lengthy derivations. Incorporating over 30% new material, this second edition includes all the topics needed for a one-semester course in seismology. Additional material has been added throughout including numerical methods, 3-D ray tracing, earthquake location, attenuation, normal modes, and receiver functions. The chapter on earthquakes and source theory has been extensively revised and enlarged, and now includes details on non-double-couple sources, earthquake scaling, radiated energy, and finite slip inversions. Each chapter includes worked problems and detailed exercises that give students the opportunity to apply the techniques they have learned to compute results of interest and to illustrate the Earth's seismic properties. Computer subroutines and datasets for use in the exercises are available at www.cambridge.org/shearer.
Author(s): Peter M. Shearer
Edition: 2
Publisher: Cambridge University Press
Year: 2009
Language: English
Pages: 412
Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface to the First Edition......Page 13
Preface to the Second Edition......Page 15
Acknowledgment......Page 16
1 Introduction......Page 17
1.1 A brief history of seismology......Page 18
1.2 Exercises......Page 31
2.1 The stress tensor......Page 33
2.1.1 Example: Computing the traction vector......Page 35
2.1.2 Principal axes of stress......Page 36
2.1.3 Example: Computing the principal axes......Page 38
2.1.4 Deviatoric stress......Page 39
2.1.5 Values for stress......Page 40
2.2 The strain tensor......Page 41
2.2.2 Example: Computing strain for a seismic wave......Page 45
2.3 The linear stress−strain relationship......Page 46
2.3.1 Units for elastic moduli......Page 48
2.4 Exercises......Page 49
3.1 Introduction: The wave equation......Page 55
3.2 The momentum equation......Page 56
3.3 The seismic wave equation......Page 58
3.4 Plane waves......Page 62
3.5 Polarizations of P and S waves......Page 64
3.6 Spherical waves......Page 66
3.7 Methods for computing synthetic seismograms......Page 67
3.8 The future of seismology?......Page 69
3.9 Equations for 2-D isotropic finite differences......Page 72
3.10 Exercises......Page 77
4.1 Snell’s law......Page 81
4.2 Ray paths for laterally homogeneous models......Page 83
4.2.1 Example: Computing X(p) and T(p)......Page 86
4.2.2 Ray tracing through velocity gradients......Page 87
4.3 Travel time curves and delay times......Page 88
4.3.2 The tau(p) function......Page 89
4.4 Low-velocity zones......Page 92
4.5 Summary of 1-D ray tracing equations......Page 93
4.6 Spherical-Earth ray tracing......Page 96
4.7 The Earth-flattening transformation......Page 98
4.8 Three-dimensional ray tracing......Page 99
4.9.1 Crustal phases......Page 102
4.9.2 Whole Earth phases......Page 103
4.9.3 PKJKP: The Holy Grail of body wave seismology......Page 104
4.10 Global body-wave observations......Page 105
4.11 Exercises......Page 114
5.1 One-dimensional velocity inversion......Page 119
5.2 Straight-line fitting......Page 122
5.2.1 Example: Solving for a layer-cake model......Page 124
5.2.2 Other ways to fit the T(X) curve......Page 125
5.3 Tau(p) Inversion......Page 126
5.3.1 Example: The layer-cake model revisited......Page 127
5.3.2 Obtaining tau(p) constraints......Page 128
5.4 Linear programming and regularization methods......Page 131
5.6 Three-dimensional velocity inversion......Page 133
5.6.1 Setting up the tomography problem......Page 134
5.6.2 Solving the tomography problem......Page 138
5.6.3 Tomography complications......Page 140
5.6.4 Finite frequency tomography......Page 141
5.7 Earthquake location......Page 143
5.7.1 Iterative location methods......Page 149
5.7.2 Relative event location methods......Page 150
5.8 Exercises......Page 151
6.1 Energy in seismic waves......Page 155
6.2 Geometrical spreading in 1-D velocity models......Page 158
6.3 Reflection and transmission coefficients......Page 160
6.3.1 SH-wave reflection and transmission coefficients......Page 161
6.3.3 Vertical incidence coefficients......Page 165
6.3.4 Energy-normalized coefficients......Page 167
6.3.5 Dependence on ray angle......Page 168
6.4 Turning points and Hilbert transforms......Page 172
6.5 Matrix methods for modeling plane waves......Page 175
6.6 Attenuation......Page 179
6.6.1 Example: Computing intrinsic attenuation......Page 180
6.6.2 t* and velocity dispersion......Page 181
6.6.3 The absorption band model......Page 184
6.6.4 The standard linear solid......Page 187
6.6.5 Earth’s attenuation......Page 189
6.6.6 Observing Q......Page 191
6.6.7 Non-linear attenuation......Page 192
6.7 Exercises......Page 193
7 Reflection seismology......Page 197
7.1 Zero-offset sections......Page 198
7.2 Common midpoint stacking......Page 200
7.3 Sources and deconvolution......Page 204
7.4 Migration......Page 207
7.4.1 Huygens’ principle......Page 208
7.4.2 Diffraction hyperbolas......Page 209
7.4.3 Migration methods......Page 211
7.5 Velocity analysis......Page 213
7.5.1 Statics corrections......Page 214
7.6 Receiver functions......Page 215
7.7 Kirchhoff theory......Page 218
7.7.1 Kirchhoff applications......Page 224
7.7.3 Kirchhoff migration......Page 226
7.8 Exercises......Page 227
8.1 Love waves......Page 231
8.1.1 Solution for a single layer......Page 234
8.2 Rayleigh waves......Page 235
8.3 Dispersion......Page 240
8.4 Global surface waves......Page 242
8.5 Observing surface waves......Page 244
8.6 Normal modes......Page 247
8.7 Exercises......Page 254
9.1 Green’s functions and the moment tensor......Page 257
9.2 Earthquake faults......Page 261
9.2.1 Non-double-couple sources......Page 264
9.3 Radiation patterns and beach balls......Page 267
9.3.1 Example: Plotting a focal mechanism......Page 275
9.4 Far-field pulse shapes......Page 276
9.4.1 Directivity......Page 278
9.4.2 Source spectra......Page 281
9.4.3 Empirical Green’s functions......Page 283
9.5 Stress drop......Page 284
9.5.1 Self-similar earthquake scaling......Page 287
9.6 Radiated seismic energy......Page 289
9.6.1 Earthquake energy partitioning......Page 293
9.7 Earthquake magnitude......Page 296
9.7.1 The b value......Page 304
9.7.2 The intensity scale......Page 306
9.8 Finite slip modeling......Page 307
9.9 The heat flow paradox......Page 309
9.10 Exercises......Page 312
10.1 The earthquake cycle......Page 317
10.2 Earthquake triggering......Page 325
10.3 Searching for precursors......Page 330
10.4 Are earthquakes unpredictable?......Page 332
10.5 Exercises......Page 334
11.1 Instruments......Page 337
11.1.1 Modern seismographs......Page 343
11.2 Earth noise......Page 346
11.3 Anisotropy......Page 348
11.3.2 Weak anisotropy......Page 353
11.3.3 Shear-wave splitting......Page 355
11.3.4 Hexagonal anisotropy......Page 357
11.3.5 Mechanisms for anisotropy......Page 359
11.3.6 Earth’s anisotropy......Page 360
11.4 Exercises......Page 362
Appendix A The PREM model......Page 365
B.1 Vector calculus......Page 369
B.2 Complex numbers......Page 374
Appendix C The eikonal equation......Page 377
Appendix D Fortran subroutines......Page 383
E.1 Convolution......Page 387
E.3 Hilbert transform......Page 389
Bibliography......Page 393
Index......Page 407
