2.8.3 Surface wave dispersion studies, 96
2.8.4 Tsunami dispersion, 99
2.9 Normal modes of the earth, 101
2.9.1 Motivation, 101
2.9.2 Modes of a sphere, 101
2.9.3 Spherical harmonics, 103
2.9.4 Torsional modes, 104
2.9.5 Spheroidal modes, 106
2.9.6 Modes and propagating waves, 106
2.9.7 Observing normal modes, 110
2.9.8 Normal mode synthetic seismograms, 111
2.9.9 Mode attenuation, splitting, and coupling, 111
Further reading, 115
Problems, 116
3 Seismology and Earth Structure, 119
3.1 Introduction, 119
3.2 Refraction seismology, 120
3.2.1 Flat layer method, 120
3.2.2 Dipping layer method, 123
3.2.3 Advanced analysis methods, 126
3.2.4 Crustal structure, 128
3.2.5 Rocks and minerals, 132
3.3 Reflection seismology, 134
3.3.1 Travel time curves for reflections, 134
3.3.2 Intercept-slowness formulation for
travel times, 137
3.3.3 Multichannel data geometry, 140
3.3.4 Common midpoint stacking, 141
3.3.5 Signal enhancement, 145
3.3.6 Deconvolution, 148
3.3.7 Migration, 152
3.3.8 Data processing sequence, 156
3.4 Seismic waves in a spherical earth, 157
3.4.1 Ray paths and travel times, 157
3.4.2 Velocity distributions, 159
3.4.3 Travel time curve inversion, 161
3.5 Body wave travel time studies, 162
3.5.1 Body wave phases, 163
3.5.2 Core phases, 166
3.5.3 Upper mantle structure, 169
3.5.4 Lower mantle structure, 171
3.5.5 Visualizing body waves, 174
3.6 Anisotropic earth structure, 177
3.6.1 General considerations, 177
3.6.2 Transverse isotropy and azimuthal
anisotropy, 177
3.6.3 Anisotropy of minerals and rocks, 179
3.6.4 Anisotropy of composite structures, 180
3.6.5 Anisotropy in the lithosphere and the
asthenosphere, 180
3.6.6 Anisotropy in the mantle and the core, 182
3.7 Attenuation and anelasticity, 185
3.7.1 Wave attenuation, 185
3.7.2 Geometric spreading, 187
3.7.3 Multipathing, 187
3.7.4 Scattering, 189
3.7.5 Intrinsic attenuation, 190
3.7.6 Quality factor, Q, 192
3.7.7 Spectral resonance peaks, 193
3.7.8 Physical dispersion due to anelasticity, 194
3.7.9 Physical models for anelasticity, 196
3.7.10 Q from crust to inner core, 197
3.8 Composition of the mantle and the core, 198
3.8.1 Density within the earth, 199
3.8.2 Temperature in the earth, 203
3.8.3 Composition of the mantle, 204
3.8.4 Composition of D″, 208
3.8.5 Composition of the core, 209
3.8.6 Seismology and planetary evolution, 210
Further reading, 212
Problems, 212
4 Earthquakes, 215
4.1 Introduction, 215
4.2 Focal mechanisms, 217
4.2.1 Fault geometry, 217
4.2.2 First motions, 219
4.2.3 Body wave radiation patterns, 220
4.2.4 Stereographic fault plane representation, 222
4.2.5 Analytical representation of fault
geometry, 228
4.3 Waveform modeling, 229
4.3.1 Basic model, 229
4.3.2 Source time function, 230
4.3.3 Body wave modeling, 231
4.3.4 Surface wave focal mechanisms, 235
4.3.5 Once and future earthquakes, 239
4.4 Moment tensors, 239
4.4.1 Equivalent forces, 239
4.4.2 Single forces, 240
4.4.3 Force couples, 241
4.4.4 Double couples, 242
4.4.5 Earthquake moment tensors, 242
4.4.6 Isotropic and CLVD moment tensors, 245
4.4.7 Moment tensor inversion, 246
4.4.8 Interpretation of moment tensors, 249
4.5 Earthquake geodesy, 251
4.5.1 Measuring ground deformation, 251
4.5.2 Coseismic deformation, 254
4.5.3 Joint geodetic and seismological earthquake
studies, 256
4.5.4 Interseismic deformation and the seismic
cycle, 259
4.6 Source parameters, 263
4.6.1 Magnitudes and moment, 263
4.6.2 Source spectra and scaling laws, 266
4.6.3 Stress drop and earthquake energy, 269
4.7 Earthquake statistics, 274
4.7.1 Frequency–magnitude relations, 274
vi Contents
2.8.4 Tsunami dispersion, 99
2.9 Normal modes of the earth, 101
2.9.1 Motivation, 101
2.9.2 Modes of a sphere, 101
2.9.3 Spherical harmonics, 103
2.9.4 Torsional modes, 104
2.9.5 Spheroidal modes, 106
2.9.6 Modes and propagating waves, 106
2.9.7 Observing normal modes, 110
2.9.8 Normal mode synthetic seismograms, 111
2.9.9 Mode attenuation, splitting, and coupling, 111
Further reading, 115
Problems, 116
3 Seismology and Earth Structure, 119
3.1 Introduction, 119
3.2 Refraction seismology, 120
3.2.1 Flat layer method, 120
3.2.2 Dipping layer method, 123
3.2.3 Advanced analysis methods, 126
3.2.4 Crustal structure, 128
3.2.5 Rocks and minerals, 132
3.3 Reflection seismology, 134
3.3.1 Travel time curves for reflections, 134
3.3.2 Intercept-slowness formulation for
travel times, 137
3.3.3 Multichannel data geometry, 140
3.3.4 Common midpoint stacking, 141
3.3.5 Signal enhancement, 145
3.3.6 Deconvolution, 148
3.3.7 Migration, 152
3.3.8 Data processing sequence, 156
3.4 Seismic waves in a spherical earth, 157
3.4.1 Ray paths and travel times, 157
3.4.2 Velocity distributions, 159
3.4.3 Travel time curve inversion, 161
3.5 Body wave travel time studies, 162
3.5.1 Body wave phases, 163
3.5.2 Core phases, 166
3.5.3 Upper mantle structure, 169
3.5.4 Lower mantle structure, 171
3.5.5 Visualizing body waves, 174
3.6 Anisotropic earth structure, 177
3.6.1 General considerations, 177
3.6.2 Transverse isotropy and azimuthal
anisotropy, 177
3.6.3 Anisotropy of minerals and rocks, 179
3.6.4 Anisotropy of composite structures, 180
3.6.5 Anisotropy in the lithosphere and the
asthenosphere, 180
3.6.6 Anisotropy in the mantle and the core, 182
3.7 Attenuation and anelasticity, 185
3.7.1 Wave attenuation, 185
3.7.2 Geometric spreading, 187
3.7.3 Multipathing, 187
3.7.4 Scattering, 189
3.7.5 Intrinsic attenuation, 190
3.7.6 Quality factor, Q, 192
3.7.7 Spectral resonance peaks, 193
3.7.8 Physical dispersion due to anelasticity, 194
3.7.9 Physical models for anelasticity, 196
3.7.10 Q from crust to inner core, 197
3.8 Composition of the mantle and the core, 198
3.8.1 Density within the earth, 199
3.8.2 Temperature in the earth, 203
3.8.3 Composition of the mantle, 204
3.8.4 Composition of D″, 208
3.8.5 Composition of the core, 209
3.8.6 Seismology and planetary evolution, 210
Further reading, 212
Problems, 212
4 Earthquakes, 215
4.1 Introduction, 215
4.2 Focal mechanisms, 217
4.2.1 Fault geometry, 217
4.2.2 First motions, 219
4.2.3 Body wave radiation patterns, 220
4.2.4 Stereographic fault plane representation, 222
4.2.5 Analytical representation of fault
geometry, 228
4.3 Waveform modeling, 229
4.3.1 Basic model, 229
4.3.2 Source time function, 230
4.3.3 Body wave modeling, 231
4.3.4 Surface wave focal mechanisms, 235
4.3.5 Once and future earthquakes, 239
4.4 Moment tensors, 239
4.4.1 Equivalent forces, 239
4.4.2 Single forces, 240
4.4.3 Force couples, 241
4.4.4 Double couples, 242
4.4.5 Earthquake moment tensors, 242
4.4.6 Isotropic and CLVD moment tensors, 245
4.4.7 Moment tensor inversion, 246
4.4.8 Interpretation of moment tensors, 249
4.5 Earthquake geodesy, 251
4.5.1 Measuring ground deformation, 251
4.5.2 Coseismic deformation, 254
4.5.3 Joint geodetic and seismological earthquake
studies, 256
4.5.4 Interseismic deformation and the seismic
cycle, 259
4.6 Source parameters, 263
4.6.1 Magnitudes and moment, 263
4.6.2 Source spectra and scaling laws, 266
4.6.3 Stress drop and earthquake energy, 269
4.7 Earthquake statistics, 274
4.7.1 Frequency–magnitude relations, 274
vi Contents