A Breviary of Seismic Tomography: Imaging the

This is the first textbook to cover the essential aspects of the topic at a level accessible to students. While focusing on applications in solid earth geophysics, the book also includes excursions into helioseismology, thereby highlighting the strong affinity between the two fields. The book provides a comprehensive introduction to seismic tomography, including the basic theory of wave propagation, the ray and Born approximations required for interpretation of amplitudes, and travel times and phases. It considers observational features while also providing practical recommendations for implementing numerical models. Written by one of the leaders in the field, and containing numerous student exercises, this textbook is appropriate for advanced undergraduate and graduate courses. It is also an invaluable guide for seismology research practitioners in geophysics and astronomy. Solutions to the exercises and accompanying tomographic software and documentation can be accessed online from www.cambridge.org/9780521882446.

Guust Nolet is the George J. Magee Professor of Geophysics Emeritus at Princeton University and currently teaches at the University of Nice/Sophia Antipolis in France.

Preface	p. xi
Introduction	p. 1
Early efforts at seismic tomography	p. 2
Ocean acoustic tomography	p. 3
Global tomography	p. 3
Some major discoveries	p. 4
Helioseismology	p. 7
Finite-frequency tomography	p. 8
Ray theory for seismic waves	p. 11
The stress tensor	p. 11
Forces in continuous media	p. 12
Newton's law and the elastodynamic equations	p. 13
The acoustic wave equation	p. 16
The ray approximation	p. 20
Ray solutions in layered and spherical systems	p. 22
Geometrical spreading	p. 25
Rays in an isotropic, elastic Earth	p. 26
Fermat's Principle	p. 29
Huygens, Fresnel and Green	p. 30
Flow: solar p-waves or ocean acoustic waves	p. 34
Appendix A: Some elements of Fourier analysis	p. 36
Ray tracing	p. 40
The shooting method	p. 40
Ray bending	p. 42
Other raytracing algorithms for 3D media	p. 46
Ray-centred coordinates	p. 49
Dynamic ray tracing	p. 50
Ray tracing on the sphere	p. 53
Computational aspects	p. 54
Wave scattering	p. 58
The acoustic Green's function	p. 60
An acoustic point scatterer	p. 62
Green's functions for elastic waves	p. 63
Green's functions in the ray approximation	p. 68
The Born approximation	p. 70
Scattering of a plane wave	p. 73
The scattering matrix	p. 77
Appendix B: The impulse response	p. 79
Body wave amplitudes: theory	p. 82
Geometrical spreading	p. 82
The quality factor Q	p. 84
The correspondence principle	p. 86
Attenuating body waves	p. 88
Scattering	p. 91
Travel times: observations	p. 93
Phase picks	p. 96
Matched filters	p. 100
Wavelet estimation	p. 103
Differential times	p. 107
Signal and noise	p. 109
Time-distance analysis in helioseismology	p. 110
Travel times: interpretation	p. 116
The ray theoretical interpretation	p. 116
Cross-correlation of seismic arrivals	p. 121
Forward scattering	p. 125
Finite frequency sensitivity: a simple example	p. 126
Finite frequency kernels: general	p. 129
Alternative arrival time measurements	p. 135
Alternative methods for kernel computation	p. 138
Computational aspects	p. 139
Body wave amplitudes: observation and interpretation	p. 145
Amplitude observations	p. 146
t* observations	p. 149
Amplitude healing	p. 151
Boundary topography	p. 152
Finite-frequency Q tomography	p. 154
Nomal modes	p. 158
The discrete spectrum	p. 159
Rayleigh's Principle	p. 166
Mode splitting	p. 168
Observations of mode splits	p. 174
Surface wave interpretation: ray theory	p. 178
The theory of surface waves	p. 180
Love and Rayleigh waves	p. 182
Measuring fundamental mode dispersion	p. 187
Measuring higher mode dispersion	p. 190
Waveform fitting	p. 192
Partitioned waveform inversion (PWI)	p. 194
Appendix C: Asymptotic theory	p. 197
Surface waves: finite-frequency theory	p. 208
Phase and amplitude perturbations	p. 209
Practical considerations	p. 214
Phase velocity maps: an incompatibility	p. 217
Model parametrization	p. 219
Global parametrization	p. 220
Local parametrization	p. 222
Numerical considerations	p. 228
Spectral analysis and model correlations	p. 229
Common corrections	p. 233
Ellipticity corrections	p. 233
Topographic and bathymetric time corrections	p. 238
Crustal time corrections	p. 240
Surface wave corrections	p. 243
Source corrections	p. 245
Amplitude corrections for body waves	p. 247
Dispersion corrections	p. 249
Instrument response	p. 250
Clock corrections	p. 253
Linear inversion	p. 255
Maximum likelihood estimation and least squares	p. 256
Alternatives to least squares	p. 260
Singular value decomposition	p. 261
Tikhonov regularization	p. 265
Bayesian inference	p. 266
Information theory	p. 270
Numerical considerations	p. 272
Appendix D: Some concepts of probability theory and statistics	p. 275
Resolution and error analysis	p. 277
Resolution matrix	p. 277
Backus-Gilbert theory	p. 281
Sensitivity tests	p. 285
Anisotropy	p. 289
The elasticity tensor	p. 290
Waves in homogeneous anisotropic media	p. 295
S-wave splitting	p. 296
Surface wave anisotropy	p. 301
Future directions	p. 306
Beyond Born	p. 306
Adjoint methods	p. 307
Global coverage of seismic sensors	p. 310
Helioseismology and astroseismology	p. 312
References	p. 313
Author index	p. 334
General index	p. 339
Table of Contents provided by Ingram. All Rights Reserved.

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A Breviary of Seismic Tomography: Imaging the Interior of the Earth and Sun

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