A breviary of seismic tomography : imaging the interior of the earth and sun

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Title:

Personal Author:

Nolet, Guust

Publication Information:

New York, NY : Cambridge University Press, 2008

Physical Description:

xiv, 344 p. : ill. ; 26 cm.

ISBN:

9780521882446

Subject Term:

Seismic tomography

Geodynamics

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Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010229484	QE538.5 N65 2008	Open Access Book	Book	Searching... Unknown

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.

Preface	p. xi
1 Introduction	p. 1
1.1 Early efforts at seismic tomography	p. 2
1.2 Ocean acoustic tomography	p. 3
1.3 Global tomography	p. 3
1.4 Some major discoveries	p. 4
1.5 Helioseismology	p. 7
1.6 Finite-frequency tomography	p. 8
2 Ray theory for seismic waves	p. 11
2.1 The stress tensor	p. 11
2.2 Forces in continuous media	p. 12
2.3 Newton's law and the elastodynamic equations	p. 13
2.4 The acoustic wave equation	p. 16
2.5 The ray approximation	p. 20
2.6 Ray solutions in layered and spherical systems	p. 22
2.7 Geometrical spreading	p. 25
2.8 Rays in an isotropic, elastic Earth	p. 26
2.9 Fermat's Principle	p. 29
2.10 Huygens, Fresnel and Green	p. 30
2.11 Flow: solar p-waves or ocean acoustic waves	p. 34
2.12 Appendix A: Some elements of Fourier analysis	p. 36
3 Ray tracing	p. 40
3.1 The shooting method	p. 40
3.2 Ray bending	p. 42
3.3 Other raytracing algorithms for 3D media	p. 46
3.4 Ray-centred coordinates	p. 49
3.5 Dynamic ray tracing	p. 50
3.6 Ray tracing on the sphere	p. 53
3.7 Computational aspects	p. 54
4 Wave scattering	p. 58
4.1 The acoustic Green's function	p. 60
4.2 An acoustic point scatterer	p. 62
4.3 Green's functions for elastic waves	p. 63
4.4 Green's functions in the ray approximation	p. 68
4.5 The Born approximation	p. 70
4.6 Scattering of a plane wave	p. 73
4.7 The scattering matrix	p. 77
4.8 Appendix B: The impulse response	p. 79
5 Body wave amplitudes: theory	p. 82
5.1 Geometrical spreading	p. 82
5.2 The quality factor Q	p. 84
5.3 The correspondence principle	p. 86
5.4 Attenuating body waves	p. 88
5.5 Scattering	p. 91
6 Travel times: observations	p. 93
6.1 Phase picks	p. 96
6.2 Matched filters	p. 100
6.3 Wavelet estimation	p. 103
6.4 Differential times	p. 107
6.5 Signal and noise	p. 109
6.6 Time-distance analysis in helioseismology	p. 110
7 Travel times: interpretation	p. 116
7.1 The ray theoretical interpretation	p. 116
7.2 Cross-correlation of seismic arrivals	p. 121
7.3 Forward scattering	p. 125
7.4 Finite frequency sensitivity: a simple example	p. 126
7.5 Finite frequency kernels: general	p. 129
7.6 Alternative arrival time measurements	p. 135
7.7 Alternative methods for kernel computation	p. 138
7.8 Computational aspects	p. 139
8 Body wave amplitudes: observation and interpretation	p. 145
8.1 Amplitude observations	p. 146
8.2 t* observations	p. 149
8.3 Amplitude healing	p. 151
8.4 Boundary topography	p. 152
8.5 Finite-frequency Q tomography	p. 154
9 Nomal modes	p. 158
9.1 The discrete spectrum	p. 159
9.2 Rayleigh's Principle	p. 166
9.3 Mode splitting	p. 168
9.4 Observations of mode splits	p. 174
10 Surface wave interpretation: ray theory	p. 178
10.1 The theory of surface waves	p. 180
10.2 Love and Rayleigh waves	p. 182
10.3 Measuring fundamental mode dispersion	p. 187
10.4 Measuring higher mode dispersion	p. 190
10.5 Waveform fitting	p. 192
10.6 Partitioned waveform inversion (PWI)	p. 194
10.7 Appendix C: Asymptotic theory	p. 197
11 Surface waves: finite-frequency theory	p. 208
11.1 Phase and amplitude perturbations	p. 209
11.2 Practical considerations	p. 214
11.3 Phase velocity maps: an incompatibility	p. 217
12 Model parametrization	p. 219
12.1 Global parametrization	p. 220
12.2 Local parametrization	p. 222
12.3 Numerical considerations	p. 228
12.4 Spectral analysis and model correlations	p. 229
13 Common corrections	p. 233
13.1 Ellipticity corrections	p. 233
13.2 Topographic and bathymetric time corrections	p. 238
13.3 Crustal time corrections	p. 240
13.4 Surface wave corrections	p. 243
13.5 Source corrections	p. 245
13.6 Amplitude corrections for body waves	p. 247
13.7 Dispersion corrections	p. 249
13.8 Instrument response	p. 250
13.9 Clock corrections	p. 253
14 Linear inversion	p. 255
14.1 Maximum likelihood estimation and least squares	p. 256
14.2 Alternatives to least squares	p. 260
14.3 Singular value decomposition	p. 261
14.4 Tikhonov regularization	p. 265
14.5 Bayesian inference	p. 266
14.6 Information theory	p. 270
14.7 Numerical considerations	p. 272
14.8 Appendix D: Some concepts of probability theory and statistics	p. 275
15 Resolution and error analysis	p. 277
15.1 Resolution matrix	p. 277
15.2 Backus-Gilbert theory	p. 281
15.3 Sensitivity tests	p. 285
16 Anisotropy	p. 289
16.1 The elasticity tensor	p. 290
16.2 Waves in homogeneous anisotropic media	p. 295
16.3 S-wave splitting	p. 296
16.4 Surface wave anisotropy	p. 301
17 Future directions	p. 306
17.1 Beyond Born	p. 306
17.2 Adjoint methods	p. 307
17.3 Global coverage of seismic sensors	p. 310
17.4 Helioseismology and astroseismology	p. 312
References	p. 313
Author index	p. 334
General index	p. 339

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