Cover

Half-title

Title

Copyright

Contents

Preface

1 Introduction

1.1 Early efforts at seismic tomography

1.2 Ocean acoustic tomography

1.3 Global tomography

1.4 Some major discoveries

1.5 Helioseismology

1.6 Finite-frequency tomography

2 Ray theory for seismic waves

2.1 The stress tensor

2.2 Forces in continuous media

2.3 Newton's law and the elastodynamic equations

2.4 The acoustic wave equation

2.5 The ray approximation

2.6 Ray solutions in layered and spherical systems

2.7 Geometrical spreading

2.8 Rays in an isotropic, elastic Earth

2.9 Fermat's Principle

2.10 Huygens, Fresnel and Green

2.11 Flow: solar p-waves or ocean acoustic waves

2.12 Appendix A: Some elements of Fourier analysis

3 Ray tracing

3.1 The shooting method

3.2 Ray bending

3.3 Other raytracing algorithms for 3D media

3.4 Ray-centred coordinates

3.5 Dynamic ray tracing

3.6 Ray tracing on the sphere

3.7 Computational aspects

4 Wave scattering

4.1 The acoustic Green's function

4.2 An acoustic point scatterer

4.3 Green's functions for elastic waves

4.4 Green's functions in the ray approximation

4.5 The Born approximation

4.6 Scattering of a plane wave

4.7 The scattering matrix

4.8 Appendix B: The impulse response

5 Body wave amplitudes: theory

5.1 Geometrical spreading

5.2 The quality factor Q

5.3 The correspondence principle

5.4 Attenuating body waves

5.5 Scattering

6 Travel times: observations

6.1 Phase picks

6.2 Matched filters

6.3 Wavelet estimation

6.4 Differential times

6.5 Signal and noise

6.6 Time–distance analysis in helioseismology

7 Travel times: interpretation

7.1 The ray theoretical interpretation

7.2 Cross-correlation of seismic arrivals

7.3 Forward scattering

7.4 Finite frequency sensitivity: a simple example

7.5 Finite frequency kernels: general

7.6 Alternative arrival time measurements

7.7 Alternative methods for kernel computation

7.8 Computational aspects

8 Body wave amplitudes: observation and interpretation

8.1 Amplitude observations

8.2 t* observations

8.3 Amplitude healing

8.4 Boundary topography

8.5 Finite-frequency Q tomography

9 Normal modes

9.1 The discrete spectrum

9.2 Rayleigh's Principle

9.3 Mode splitting

9.4 Observations of mode splits

10 Surface wave interpretation: ray theory

10.1 The theory of surface waves

10.2 Love and Rayleigh waves

10.3 Measuring fundamental mode dispersion

10.4 Measuring higher mode dispersion

10.5 Waveform fitting

10.6 Partitioned waveform inversion (PWI)

10.7 Appendix C: Asymptotic theory

11 Surface waves: finite-frequency theory

11.1 Phase and amplitude perturbations

11.2 Practical considerations

11.3 Phase velocity maps: an incompatibility

12 Model parametrization

12.1 Global parametrization

12.2 Local parametrization

12.3 Numerical considerations

12.4 Spectral analysis and model correlations

13 Common corrections

13.1 Ellipticity corrections

13.2 Topographic and bathymetric time corrections

13.3 Crustal time corrections

13.4 Surface wave corrections

13.5 Source corrections

13.6 Amplitude corrections for body waves

13.7 Dispersion corrections

13.8 Instrument response

13.9 Clock corrections

14 Linear inversion

14.1 Maximum likelihood estimation and least squares

14.2 Alternatives to least squares

14.3 Singular value decomposition

14.4 Tikhonov regularization

14.5 Bayesian inference

14.6 Information theory

14.7 Numerical considerations

14.8 Appendix D: Some concepts of probability theory and statistics

15 Resolution and error analysis

15.1 Resolution matrix

15.2 Backus-Gilbert theory

15.3 Sensitivity tests

16 Anisotropy

16.1 The elasticity tensor

16.2 Waves in homogeneous anisotropic media

16.3 S-wave splitting

16.4 Surface wave anisotropy

17 Future directions

17.1 Beyond Born

17.2 Adjoint methods

17.3 Global coverage of seismic sensors

17.4 Helioseismology and astroseismology

References

Author index

General index