- Title: FUNDAMENTALS OF SEISMIC WAVE PROPAGATION
- Author: CHRIS H. CHAPMAN-Schlumberger Cambridge Research
- Page: 634
- Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press. The Edinburgh Building, Cambridge , UK - © C. H. Chapman 2004
- Contents:
Preface page ix
Preliminaries xi
0.1 Nomenclature xi
0.2 Symbols xviii
0.3 Special functions xxii
0.4 Canonical signals xxii
1 Introduction 1
2 Basic wave propagation 6
2.1 Plane waves 6
2.2 A point source 12
2.3 Travel-time function in layered media 16
2.4 Types of ray and travel-time results 26
2.5 Calculation of travel-time functions 45
3 Transforms 58
3.1 Temporal Fourier transform 58
3.2 Spatial Fourier transform 65
3.3 Fourier–Bessel transform 68
3.4 Tau-p transform 69
4 Review of continuum mechanics and elastic waves 76
4.1 Infinitesimal stress tensor and traction 78
4.2 Infinitesimal strain tensor 84
4.3 Boundary conditions 86
4.4 Constitutive relations 89
4.5 Navier wave equation and Green functions 100
4.6 Stress glut source 118
5 Asymptotic ray theory 134
5.1 Acoustic kinematic ray theory 134
5.2 Acoustic dynamic ray theory 145
5.3 Anisotropic kinematic ray theory 163
5.4 Anisotropic dynamic ray theory 170
5.5 Isotropic kinematic ray theory 178
5.6 Isotropic dynamic ray theory 180
5.7 One and two-dimensional media 182
6 Rays at an interface 198
6.1 Boundary conditions 200
6.2 Continuity of the ray equations 201
6.3 Reflection/transmission coefficients 207
6.4 Free surface reflection coefficients 224
6.5 Fluid–solid reflection/transmission coefficients 225
6.6 Interface polarization conversions 228
6.7 Linearized coefficients 231
6.8 Geometrical Green dyadic with interfaces 237
7 Differential systems for stratified media 247
7.1 One-dimensional differential systems 247
7.2 Solutions of one-dimensional systems 253
8 Inverse transforms for stratified media 310
8.1 Cagniard method in two dimensions 313
8.2 Cagniard method in three dimensions 323
8.3 Cagniard method in stratified media 340
8.4 Real slowness methods 346
8.5 Spectral methods 356
9 Canonical signals 378
9.1 First-motion approximations using the Cagniard method 379
9.2 First-motion approximations for WKBJ seismograms 415
9.3 Spectral methods 433
10 Generalizations of ray theory 459
10.1 Maslov asymptotic ray theory 460
10.2 Quasi-isotropic ray theory 487
10.3 Born scattering theory 504
10.4 Kirchhoff surface integral method 532
Appendices
A Useful integrals 555
B Useful Fourier transforms 560
C Ordinary differential equations 564
D Saddle-point methods 569
Bibliography 587
Author index 599
Subject index 602
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