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Preface | ||
1 | Introduction | 1 |
2 | The Elastodynamic Equation and its Simple Solutions | 7 |
2.1 | Linear Elastodynamics | 8 |
2.2 | Elastic Plane Waves | 19 |
2.3 | Elastic Plane Waves Across a Plane Interface | 37 |
2.4 | High-Frequency Elastic Waves in Smoothly Inhomogeneous Media | 53 |
2.5 | Point-Source Solutions. Green Functions | 73 |
2.6 | Application of Green Functions to the Construction of More General Solutions | 89 |
3 | Seismic Rays and Travel Times | 99 |
3.1 | Ray Tracing Systems in Inhomogeneous Isotropic Media | 102 |
3.2 | Rays in Laterally Varying Layered Structures | 117 |
3.3 | Ray Tracing | 124 |
3.4 | Analytical Ray Tracing | 129 |
3.5 | Ray Tracing in Curvilinear Coordinates | 137 |
3.6 | Ray Tracing in Inhomogeneous Anisotropic Media | 148 |
3.7 | Ray Tracing and Travel-Time Computations in 1-D Models | 160 |
3.8 | Direct Computation of Travel Times and/or Wavefronts | 178 |
3.9 | Perturbation Methods for Travel Times | 189 |
3.10 | Ray Fields | 199 |
3.11 | Boundary-Value Ray Tracing | 217 |
3.12 | Surface-Wave Ray Tracing | 228 |
4 | Dynamic Ray Tracing. Paraxial Ray Methods | 234 |
4.1 | Dynamic Ray Tracing in Ray-Centered Coordinates | 237 |
4.2 | Hamiltonian Approach to Dynamic Ray Tracing | 259 |
4.3 | Propagator Matrices of Dynamic Ray Tracing Systems | 278 |
4.4 | Dynamic Ray Tracing in Isotropic Layered Media | 289 |
4.5 | Initial Conditions for Dynamic Ray Tracing | 310 |
4.6 | Paraxial Travel-Time Field and Its Derivatives | 322 |
4.7 | Dynamic Ray Tracing in Cartesian Coordinates | 331 |
4.8 | Special Cases. Analytical Dynamic Ray Tracing | 341 |
4.9 | Boundary-Value Ray Tracing for Paraxial Rays | 348 |
4.10 | Geometrical Spreading in a Layered Medium | 356 |
4.11 | Fresnel Volumes | 372 |
4.12 | Phase Shift Due to Caustics. KMAH Index | 380 |
4.13 | Dynamic Ray Tracing Along a Planar Ray. 2-D Models | 384 |
4.14 | Dynamic Ray Tracing in Inhomogeneous Anisotropic Media | 400 |
5 | Ray Amplitudes | 417 |
5.1 | Acoustic Case | 419 |
5.2 | Elastic Isotropic Structures | 449 |
5.3 | Reflection/Transmission Coefficients for Elastic Isotropic Media | 477 |
5.4 | Elastic Anisotropic Structures | 504 |
5.5 | Weakly Dissipative Media | 542 |
5.6 | Ray Series Method. Acoustic Case | 549 |
5.7 | Ray-Series Method. Elastic Case | 567 |
5.8 | Paraxial Displacement Vector. Paraxial Gaussian Beams | 582 |
5.9 | Validity Conditions and Extensions of the Ray Method | 607 |
6 | Ray Synthetic Seismograms | 621 |
6.1 | Elementary Ray Synthetic Seismograms | 622 |
6.2 | Ray Synthetic Seismograms | 630 |
6.3 | Ray Synthetic Seismograms in Weakly Dissipative Media | 639 |
6.4 | Ray Synthetic Particle Ground Motions | 643 |
App. A | Fourier Transform, Hilbert Transform, and Analytical Signals | 661 |
References | 667 | |
Index | 697 |
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