Seismic Ray Theory Book

	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