REPORT 2
Oct 1, 1993 - Sep 30, 1994

Seismic Ray Theory

Vlastislav Cerveny

Contents

1 Introduction

2 Elastodynamic equation and its simple solutions

2.1 Linear elastodynamics

2.2 Elastic plane waves

2.3 Elastic plane waves across a plane interface

2.4 High-frequency elasticwaves in slightly inhomogeneousmedia

2.5 Point source solutions of acoustic and elastodynamicwave equations

3 Seismic rays and travel times

3.1 Ray tracing systems

3.2 Rays in laterally varying layered structures

3.3 Ray tracing

3.4 Analytical ray tracing

3.5 Ray tracing in curvilinear coordinates

3.6 Ray tracing in inhomogeneousanisotropicmedia

3.7 Ray tracing and travel-time computations in 1-D models

3.8 Direct computation of travel times. Network ray tracing

3.9 Linearized equations for travel times. Frozen rays

3.10 Ray fields

3.11 Initial value and boundary value ray tracing

3.12 Approximation of the model

3.13 Raycodes in layered and block structures

4 Dynamic ray tracing. Paraxial ray methods

4.1 Ray-centred coordinates

4.2 Dynamic ray tracing in ray-centred coordinates

4.3 Ray propagator matrix

4.4 Dynamic ray tracing in layered media

4.5 Initial conditions for dynamic ray tracing

4.6 Paraxial travel time field and its derivatives

4.7 Dynamic ray tracing in Cartesian coordinates

4.8 Special cases. Analytical dynamic ray tracing

4.9 Boundary value ray tracing for paraxial rays

4.10 Geometrical spreading in a layered medium

4.11 Phase shift due to caustics

4.12 Fresnel volume

4.13 Dynamic ray tracing along a planar rays. 2-D models

4.14 Dynamic ray tracing in anisotropic inhomogeneous media

5 Ray amplitudes

5.1 Acoustic case

6 Ray synthetic seismograms

6.1 Hilbert transform

6.2 Analytical signal

6.4 Ray synthetic seismograms

6.5 Paraxial ray approaches in the computation of synthetic seismograms

7 Particle ground motions of seismic body waves

7.1 Polarization of seismic body waves

7.2 Particle motion diagrams of seismic body waves at the Earth's surface

7.3 Quasi-elliptical polarization of seismic body waves in layered structures

7.4 Partical motion in complex structures

Selected references

SW3D