Complete seismic-ray tracing in three-dimensional structures

Contents

1. Introduction

2. Coordinate system

2.1 Metric tensor and Christoffel symbols

2.2 Examples of most important coordinate systems

2.2.1 Cartesian coordinate system

2.2.2 Polar spherical coordinate system

2.2.3 Geographic spherical coordinate system

2.2.4 Other coordinate systems

3. Model of the medium

3.1 The model

3.2 The data and routines specifying the model

3.2.1 Data specifying the model

3.2.2 Specification of smooth surfaces

3.2.3 Specification of the parameters of the medium

3.3 Auxiliary procedures

3.3.1 Determination of the index of a block

3.3.2 Transformation of the parameters of the medium

3.4 Examples

4. Codes of elementary waves

5. Complete ray tracing

5.1 Theory

5.1.1 Ray tracing and the travel time computation

5.1.2 Polarization vectors

5.1.3 Dynamic ray tracing. Propagator matrix

5.1.4 Vectorial reduced amplitudes

5.2 The quantities computed along a ray

5.2.1 Basic quantities computed along a ray

5.2.2 Auxiliary quantities computed along a ray

5.2.3 The quantities for identification of caustics

5.3 Auxiliary surfaces

5.4 Termination of tracing a ray

5.5 Storing of the computed quantities

5.5.1 Storing of the quantities along a ray

5.5.2 Storing of the quantities at the specified surfaces

5.5.3 Storing of the quantities at the endpoints of rays of elementary waves

5.5.4 List of stored quantities

5.6 Data for complete ray tracing

5.7 Complete ray tracing

5.8 Complete ray tracing through a complex block

5.8.1 A short description of routine RAYEL for the ray tracing through one block

5.8.2 Right-hand sides of the differential equations (subroutine FCT)

5.8.3 Subroutine OUTP

5.8.4 Auxiliary procedures

5.9 Complete ray tracing across a curved interface

5.9.1 Transformation of auxiliary quantities, travel time and coordinates

5.9.2 Metric tensor and velocities

5.9.3 Transformation of the slowness vector and of the polarization vectors

5.9.4 The curvature of the interface and the velocity gradients in the local Cartesian coordinate system

5.9.5 The dynamic ray tracing across a curved interface

5.9.6 Transformation of reduced amplitudes

5.9.7 The reflection//transmission coefficients

6. Initial points of rays

6.1 Important quantities at the initial point of the ray

6.2 Initial values for the complete ray tracing

7. Applications and processing of the results of the complete ray tracing

7.1 Travel time. Imaginary travel time

7.2 Slowness vector. First partial derivatives of the travel time field

7.3 Vector basis of the ray-centred coordinate system

7.4 Ray propagator matrix

7.5 Matrix of geometrical spreading Q

7.6 Transformation matrix P

7.7 Geometrical spreading

7.8 Matrix of second derivatives of the travel time field

7.9 Curvature of the wavefront

7.10 Paraxial travel times

7.11 Paraxial rays

7.12 Two point ray tracing for paraxial rays

7.13 Fresnel volumes

7.14 Phase shift due to caustics. KMAH index

7.15 Ray amplitudes

7.16 Paraxial ray approximation for the ray amplitudes

7.17 Amplitudes at structural interfaces or at the Earth's surface

7.18 Ray amplitudes in slightly dissipative media

7.19 Displacement vector

7.20 Ray synthetic body wave seismograms

7.21 Ray theory elastodynamic Green function

7.22 Moment tensor point source

7.23 Particle motion diagrams

7.24 Gaussian beams and Gaussian packets

7.25 Summation of Gaussian beams and Gaussian packets

7.26 Integrals of the ray propagator matrix along the ray

7.27 Other applications

References

Whole paper

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