- 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

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In: Doornbos, D.J. (ed.), Seismological Algorithms, pp. 89-168, Academic Press, New York, 1988.

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