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Published February 1980 | Published
Journal Article Open

Solving two-point seismic-ray tracing problems in a heterogeneous medium. Part 1. A general adaptive finite difference method


A study of two-point seismic-ray tracing problems in a heterogeneous isotropic medium and how to solve them numerically will be presented in a series of papers. In this Part 1, it is shown how a variety of two-point seismic-ray tracing problems can be formulated mathematically as systems of first-order nonlinear ordinary differential equations subject to nonlinear boundary conditions. A general numerical method to solve such systems in general is presented and a computer program based upon it is described. High accuracy and efficiency are achieved by using variable order finite difference methods on nonuniform meshes which are selected automatically by the program as the computation proceeds. The variable mesh technique adapts itself to the particular problem at hand, producing more detailed computations where they are needed, as in tracing highly curved seismic rays. A complete package of programs has been produced which use this method to solve two- and three-dimensional ray-tracing problems for continuous or piecewise continuous media, with the velocity of propagation given either analytically or only at a finite number of points. These programs are all based on the same core program, PASVA3, and therefore provide a compact and flexible tool for attacking ray-tracing problems in seismology. In Part 2 of this work, the numerical method is applied to two- and three-dimensional velocity models, including models with jump discontinuities across interfaces.

Additional Information

© 1979 Seismological Society of America Manuscript received May 26, 1978. We wish to thank Dr. Bruce Julian of the U.S. Geological Survey for providing a copy of his paper with D. Gubbins on three-dimensional seismic ray tracing prior to publication, and to the referee for his very careful and critical reading. The first author would like to acknowledge several very interesting conversations with Dr. J. A. Rial of the Caltech Seismological Laboratory. This work was supported by U.S. Geological Survey Contract 14-08-0001-16777.

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August 19, 2023
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