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Ray Tracing in Two-Dimensional Inhomogeneous Media

Y. Xu, John A. McDonald

In this paper, we present an algorithm for tracing rays in two-dimensional inhomogeneous isotropic media with curved interfaces. The model is controlled by the rectangular grids and interfaces. The velocity at any position in the model is interpolated by the velocity values at the grid points and the control points along the interfaces. The curved interfaces are interpolated by spline methods. Ray tracing is done by solving the three first-order differential ray equations with a numerical integral method, a special Runge-Kutta method. The accuracy of such ray positions is checked at every step to ensure the precision of the ray paths. The program can be used to trace the reflected, refracted, and multiple rays from any layer. The fixed source and receiver position ray tra ing is done by an iterative method. The method is very flexible, the source can be anywhere, and the output can be shot records or vertical seismic profile records. Our program has the advantage over others in that the velocity can change in two dimensions and is only controlled by the grid points and interfaces; they need not follow any specified functions. This makes the program more flexible, closer to real subsurface cases, more convenient to use, and more applicable to real geology. This algorithm was run on a VAX-11/780 computer and was found to be efficient and convenient.

AAPG Search and Discovery Article #91035©1988 AAPG-SEPM-SEG Pacific Sections and SPWLA Annual Convention, Santa Barbara, California, 17-19 April 1988.