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.