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A fast, two-point, three-dimensional raytracing algorithm using a simple step search method

DEPARTMENT OF GEOLOGICAL SCIENCES UNIVERSITY OF CALIFORNIA, SANTA BARBARA, SANTA BARBARA, CALIFORNIA 93106

Abstract

The simplex method of function minimization is used to find the ray that follows the path of minimum time through an arbitrary three-dimensionally varying medium. The advantage of this method is that it is extremely fast, always converges, and lends itself to a variety of velocity parameterizations. The first step in the algorithm is to find the minimum time circular arc path between the source and receiver using an exhaustive search method. Then perturbations, consisting of a sum of N sine wave harmonics with their zero crossings at the endpoints, are made to the circular arc path. The simplex method searches for the amplitude coefficients that produce the path of least time. On a VAX-750 running the VMS operating system, the first arriving ray for a station receiver distance of 96 km is computed to an accuracy of 0.02 sec, computed in a southern California velocity structure using less than 26 sec of computer time. The required computer time decreases as the ray path distance decreases.

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