In this article, we present a method for determining the minimum time ray path from a planar wavefront at depth to a fixed point at the surface through a 3-D heterogeneous velocity structure. The program is based on the two point raytracer of Prothero et al. (1988), with a modification to use odd quarter-cycles of sinusoids to distort the rays. These functions produce zero displacement at the fixed receiver but non zero displacement at the wavefront. This allows the raytracer to explore a wide variety of ray paths starting at different points on the wavefront, while the rays leaving the wavefront remain normal to it. To find the minimum time path, amplitudes of these functions are systematically perturbed using the simplex algorithm. The approach is analogous to using a Fourier series to fit a curve with specific properties at each end.
Development of this raytracer was motivated by the desire to model our observations of large perturbations in the bearings and phase velocities of teleseismic P waves recorded in Long Valley caldera, California. These observations clearly show the inadequacy of 1-D raytracing in regions having complex, three-dimensionally varying velocity structure. This raytracer provides a basic tool with which to study the effects of ray bending on tomographic results from these kinds of environments.