Abstract
The problem of validating computer codes for numerical ray tracing in range-dependent, sound-speed profiles will be discussed. To find accurate travel times for eigenray computation, one must obtain precise solutions of the ray equations parametrized by time. A method for finding nontrivial sound-speed variations based on conformal transformations is described that allows analytic solutions from simpler ray-tracing problems to be used for computing ray paths through the resulting range-varying medium. Besides its application to validating computer codes, the method can be used to convert a ray-tracing or eigenray-finding problem originally formulated in terms of a circular or elliptical coordinate system into an associated problem on a Cartesian coordinate system. Sound-speed fields specified on the natural grid for the non-Cartesian system map directly onto the Cartesian grid, allowing the use of more computationally efficient Cartesian ray-tracing algorithms. Travel times are not affected by the transformation. Hence, the method is particularly suited to predicting arrival times associated with eigenrays. Illustrative ray traces and results will be shown.
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