Rapid seismic ray tracing in a spherically symmetric earth via interpolation of rays

Abstract

From the equations for seismic ray tracing in a general three-dimensionally heterogeneous isotropic elastic medium, we derive equations appropriate for a spherically symmetric earth, with path length as the independent parameter. Numerical integration of these equations, plus their derivatives with respect to take-off angle, leads to a set of reference rays for the direct P phase. From a modest number of reference rays, which need be computed only once for a given earth model, ray path coordinates and travel times can be rapidly and accurately computed by Hermite cubic interpolation using specific algorithms which we outline. Because of the speed of the interpolation and the explicit parameterization in terms of path length, this technique is ideally suited for use in a tomographic inversion of global P-wave travel-time observations to obtain an estimate of lateral velocity heterogeneity in the mantle.