The Two-Dimensional Gaussian Beam Synthetic Method' Testing and Application

The Gaussian beam method of •erven9 et al. (1982) is an asymptotic method for the computation of wave fields in inhomogeneous media. The method consists of tracing rays and then solving the wave equation in "ray-centered coordinates." The parabolic approximation is applied to find the asymptotic local solution in the neighborhod of each ray. The approximate global solution for a given source is then constructed by a superposition of Gaussian beams along nearby rays. The Gaussian beam method is tested in a two-dimensional inhomogeneous medium using two approaches. One is the application of the reciprocal theorem for Green's functions in an arbitrarily heterogeneous medium. The discrepancy between synthetic seismograms for reciprocal cases is considered as a measure of the error. The other approach is to apply Gaussian beam synthesis to cases for which solutions are known by other approximate methods. This includes the soft basin problem that has been studied by finite difference, finite element, discrete wavenumber, and glorified optics. We found that the results of these tests were in general satisfactory. We have used the Gaussian beam method for two applications. First, the method is used to study volcanic earthquakes at Mount Saint Helens. The observed large differences in amplitude and arrival time between a station inside the crater and stations on the flanks can be explained by the combined effects of an anomalous velocity structure and a shallow focal depth. The method is also applied to scattering of teleseismic P waves by a lithosphere with randomly fluctuating velocities.