Wave Propagation in Laterally Varying Mcdia and Iterative Inversion for Velocity

The Gaussian beam method of Cerveny et. al. [1982] is an asymptotic method for the computation of wavefields 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 neighborhood 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 2-D 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 which 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 Mt. St. 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