Gaussian beam synthetic seismograms

Abstract

This presentation is a tutorial on the Gaussian beam method used for the asymptotic synthesis of seismic and acoustic wave fields in inhomogeneous media. The method is based on the superposition of beam solutions, each of which is an approximate solution of the wave equation along particular rays. Smoothness conditions on the medium are required for the approximate propagation of beam solutions. Within a smoothly varying medium, various choices of the beam parameters can be used. Specifying broad planar beams at the source would result in a plane-wave decomposition of the visible spectrum. The standard ray method would result by specifying narrow planar beams at the receiver. Another choice is to specify the minimum integral beam width along each ray. There are several advantages of the Gaussian beam method, including finite amplitudes at caustics, smoothing of endpoint errors, and the reduction of amplitude variability resulting from model parameterization. Several numerical examples will be given in 2-D and 3-D, and comparisons will be shown with other numerical methods.