Scattering of elastic waves by a spherical inclusion—I. Theory and numerical results

Abstract

A complete and exact solution for the problem of an incident P wave scattered by an elastic spherical inclusion is presented and described. The solution can be obtained from either analytical formulae or stable numerical procedures. A method of estimating the number of terms that must be retained in the harmonic series in order to achieve a specified accuracy is given. The results are investigated by calculating synthetic seismograms, scattering diagrams, and scattering cross‐sections for a broad frequency band and for both low‐velocity and high‐velocity inclusions. The fields within the shadow zone are formed primarily from three different types of waves, P waves transmitted through the sphere, P waves diffracted around the sphere, and S waves converted at the boundary of the sphere. The relative contribution from these different waves depends upon the distance of the observation point from the sphere. Copyright © 1993, Wiley Blackwell. All rights reserved