Acoustic scattering by a partially buried three-dimensional elastic obstacle

Abstract

A transition-matrix solution for the spectral scattering response of an elastic obstacle that penetrates a plane-stratified fluid host is formulated. The field scattered from the segment in each layer is expanded in a global outgoing basis centered on that segment and these segment fields are superposed at the field point. A manageable structure for the transition matrix is maintained by using the boundary conditions to couple these segment fields to the interior field of the obstacle via exterior surface field expansions centered on the primary origin of the obstacle. Two formulations are presented and compared in which the surface fields are expanded in either the standard set of regular spherical eigenfunctions of the Helmholtz equation or the spherical harmonics. Numerical tests for an axisymmetric spheroid indicate both formulations are viable but exhibit different convergence and stability characteristics. However, in both cases, convergence is better for flattened shapes (oblate) than elongated shapes (prolate). Examples are presented to illustrate environmental effects on the backscatter by a bubble and elastic spheres and spheroids that penetrate a water/sediment interface.