Multiple scattering by many bounded obstacles in a multilayered acoustic medium

Abstract

Recently, a multicentered, transition (T) matrix formalism was suggested for scattering calculations involving many bounded obstacles in homogeneous fluid and solid hosts [Lim and Hackman, J. Acoust. Soc. Am. 91, 613–638 (1992)]. In this paper, an extension of that formalism to the problem of multiple scattering by many bounded obstacles arbitrarily distributed in a plane-stratified acoustic medium is presented. Hackman and Sammelmann [J. Acoust. Soc. Am. 84, 1813–1825 (1988)] have given an elegant solution for scattering within a waveguide containing a single obstacle. The present extension is obtained by expanding the multiply scattered field from each obstacle within a layered fluid using their obstacle-waveguide T matrix. Obstacle-centered, outgoing eigenfunctions appropriate to the layered medium are used to expand the field scattered from each obstacle. Green functions of the layered medium are expanded in appropriate regular eigenfunctions to get the incident field coefficients required for the scattered field calculation. To complete the formulation in analogy to multiple scattering in an infinite, homogeneous medium, interactions are accounted for by matrices that translate the origin of these eigenfunctions among the obstacles present. The translation matrices are derived and incorporated into a transition supermatrix in the obstacle index. The resulting solution is formally exact to all orders of multiple scattering between the obstacles and between the obstacles and the layered host. Also, the formalism does not restrict the distribution of obstacles to a single layer and the method is simply extended to obtain the field scattered from infinite, periodic arrays insonified by plane waves in the stratified medium.