Multiple scattering from many bounded obstacles in a multilayered acoustic medium.

Abstract

At a previous meeting of the Society, 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. Suppl. 1 87, S40 (1990)]. In this paper, an extension of that formalism to the problem of multiple scattering from 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 waveguide-obstacle T matrix and obstacle-centered, outgoing eigenfunctions appropriate to the layered medium. Waveguide Green functions 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, the translation matrices for these eigenfunctions are derived. The resulting solution is formally exact to all orders of multiple scattering among the obstacles and the waveguide. Also, it is simple to extend the method to calculate the field scattered from infinite, periodic arrays insonified by plane waves in the waveguide.