Acoustic scattering by penetrable homogeneous objects

The scattered field is found when a time harmonic acoustic wave is incident upon a finite object characterized by a density and wavenumber different from that of the surrounding medium. The interface is assumed to be either Lyapunoff or piecewise Lyapunoff. The problem is cast as a pair of coupled surface integral equations for the total field and its normal derivative on the interface. The Neumann series obtained by straightforward iteration is proven to be convergent for ranges of density and wavenumber, and specific bounds on these ranges are given. For small enough wavenumbers, the series converges for all values of the interior density. The iteration appears simpler than the usual Born approximation, which involves volume as well as surface integrals. The method is illustrated in the case of a spherical interface.