On spherical-wave scattering by a spherical scatterer and related near-field inverse problems

A spherical acoustic wave is scattered by a bounded obstacle. A generalizat ion of the,optical theorem' (which relates the scattering cross-section to the far-field pattern in the forward direction for an incident plane wave) is proved. For a spherical scatterer, low-frequency results are obtained by approximating the known exact solution (separation of variables). In parti cular, a closed-form approximation for the scattered wavefield at the sourc e of the incident spherical wave is obtained. This leads to the explicit so lution of some simple near-field inverse problems, where both the source an d coincident receiver are located at several points in the vicinity of a sm all sphere.