Direct and Inverse Acoustic Spherical Wave Scattering by a Small Layered Sphere with Soft Core

A spherical acoustic wave is scattered by a three layered sphere with a soft core. Exact expressions of the fields in every layer and the exterior of the scatterer are established. Low frequency results are then obtained by approximating the exact expression of the scattering cross section. The inverse problem of determining the sphere's center and the layers radii is treated from the knowledge of the scattering cross section's low frequency expansion