Inverse scattering for the penetrable ellipsoid and ellipsoidal boss

The inverse scattering problem for low-frequency plane-wave excitation of either a penetrable ellipsoid specified by its relative mass density and relative compressibility, or the corresponding ellipsoidal boss on a rigid base plane, is considered. For either situation, scatterer shape and orientation, as well as one of the constitutive parameters, may be obtained from a finite number of measurements of the leading order term in the low-frequency expansion of the scattering amplitude. Rayleigh’s result for this O(k3) contribution provides the analytical expression needed for the data inversion.