Inverse scattering from an elastic sphere

Abstract

The echoes (or cross sections) returned by an elastic sphere of unknown material composition can be used to determine its composition. Three parameters uniquely define the composition: the density ρ and the speeds of dilatational and shear waves, Cd,Ct. We propose an approach which capitalizes on the findings of the resonance scattering theory, which has shown how to isolate the modal resonances contained within a cross section by a process of background subtraction. These modal resonances, or equivalently the modal mechanical impedances (n = 0,1,2,…) contain all the information required to completely and uniquely determine the composition in an asymptotic way. The problem splits naturally into two types of compositions (rubbery, or nonmetallic, and metallic), and the available cross sections can be of the monostatic or bistatic types. In all combinations of cases, the modal resonances or the modal impedances, can be used to determine the composition in an accurate way that could become the standard method for composition determination by remote sensing. Material composition can be determined as easily a the modal resonances can be extracted from the return, and we illustrate in detail how this is done in several instances.