T-matrix formalism for scattering from a porous saturated inclusion embedded within a porous saturated medium.

Abstract

The scattering from an inclusion embedded within a host is analyzed within the framework of Biot’s theory for wave propagation in porous saturated media. The inclusion and host are assumed to be porous saturated media with distinct material parameters. Norris has derived a solution for radiation from a point source and he has considered a Green’s function analysis of the scattering problem [A. N. Norris, J. Acoust. Soc. Am. 77, 2012–2022 (1985)]. A transition (T-) matrix scattering formalism has been developed within the full Biot theory (i.e., including attenuation mechanisms) for an arbitrarily shaped inclusion. In implementing a T-matrix formalism, Betti’s identity from elastic wave scattering [Y. H. Pao, J. Acoust. Soc. Am. 64, 302–310 (1978)] was generalized to porous media where the additional slow longitudinal wave is present. The T-matrix formalism is specialized to a spherical inclusion and calculations of extinction, scattering, and absorption cross sections for ideal porous media (no attenuation) will be discussed. Elastic wave scattering is recovered as the porosity of each media approaches zero and the solid constituent is considered to be perfectly elastic.