Scattering of a compressional wave in a poroelastic medium by an ellipsoidal inclusion

Abstract

We study the interaction of a plane elastic wave in a poroelastic medium with an elliptical heterogeneity of another porous material. The behaviour of both the inclusion and the host medium is described by Biot's equations of poroelasticity with the standard interface conditions of Deresiewicz and Skalak at the inclusion's surface. The scattering problem is studied in the Born approximation, which is valid for low contrast of the inclusion's properties with respect to the host medium. The resulting scattered wavefield consists of the scattered normal compressional and shear waves and a Biot slow wave, which attenuates rapidly with distance from the inclusion. The Born approximation also allows us to derive explicit analytical formulae for the amplitudes of these scattered waves and to compute the amount of energy scattered by the inclusion into these waves. The amplitude and scattering cross-section for the Biot slow wave depend on the relationship between the dimensions of the inclusion and the wavelength of the Biot slow wave.