Elastic Wave Scattering by Two Spherical Inclusions in a Poroelastic Medium

Abstract

This study considers the most fundamental problem of multiple scattering in a poroelastic medium. It treats the interaction of a plane compressional elastic wave with a cluster of two of spherical inhomogeneities in a boundless fluid-saturated porous elastic formation. The novel features of Biot classic model for dynamic description of poroelastic material behavior along with the appropriate wave field expansions, the pertinent boundary conditions, and the translational addition theorems for spherical wave functions are employed to develop a closed-form solution in the form of infinite series. The analytical results are illustrated with numerical examples in which a pair of spherical inclusions is insonified by a plane (fast) compressional wave at end-on incidence. The effects of incident wave frequency, proximity of the two inclusions, and inclusion type are examined. Particular attention has been focused on multiple scattering interactions in addition to the slow wave coupling effects which is known to be the primary distinction of the scattering phenomenon in poroelasticity from the classical elastic case. The limiting case involving two elastic spheres submerged in an ideal unbounded fluid medium is considered and fair agreement with a well-known solution is established.