Scattering characteristics of elastic waves by an elastic heterogeneity

Abstract

Abstract Elastic wave scattering by a general elastic heterogeneity having slightly different density and elastic constants from the surrounding medium is formulated using the equivalent source method and Born approximation. In the low-frequency range (Rayleigh scattering) the scattered field by an arbitrary heterogeneity having an arbitrary variation of density and elastic constants can be equated to a radiation field from a point source composed of a unidirectional force proportional to the density contrast between the heterogeneity and the medium, and a force moment tensor proportional to the contrasts of elastic constant. It is also shown that the scattered field can be decomposed into an 'impedance-type' field, which has a main lobe in the backscattering direction and no scattering in the exact forward direction, and a 'velocity type' scattered field, which has a main lobe in the forward scattering direction and no scattering in the exact backward direction. For Mie scattering we show that the scattered far field is a product of two factors: (1) elastic Rayleigh scattering of a unit volume, and (2) a scalar wave scattering factor for the parameter variation function of the heterogeneity which we call 'volume factor.' For the latter we derive the analytic expressions for a uniform sphere and for a Gaussian heterogeneity. We show the relations between volume factors and the 3-D Fourier transform (or 1-D Fourier transform in the case of spherical symmetry) of the parameter variations of the heterogeneity. The scattering spatial pattern varies depending upon various combinations of density and elastic-constant perturbations. Some examples of scattering pattern are given to show the general characteristics of the elastic wave scattering.