Scattering of elastic waves in heterogeneous media with local isotropy

The scattering of elastic waves in heterogeneous media is discussed. Explicit expressions are derived for the attenuation of longitudinal and transverse elastic waves in terms of the statistics of the density and Lamé parameter fluctuations. The derivation is based upon diagrammatic methods with the problem posed in terms of the Dyson equation. The Dyson equation is solved for the mean field response. The results are given here in a straightforward manner, in which the attenuations reduce to simple integrals on the unit circle. The medium is assumed statistically homogeneous and statistically isotropic. This model, with assumed local isotropic properties, is expected to apply to many materials.