An application of the forward‐scattering theorem to elastic wave attenuation in inhomogeneous materials

Abstract

The forward‐scattering amplitude of two adjacent scatterers f(2) may be used to construct an effective medium theory of inhomogeneous media containing random distributions of scatterers. The amplitude f(2) may be thought of as the lowest‐order approximation of the amplitude f(n), of an interacting cluster of n scatterers contributing to the formation of the coherent elastic wave. Since the elastic wave encounters all orientations of pairs, the averaged nearest‐neighbor forward‐scattering amplitude is studied. Specific orientations that are dictated by the dynamics of the scattering processes are also considered. The average forward‐scattering amplitude is analyzed in terms of the direct σpp mode conversion, σpp, and absorption cross sections for random distributions of viscoelastic spherical scatterers in elastic matrix materials. Estimates of longitudinal wave attenuation due to these three mechanisms in specific materials are presented.