Scattering of Elastic Waves from a Spherical Cavity in a Solid Medium

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Abstract
Cross sections are computed for the scattering of a plane transverse wave from a spherical cavity embedded in an infinite, isotropic, homogeneous, elasticsolid. Analytical expressions are derived for the matrix elements indicated by Einspruch, Witterholt, and Truell, and the resulting matrix equations are solved numerically. The dependence of the scattering cross section upon K 1 a (K 1 is the transverse propagation constant, a is the cavity radius) over the range 0.01–10 is computed for various host materials, and the results are compared with the case of incident longitudinal waves computed by Johnson and Truell. The sensitivity of the cross section to the elastic properties of the medium, and the behavior in the Rayleigh limit approximation are discussed. The relative contributions of the various components of both the longitudinal and transverse scattering cross sections are isolated, and their dependence upon K 1 a, k 1 a (k 1 is the longitudinal propagation constant) and host material is elucidated. A peaking behavior analoguous to that occurring in the longitudinal case is observed in the longitudinal component of the scattered transverse wave.

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