| This dissertation considers the multiple scattering of elastic waves by a distribution of identical elastic spheres embedded in an elastic host medium. The solution is given in terms of the scattering amplitudes which take into account the matrix of the scatterers. In addition, we derive relations for the propagation parameters for the composite medium. Throughout, we use the results of Twersky developed for electromagnetic and scalar multiple scattering problems.;To derive our results we consider the single scatterer in isolation, a fixed configuration of N-identical scatterers, and a statistically homogeneous ensemble of configurations of N-identical scatterers. Our results lead immediately to the coherent wave solution once the ensemble average scattering amplitudes are known. Our results are in terms of the standard boundary conditions used at the surface of the single scatterer.;We use the self-consistent approach of Foldy extended by Twersky and the quasi-crystalline approximation of Lax to obtain a pair of surface integral equations for the ensemble average scattering amplitudes in terms of the known scattering amplitudes of the scatterer in isolation. We consider two types of leading term approximations. The Rayleigh scattering corresponding to the conventional elastic scattering approximation and the two-space scatterer formalism leading term approximation which gives, for the dilute case, the forward scattering results of Devaney.;As an example, we treat the case of the rigid sphere. We give the solution corresponding to Rayleigh scattering. The necessary information for the two-space scattering formalism corresponding to the rigid sphere is in Appendix B.;In the course of our development we derive reciprocity relations for the individual and multiple scattering amplitudes. The elastic reciprocity relations are not only an extension of well-known relations of acoustics and electromagnetics, but also represent a structural base for computing scattering cross sections corresponding to any direction of the incident wave. |
