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Propagation of P and SV waves in an elastic solid containing randomlydistributed inclusions in a half-space is investigated. The approach is basedon a multiple scattering analysis similar to the one proposed by Fikioris andWaterman for scalar waves. The characteristic equation, the solution of whichyields the effective wave numbers of coherent elastic waves, is obtained in anexplicit form without the use of any renormalisation methods. Twoapproximations are considered. First, formulae are derived for the effectivewave numbers in a dilute random distribution of identical scatterers. Theseequations generalize the formula obtained by Linton and Martin for scalarcoherent waves. Second, the high frequency approximation is compared with theWaterman and Truell approach derived here for elastic waves. The Fikioris andWaterman approach, in contrast with Waterman and Truell's method, shows that Pand SV waves are coupled even at relatively low concentration of scatterers.Simple expressions for the reflected coefficients of P and SV waves incident onthe interface of the half space containing randomly distributed inclusions arealso derived. These expressions depend on frequency, concentration ofscatterers, and the two effective wave numbers of the coherent wavespropagating in the elastic multiple scattering medium.

Effective wavenumbers and reflection coefficients for an elastic medium containing random configurations of cylindrical scatterers