Fundamental solutions for SH-waves in a continuum with large randomness

Fundamental solutions for horizontally polarized shear (SH) waves propagati ng in continuous medium with an arbitrarily large random wave number an der ived herein. These fundamental solutions, or Green's functions, besides bei ng useful in their own right, also serve as kernel functions for integral e quation formulations that can be used in the numerical solution of elastic wave scattering problems of practical importance. Thus, the present work se rves as an extension of earlier derivations of boundary integral equation s tatements based on the perturbation approach by removing the assumption of small fluctuations of key medium properties about their mean values. The me thodology developed here is based on a series expansion of the fundamental solutions of the SH wave equation under time harmonic conditions using an o rthogonal polynomial basis (polynomial chaos) for the randomness. The posit ion-dependent coefficients of this expansion are subsequently found from th e resulting vector wave equation, which is uncoupled through use of the eig ensolution of its system matrix. Finally, some representative cases are sol ved and the results are contrasted with those obtained by the perturbation method. At the same time, the accuracy of the solution to the number of ter ms used in the polynomial expansion is investigated. (C) 1999 Elsevier Scie nce Ltd. All rights reserved.