We consider the self-adjoint operator governing the propagation of elastic
waves in a perturbed isotropic half-space (perturbation with compact suppor
t of a homogeneous isotropic half-space) with a free boundary condition. We
propose a method to obtain, numerical values included, a complete set of g
eneralized eigenfunctions that diagonalize this operator. The first step gi
ves an explicit representation of these functions using a perturbative meth
od. The unbounded boundary is a new difficulty compared with the method use
d by Wilcox [25], who set the problem in the complement of bounded open set
. The second step is based on a boundary integral equations method which al
lows us to compute these functions. For this, we need to determine explicit
ly the Green's function of (A(0) - omega(2)), where A(0) is the self-adjoin
t operator describing elastic waves in a homogeneous isotropic half-space.
Copyright (C) 2000 John Wiley & Sons, Ltd.