Study of generalized eigenfunctions of a perturbed isotropic elastic half-space

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.