SPECTRAL DECOMPOSITION OF GREEN'S FUNCTION IN TERMS OF DISCRETE AND CONTINUOUS EIGENVALUE PROBLEMS

Abstract

The purpose of this research is to represent Green's function for liquid layered medium in terms of spectral theory. In general, Green's function represented by wavenurnber intagration can be separated into residue terms and branch line integrals. This reserch shows that the residue terms are related to the discrete eigenvalue problem and the branch line integrals to the continuous eigenvalue problem. This research also shows that the integrand of the branch line integral can be decomposed into the continuous eigenfunctions. By the decomposition, Green's function can be synthesized by using the continous and discrete eigenfunctions for the wave field.