RADIATION CONDITION AND SCATTERING PROBLEM FOR TIME-HARMONIC ACOUSTIC-WAVES IN A STRATIFIED MEDIUM WITH A NONSTRATIFIED INHOMOGENEITY

In this paper, a generalized Sommerfeld radiation condition is present ed for the scattering waves in a stratified medium with a nonstratifie d inhomogeneity. Using integral equation methods, the uniqueness and e xistence of the direct scattering problem are proved. Relations betwee n the scattered acoustic waves in the far field and the sound profile of the inhomogeneity are obtained. Using these relations, the author p roves three reciprocity relations between the free-wave far-field patt erns and the guided-wave far-field pattern vectors corresponding to in cident distorted plane waves and normal mode waves. Then conditions un der which a set of far-field patterns is complete in a Hilbert space a re determined using the reciprocity relation. These properties are imp ortant in investigating inverse scattering problems.