Radiation condition and scattering problem for time-harmonic acoustic waves in a stratified medium with a nonstratified inhomogeneity

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Abstract
In this paper, a generalized Sommerfeld radiation condition is presented for the scattering waves in a stratified medium with a nonstratified inhomogeneity. Using integral equation methods, the uniqueness and existence of the direct scattering problem are proved. Relations between the scattered acoustic waves in the far field and the sound profile of the inhomogeneity are obtained. Using these relations, the author proves three reciprocity relations between the free-wave far-field patterns and the guided-wave far-field pattern vectors corresponding to incident distorted plane waves and normal mode waves. Then conditions under which a set of far-field patterns is complete in a Hilbert space are determined using the reciprocity relation. These properties are important in investigating inverse scattering problems.