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 conditionis presented for the scattering waves in a stratified mediumwith a nonstratified inhomogeneity. Using integral equationmethods, the uniqueness and existence of the direct scatteringproblem are proved. Relations between the scattered acousticwaves in the far field and the sound profile of the inhomogeneityare obtained. Using these relations, the author proves threereciprocity relations between the free-wave far-field patternsand the guided-wave far-field pattern vectors correspondingto incident distorted plane waves and normal mode waves. Thenconditions under which a set of far-field patterns is completein a Hilbert space are determined using the reciprocity relation.These properties are important in investigating inverse scatteringproblems.