Reciprocity relations and completeness of far‐field pattern vectors for obstacle scattering of acoustic wave in a stratified medium

摘要

AbstractUnder a generalized Sommerfeld radiation condition, we proved the uniqueness and existence of the direct obstacle scattering problem of time‐harmonic acoustic waves in a stratified medium 8. In this paper, we study the asymptotic behaviour of the scattered waves and prove three reciprocity relations among 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 we prove conditions under which a set of far‐field patterns is complete in a Hilbert space based on the reciprocity relation. These properties are important in investigating the inverse obstacle scatteri