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Reciprocity relations and completeness of far‐field pattern vectors for obstacle scattering of acoustic wave in a stratified medium
Author(s) -
Xu Yongzhi
Publication year - 1995
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670180104
Subject(s) - near and far field , mathematics , completeness (order theory) , reciprocity (cultural anthropology) , obstacle , scattering , mathematical analysis , field (mathematics) , calculus (dental) , acoustics , pure mathematics , optics , physics , geography , psychology , social psychology , medicine , archaeology , dentistry
Under 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 scattering problems.