Reciprocity relations and completeness of far-field pattern vectors for obstacle scattering of acoustic wave in a stratified medium
✍ Scribed by Yongzhi Xu
- Publisher
- John Wiley and Sons
- Year
- 1995
- Tongue
- English
- Weight
- 565 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0170-4214
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✦ Synopsis
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.