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The propagation problem and far‐field patterns in a stratified finite‐depth ocean
Author(s) -
Gilbert R. P.,
Xu Yongzhi
Publication year - 1990
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.1670120303
Subject(s) - mathematics , near and far field , mathematical analysis , plane (geometry) , inverse problem , field (mathematics) , dirichlet problem , representation (politics) , inverse scattering problem , geometry , pure mathematics , boundary value problem , optics , physics , politics , political science , law
In this paper we investigate the direct problem associated with the scattering of ‘plane waves’ from an object submerged in an ocean of finite depth. An integral representation for the Dirichlet problem is found, from which a formula for the far‐field pattern evolves. A density theorem is established concerning the set of all far‐field patterns. This theorem is essential for the reconstruction of the submerged object, the ‘inverse’ problem [2], [4], [5].