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Scattering Theorems for Acoustic Excitation of a Layered Obstacle by an Interior Point Source

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Interesting scientific and technological applications motivate the study of scattering problems, where a layered scatterer is excited by a spherical acoustic wave generated by a point-source located in its interior. The scatterer's core may be acoustically soft, hard, resistive, or penetrable. This paper initiates the investigation of scattering theorems, corresponding to the excitation of a layered scatterer by a point source in its interior. Reciprocity and general scattering theorems are established, relating the total fields and the corresponding far-field patterns. The optical theorem, relating the scattering cross-section with the field in the layer containing the source, is recovered as a corollary of the general scattering theorem. Furthermore, for a scatterer excited by a spherical and a plane wave, mixed scattering theorems are derived. Numerical implementations of the optical theorem in concrete scattering applications are analyzed.
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Document Type: Research Article

Affiliations: University of Athens

Publication date: May 1, 2007

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