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

Research areas:
Year:
2007
Type of Publication:
Article
Authors:
Journal:
Studies in Applied Mathematics
Volume:
118
Number:
4
Pages:
397-418
Abstract:
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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