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21. Some inverse problems arising from elastic scattering by rigid obstacles.

Author

Hu, Guanghui, Kirsch, Andreas, and Sini, Mourad

Subjects
*SHEAR waves, *MATHEMATICAL decoupling, *FACTORIZATION, *POLYHEDRA, *LIPSCHITZ spaces, *INTERNAL friction
Abstract

In the first part of this paper, it is proved that a C2-regular rigid scatterer in can be uniquely identified by the shear part (i.e. S-part) of the far-field pattern corresponding to all incident shear waves at any fixed frequency. The proof is short and it is based on a kind of decoupling of the S-part of scattered wave from its pressure part (i.e. P-part) on the boundary of the scatterer. Moreover, uniqueness using the S-part of the far-field pattern corresponding to only one incident plane shear wave holds for a ball or a convex Lipschitz polyhedron. In the second part, we adapt the factorization method to recover the shape of a rigid body from the scattered S-waves (resp. P-waves) corresponding to all incident plane shear (resp. pressure) waves. Numerical examples illustrate the accuracy of our reconstruction in . In particular, the factorization method also leads to some uniqueness results for all frequencies excluding possibly a discrete set. [ABSTRACT FROM AUTHOR]

Published
2013
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