• DOI:10.1088/0266-5611/29/1/015009
• Corpus ID: 56234240

Some inverse problems arising from elastic scattering by rigid obstacles

@article{Hu2012SomeIP,
  title={Some inverse problems arising from elastic scattering by rigid obstacles},
  author={Guanghui Hu and Andreas Kirsch and Mourad Sini},
  journal={Inverse Problems},
  year={2012},
  volume={29}
}

• G. Hu, A. Kirsch, M. Sini
• Published 2012
• Mathematics
• Inverse Problems

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.