WIAS Preprint No. 1727, (2012)

Some inverse problems arising from elastic scattering by rigid obstacles



Authors

  • Hu, Guanghui
  • Kirsch, Andreas
  • Sini, Mourad

2010 Mathematics Subject Classification

  • 35R30 74B05 78A45

Keywords

  • Linear elasticity, inverse scattering, factorization method, uniqueness

Abstract

In the first part, it is proved that a $C^2$-regular rigid scatterer in $R^3$ 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 $R^2$. In particular, the factorization method also leads to some uniqueness results for all frequencies excluding possibly a discrete set.

Appeared in

  • Inverse Problems, 29 (2013) pp. 015009/1--015009/21.

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