Identification of obstacles using only the scattered P-waves or the scattered S-waves

Drossos Gintides; Mourad Sini

doi:10.3934/ipi.2012.6.39

Article Contents

2012, Volume 6, Issue 1: 39-55. Doi: 10.3934/ipi.2012.6.39

This issue Previous Article On the numerical solution of a Cauchy problem for the Laplace equation via a direct integral equation approach Next Article Positive definiteness of Diffusion Kurtosis Imaging

Identification of obstacles using only the scattered P-waves or the scattered S-waves

Drossos Gintides^1, and
Mourad Sini^2,

1.
Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens
2.
RICAM, Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040, Linz

Received: September 30, 2010

Revised: September 30, 2011

Published: January 2012

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Abstract

In this work, we are concerned with the inverse scattering by obstacles for the linearized, homogeneous and isotropic elastic model. We study the uniqueness issue of detecting smooth obstacles from the knowledge of elastic far field patterns. We prove that the 'pressure' parts of the far field patterns over all directions of measurements corresponding to all 'pressure' (or all 'shear') incident plane waves are enough to guarantee uniqueness. We also establish that the shear parts of the far field patterns corresponding to all the 'shear' (or all 'pressure') incident waves are also enough. This shows that any of the two different types of waves is enough to detect obstacles at a fixed frequency. The proof is reconstructive and it can be used to set up an algorithm to detect the obstacle from the mentioned data.

Keywords:

Inverse scattering problem,
linear elasticity.

Mathematics Subject Classification: Primary: 35R30, 35J40, 74B05.

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