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Transient elasticity imaging and time reversal

Published online by Cambridge University Press:  15 November 2011

Habib Ammari ,
Lili Guadarrama Bustos ,
Hyeonbae Kang  and
Hyundae Lee
Habib Ammari
Affiliation:
Department of Mathematics and Applications, Ecole Normale Supérieure, 45 Rue d'Ulm, 75005 Paris, France (habib.ammari@ens.fr)
Lili Guadarrama Bustos
Affiliation:
Institut Langevin, CNRS UMR 7587 and ESPCI, 10 rue Vauquelin, 75231 Paris Cedex 05, France (lili.guadarrama@espci.fr)
Hyeonbae Kang
Affiliation:
Department of Mathematics, Inha University, Incheon 402-751, South Korea (hbkang@inha.ac.kr; hdlee@inha.ac.kr)
Hyundae Lee
Affiliation:
Department of Mathematics, Inha University, Incheon 402-751, South Korea (hbkang@inha.ac.kr; hdlee@inha.ac.kr)
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Abstract

We consider a purely quasi-incompressible elasticity model. We rigorously establish asymptotic expansions of near- and far-field measurements of the transient elastic wave induced by a small elastic anomaly. Our proof uses layer potential techniques for the modified Stokes system. Based on these formulae, we design asymptotic imaging methods leading to a quantitative estimation of elastic and geometrical parameters of the anomaly.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 141 , Issue 6 , December 2011 , pp. 1121 - 1140
Copyright
Copyright © Royal Society of Edinburgh 2011

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