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Time-reversal algorithms in viscoelastic media†

Published online by Cambridge University Press:  03 April 2013

HABIB AMMARI ,
ELIE BRETIN ,
JOSSELIN GARNIER  and
ABDUL WAHAB
HABIB AMMARI
Affiliation:
Department of Mathematics and Applications, Ecole Normale Supérieure, 45 Rue d'Ulm, 75005 Paris, France email: habib.ammari@ens.fr
ELIE BRETIN
Affiliation:
Centre de Mathématiques Appliquées, CNRS UMR 7641, École Polytechnique, 91128 Palaiseau, France email: bretin@cmap.polytechnique.fr
JOSSELIN GARNIER
Affiliation:
Laboratoire de Probabilités et Modèles Aléatoires & Laboratoire Jacques-Louis Lions, Université Paris VII, 75205 Paris Cedex 13, France email: garnier@math.jussieu.fr
ABDUL WAHAB
Affiliation:
Department of Mathematics, COMSATS Institute of Information Technology, G.T. Road, Wah Cantt. 47040, Pakistan email: wahab@ciitwah.edu.pk
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Abstract

In this paper we consider the problem of reconstructing sources in a homogeneous viscoelastic medium from wavefield measurements. We first present a modified time-reversal imaging algorithm based on a weighted Helmholtz decomposition and justify mathematically that it provides a better approximation than by simply time reversing the displacement field, where artifacts appear due to the coupling between the pressure and shear waves. Then we investigate the source inverse problem in an elastic attenuating medium. We provide a regularized time-reversal imaging which corrects the attenuation effect at the first order. The results of this paper yield the fundamental tools for solving imaging problems in elastic media using cross-correlation techniques.

Keywords

Elastic wave propagationTime-reversal algorithmsAttenuation correctionWeighted Helmholtz decompositionHelmholtz–Kirchhoff identity
Type
Papers
Information
European Journal of Applied Mathematics , Volume 24 , Issue 4 , August 2013 , pp. 565 - 600
Copyright
Copyright © Cambridge University Press 2013 

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Footnotes

†

This work was supported by the ERC Advanced Grant Project MULTIMOD–267184.

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