Time reversal for obstacle location in elastodynamics from acoustic recording

Franck Assous; Moshe Lin

doi:10.1016/j.crme.2019.02.001

Time reversal for obstacle location in elastodynamics from acoustic recording

Franck Assous ¹ ; Moshe Lin ¹

¹ Department of Mathematics, Ariel University, 40700 Ariel, Israel

Comptes Rendus. Mécanique, Volume 347 (2019) no. 6, pp. 455-462.

Abstract
Résumé

The Note is concerned with a feasibility study of time reversal in a non-homogeneous elastic medium, from data recorded in an acoustic medium. Our aim here is to determine the presence and some physical properties of elastic “inclusions” (unknown, not observable solid objects, characterized by their elastic properties) from partial observations of acoustic waves scattered by these inclusions. A finite element numerical method, based on a variational acousto-elastodynamics formulation, is derived and used to solve the forward, and then, the time-reversed problem. A criterion, derived from the reverse time migration framework, is introduced, to help construct images of the inclusions to be determined. Numerical illustrations on configurations that mimic the breast cancer configuration are proposed, and show that one can differentiate between two inclusions, even with different properties.

Le but de cette note est d'étudier le retourné temporel d'un problème posé dans un milieu acousto-élastique non homogène. On cherche à déterminer la présence d'inclusions élastiques à partir d'observations partielles et bruitées, enregistrées dans la partie acoustique du milieu. On dérive tout d'abord une formulation variationnelle acousto-élastique des équations, puis on construit un solveur élément finis, pour résoudre numériquement les problèmes direct et retourné temporellement. En s'inspirant de travaux sur la migration sismique, on introduit un critère objectif, qui nous permet de construire une image des inclusions a déterminer. Des illustrations numériques, sur des données qui simulent la configuration du cancer du sein, sont proposées et montrent qu'il est possible de différencier des inclusions, même avec des propriétés différentes.

Received: 2018-12-04
Accepted: 2019-02-04
Published online: 2019-02-18

DOI: 10.1016/j.crme.2019.02.001

Keywords: Time reversal, Wave propagation, Inverse problem, Acousto-elastodynamics, Numerical simulation, Identification
Mots-clés : Retournement temporel, Propagation d'ondes, Problèmes inverses, Acousto-élastodynamique, Simulation numérique, Identification

Author's affiliations:

Franck Assous ¹; Moshe Lin ¹

¹ Department of Mathematics, Ariel University, 40700 Ariel, Israel

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     title = {Time reversal for obstacle location in elastodynamics from acoustic recording},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {455--462},
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     volume = {347},
     number = {6},
     year = {2019},
     doi = {10.1016/j.crme.2019.02.001},
     language = {en},
}

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Franck Assous; Moshe Lin. Time reversal for obstacle location in elastodynamics from acoustic recording. Comptes Rendus. Mécanique, Volume 347 (2019) no. 6, pp. 455-462. doi : 10.1016/j.crme.2019.02.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.02.001/

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