Time-reversal methods for acousto-elastic equations and applications VII International Conference on Computational Methods for Coupled Problems in Science and Engineering COUPLED PROBLEMS 2017 M. Papadrakakis, E. O˜ nate and B. Schrefler (Eds) TIME-REVERSAL METHODS FOR ACOUSTO-ELASTIC EQUATIONS AND APPLICATIONS Franck Assous * and Moshe Lin * * Department of Mathematics Ariel University, Ariel, 40700, Israel. e-mail: franckassous55@gmail.com e-mail: moshelin1@walla.co.il Key words: Time Reverse, Elastodynamics, Wave propagation, Finite Element, Inverse problems Abstract. Time reversal (TR) is a subject of very active research. The principle is to take advantage of the reversibility of wave propagation phenomena, for example in acous- tics, elastic or electromagnetism in an unknown medium, to back-propagate signals to the sources that emitted them. In a previous paper [1], we introduced a time-reversed method for acoustic equation. In this paper, our aim is to extend this approach to elastodynam- ics equations. As the application we have in mind are concerned with ultrasound-based elasticity imaging methods, we consider both elastic and acousto-elastic systems of equa- tions. We stress that our method does not rely on any a priori knowledge of the physical properties of the inclusion. 1 INTRODUCTION Time reversal (TR) is a subject of very active research. The principle is to take advantage of the reversibility of wave propagation phenomena, for example in acoustics, 972