The aim of this paper is to study the feasibility of time-reversal methods in a non homogeneous elastic medium, from data recorded in an acoustic medium. We aim to determine, from partial aperture boundary measurements, the presence and some physical properties of elastic unknown “inclusions”, i.e. not observable solid objects, located in the elastic medium. We first derive a variational formulation of the acousto-elastic problem, from which one constructs a time-dependent finite element method to solve the forward, and then, the time reversed problem. Several criteria, derived from the reverse time migration framework, are then proposed to construct images of the inclusions, and to determine their locations. The dependence of the approach to several parameters (aperture, number of sources, etc.) is also investigated. In particular, it is shown that one can differentiate between a benign and malignant close inclusions. This technique is fairly insensitive to noise in the data.

本文的目的是根据声介质中记录的数据研究非均匀弹性介质中时间反转方法的可行性。我们旨在通过部分孔径边界测量来确定位于弹性介质中的未知弹性“夹杂物”（即不可观察的固体物体）的存在和某些物理性质。我们首先得出声弹问题的变分形式，从中构造出一种时变有限元方法来求解正向问题，然后求解时间倒转问题。然后提出了一些从逆时迁移框架中得出的标准，以构造包含物的图像并确定其位置。还研究了该方法对几个参数（孔径，光源数量等）的依赖性。尤其是，结果表明，可以区分良性和恶性的紧密包涵体。此技术对数据中的噪声非常不敏感。