Time Reversal for Elastic Wave Refocusing and Scatterer Location Recovery

Abstract

Time reversal is a powerful procedure in application fields involving wave propagation. It is based on the invariance of the wave equations, in the absence of dissipation, in the time direction. This allows going backward in time to recover past events. We use time reversal to recover the location of a source applied at the initial time based on measurements at a later time. We generalize the procedure previously developed for the scalar wave equation1 to elastodynamics. We show that the technique is quite robust, sometimes even in the presence of very high noise levels. Also it is not very sensitive to the medium characterizations, when a sufficient amount of measurement data is available. We extend previous work to get good refocusing for multiple sources. We introduce a new score to assess the quality of the numerical solution for the refocusing problem which produces good results. Furthermore, we use the refocusing technique as a basis for scatterer location recovery. By adding noise in a controlled manner we improve the scheme of finding the location of the scatterer.