Robustness of time reversal for waves in time-dependent random media

Abstract

This paper addresses the impact of time fluctuations of a random medium on refocusing during a time-reversal experiment. Even in the presence of moderate timeperturbations a coherent refocused pulse is observed. The theory predicts the level of recompression observed as well as the conditions for the loss of statistical stabilization. It is shown that the statistical properties of the refocused pulse depend on a simple set of parameters that describe the correlation degree of the medium. The refocused pulse has in general a random shape that can be described in terms of a system of stochastic transport equations driven by a single Brownian motion. Pulse stabilization is also demonstrated for some particular configurations, and the convolution kernel that describes the pulse reshaping is explicitly computed. Numerical simulations are presented and show a very good agreement with the theoretical predictions, thus providing a clear illustration of the robustness of time reversal.

Time reversal for inclusion detection in one-dimensional randomly layered media

“…In this particular case (i.e. when Z 0 = −∞) we have that the refocused pulse is statistically stable, this is related to the fact that the propagation velocity remains unperturbed as was remarked in [14]. We refer to the interval [Z 0 , 0] as the unperturbed propagation velocity region (or slab).…”

“…This appendix contains a generalization of some results that were presented in [13,14], concerning time reversal in reflection in a changing medium. More specifically, we consider the case where the background as well as the random fluctuations of the media involved in the time reversal procedure are different, but assume that the homogeneous half-space remains unchanged.…”

“…the last recorded part is reemitted first), into the second medium. This procedure generalizes the case where the medium remains unchanged during the whole experiment [7,13,14].…”

Time reversal of waves in a weakly perturbed random medium

“…Time reversal in the context of medium perturbations was studied in [1] for randomly layered media. The main result then states that the pulse shape is described by a random function, implying that the statistical stabilization property is lost, i.e., the refocused pulse is not statistically stable.…”