Time reversal detection in one-dimensional random media

In this paper, we study time reversal in the reflection of an acoustic wave in a one-dimensional random medium with an embedded reflector. The main result is that time reversal allows us to find the location of a reflector even in the absence of a coherent reflection. We carry out the analysis in the asymptotic regime of separation of scales, where the probing pulse is large compared to the medium inhomogeneities but small relative to the depth of the reflector. In the limit, the quantity of interest, namely the density of the time reversal refocusing kernel, is given as a solution to a deterministic system of transport equations, which is solved by using Monte Carlo simulations.