Focusing of time-reversed reflections

Abstract

Recently time-reversal techniques have emerged as a new, important and fascinating discipline within wave propagation. Many of the problems involved can best be understood, analysed and optimized based on a random field model for the medium. Here we discuss stable refocusing of second-order time-reversed reflections. This phenomenon may appear as surprising at first. However, we show how it can be understood in very simple terms viewing the wavefield as a stochastic process. We give sufficient conditions on Green's function of the propagation problem for the phenomenon to happen. In particular we discuss acoustic wave propagation in the regime of weak random medium fluctuations and explicitly give the derivation of stable refocusing in this case, illustrating it with numerical examples.