Communications in Mathematical Sciences

Volume 6 (2008)

Number 2

Time reversal of waves in a weakly perturbed random medium

Pages: 331 – 360



D. G. Alfaro Vigo

K. Solna


In a time reversal experiment, a signal recorded by an array of transducers and sent back time-reversed into the same medium approximately refocuses on the original source center. The refocusing resolution is improved in an inhomogeneous medium. In this work we study the effect of changes in the medium, namely, the case when back propagation takes place in a perturbed medium.

Under the paraxial approximation assumption for a medium with weak inhomogeneities we consider a high frequency white noise regime. We show that relatively small perturbations do not affect the stable refocusing (self-averaging) for a localized source, but produce an interesting blurring of the refocused time signal. In some simple situations this effect can be explicitly quantified and related to the statistical model for the medium.


Random media, asymptotic theory, random Liouville equation, time reversal

2010 Mathematics Subject Classification

35L05, 35Q60, 60H15

Published 1 January 2008