Open Access
June 2008 Time reversal of waves in a weakly perturbed random medium
D. G. Alfaro Vigo, K. Solna
Commun. Math. Sci. 6(2): 331-360 (June 2008).


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.


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D. G. Alfaro Vigo. K. Solna. "Time reversal of waves in a weakly perturbed random medium." Commun. Math. Sci. 6 (2) 331 - 360, June 2008.


Published: June 2008
First available in Project Euclid: 1 July 2008

zbMATH: 1163.35426
MathSciNet: MR2433699

Primary: 35L05 , 35Q60 , 60H15

Keywords: Asymptotic theory , random Liouville equation , Random media , Time reversal

Rights: Copyright © 2008 International Press of Boston

Vol.6 • No. 2 • June 2008
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