A general framework for waves in random media with long-range correlations

Details A general framework for waves in random media with long-range correlations A general framework for waves in random media with long-range correlations

2010-12-30

arxiv.org/abs/1101.0060v1

Annals of Applied Probability 2011, Vol. 21, No. 1, 115-139

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AAP689 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/10-AAP689

We consider waves propagating in a randomly layered medium with long-range correlations. An example of such a medium is studied in \citeMS and leads, in particular, to an asymptotic travel time described in terms of a fractional Brownian motion. Here we study the asymptotic transmitted pulse under very general assumptions on the long-range correlations. In the framework that we introduce in this paper, we prove in particular that the asymptotic time-shift can be described in terms of non-Gaussian and/or multifractal processes.

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