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

Renaud Marty (1) , Knut Solna (2)

1 IECN - Institut Élie Cartan de Nancy
2 Department of Mathematics [Irvine]

We consider waves propagating in a randomly layered medium with long-range correlations. An example of such a medium is studied in [19] 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.

Domaines: Probabilités [math.PR]

Renaud Marty, Knut Solna. A general framework for waves in random media with long-range correlations. The Annals of Applied Probability, 2011, 21 (1), pp.115-139. ⟨10.1214/10-AAP689⟩. ⟨hal-00401573⟩