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.
Publié le : 2011-02-15
Classification:
Waves in random media,
long-range dependence,
fractional and multifractional processes,
34F05,
34E10,
37H10,
60H20
@article{1292598029,
author = {Marty, Renaud and S\o lna, Knut},
title = {A general framework for waves in random media with long-range correlations},
journal = {Ann. Appl. Probab.},
volume = {21},
number = {1},
year = {2011},
pages = { 115-139},
language = {en},
url = {http://dml.mathdoc.fr/item/1292598029}
}
Marty, Renaud; Sølna, Knut. A general framework for waves in random media with long-range correlations. Ann. Appl. Probab., Tome 21 (2011) no. 1, pp. 115-139. http://gdmltest.u-ga.fr/item/1292598029/