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

TL;DR

This paper develops a comprehensive framework to analyze wave propagation in media with long-range correlations, revealing that the asymptotic transmitted pulse can be characterized by complex stochastic processes beyond Gaussian models.

Contribution

It introduces a general theoretical framework for waves in long-range correlated media, extending previous models to include non-Gaussian and multifractal processes.

Findings

Asymptotic time-shift described by non-Gaussian processes

Framework applicable to very general long-range correlations

Generalization beyond fractional Brownian motion models

Abstract

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.