Paper Info
Title
Pulse Propagation in Random Media with Long-Range Correlation
Abstract
This paper analyzes wave propagation in a one-dimensional random medium with long-range correlations. The asymptotic regime where the fluctuations of the medium parameters are small and the propagation distance is large is studied. In this regime pulse propagation is characterized by a random time shift described in terms of a fractional Brownian motion and a deterministic spreading described by a pseudodifferential operator. This operator is characterized by a frequency-dependent attenuation that obeys a power law with an exponent ranging from 1 to 2 that is related to the power decay rate of the autocorrelation function of the fluctuations of the medium parameters. This frequency-dependent attenuation is associated with a frequency-dependent phase, which ensures causality of the filter that realizes the approximation. A discussion is provided showing that the mean-field theory cannot capture the correct attenuation rate; this is because it also averages the random time delay. Numerical results are given to illustrate the accuracy of the asymptotic theory.
Year
DOI
Venue
2008
10.1137/080723193
MULTISCALE MODELING & SIMULATION
Keywords
Field
DocType
wave propagation,random media,long-range processes
Wave propagation,Exponent,Mathematical analysis,Operator (computer programming),Time shifting,Attenuation,Fractional Brownian motion,Power law,Mathematics,Autocorrelation
Journal
Volume
Issue
ISSN
7
3
1540-3459
Citations 
PageRank 
References 
0
0.34
3
Authors
2
Name
Order
Citations
PageRank
Josselin Garnier132647.70
Knut Sølna214246.02