4.4 Article

PULSE PROPAGATION IN RANDOM MEDIA WITH LONG-RANGE CORRELATION

Journal

MULTISCALE MODELING & SIMULATION
Volume 7, Issue 3, Pages 1302-1324

Publisher

SIAM PUBLICATIONS
DOI: 10.1137/080723193

Keywords

wave propagation; random media; long-range processes

Funding

  1. ONR [N00014-02-1-0089]
  2. DARPA [N00014-05-1-0442]
  3. NSF [DMS0709389]
  4. Sloan Foundation

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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.

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