Wave field correlations in weakly mismatched random media
  This paper concerns the derivation of a Fokker-Planck equation for the correlation of two high frequency wave fields propagating in two different random media. The mismatch between the random media need be small, on the order of the wavelength, and their correlation length need be large relative to the wavelength. The loss of correlation caused by the mismatch in the random media is quantified and the limit process for the phase difference is obtained. The derivation is based on a random Liouville equation to model high frequency correlations and on the method of characteristics to characterize mixing in the random Liouville equation. Applications of such correlation loss include the monitoring in time of random media and the analysis of time reversed waves in changing heterogeneous domains. 
Guillaume Bal and Lenya Ryzhik