2005/11/03 by Guillaume Bal, Bal, Guillaume, Lenya Ryzhik +1
Earth and Planetary Sciences · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Ultrasonics and Acoustic Wave Propagation #Underwater Acoustics Research #math.AP
paper · pdf · doi:10.48550/arxiv.math/0511091
arxiv created 2005/11/03 · openalex publication_date 2005/11/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.