Transport equation for acoustic waves in random media with
localized scatterers
Kui Ren
In this talk, we generalize well-established derivations of
the radiative transport equation from first principles to
model the energy density of time-dependent and monochromatic
high frequency waves propagating in a random medium composed
of localized scatterers. The major tools for the derivation is Wigner
transform
and multiscale expansions. Our main assumption is that
the correlation length of the random scatterers is small
compared to the overall distance of propagation so that
ensemble averaging may take place. The correlation length
may be either comparable to the typical wavelength in the
system (the weak-coupling regime) or larger than the
wavelength (the low-density regime).
We will also mention briefly the application of the derived
transport equation to imaging in random media. This is a
joint work with Guillaume Bal at Columbia University.