Abstract:
Radiative transfer equations have long been used to model the energy
density of waves in random media, with applications in light propagating
through turbulent atmospheres, underwater acoustics, and elastic wave
propagation in the Earth's crust to name a few. In this talk I will
derive such models from first principles, i.e., from equations for the
wave fields in the high frequency regime. A very useful tool in such a
derivation is the Wigner transform applied to the wave fields. I will
also show how the correlations of two wave fields propagating in possibly
different media can be estimated in the high frequency regime and present
applications of the theory to the understanding of time reversed waves
propagating in highly heterogeneous media. Finally I will present recent
numerical simulations performed on parallel architectures of twodimensional
acoustic wave propagation in random media on large domains (on the order
of 500 times 500 wavelengths) and show the very good accuracy of the
macroscopic radiative transfer models to describe the energy density
of the acoustic waves. Applications to detection and imaging of buried
inclusions in highly cluttered environment will also be mentioned.
[LECTURE SLIDES]
