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Wave Propagation and Imaging in Random Waveguides

Wednesday, January 16, 2013 - 3:15pm - 4:05pm
Keller 3-180
Liliana Borcea (Rice University)
We analyze long range wave propagation in three-dimensional random
waveguides. The waves are trapped by top and bottom boundaries, but
the medium is unbounded in the two remaining directions. We consider
scalar waves, and motivated by applications in underwater acoustics,
we take a pressure release boundary condition at the top surface and
a rigid bottom boundary. The wave speed in the waveguide is known
and smooth, but the top boundary has small random fluctuations that
cause significant cumulative scattering of the waves over long
distances of propagation. To quantify the scattering effects, we
study the evolution of the random amplitudes of the waveguide modes.
We obtain that in the long range limit they satisfy a system of
paraxial equations driven by a Brownian field. We use this
system to estimate three important mode-dependent scales: the
scattering mean free path, the cross-range decoherence length and
the decoherence frequency. Understanding these scales is important
in imaging and communication problems, because they encode
the cumulative scattering effects in the wave field measured by
remote sensors. As an application of the theory, we analyze time
reversal and coherent interferometric imaging in strong cumulative
scattering regimes.
MSC Code: 
81Q37
Keywords: