Background velocity estimation with cross correlations of incoherent waves in the parabolic scaling

In this paper the incoherent waves reflected by a random medium in the parabolic regime are considered. The case in which the medium has anisotropic three-dimensional rapid random fluctuations and one-dimensional slow variations is analyzed. First, it is shown how the second-order statistics of the reflected wave is determined by the slow spatial variations of the background velocity, the scattering coefficient and the absorption coefficient of the medium via a system of transport equations. Next, it is shown how observations of the time-dependent intensity, spatial radius and spectral radius of the reflected wave can be used to invert this system in order to reconstruct the parameters of the medium. Finally, it is shown that the analytic framework set forth can also be used to analyze the time dynamics of weak localization.

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