An original model of wave propagation in strongly scattering transparent random structures with arbitrary correlated disorder is derived from the first principles. In particular, it is shown that the mean arrival (or diffuse) time of a short narrowband pulse can be presented as a linear integral transform of the microstructure's power spectrum. Moreover, this integral transform is invertible, which allows one, in principle, to reconstruct the correlation function of a heterogeneous medium by measuring the angular distributions of the diffuse time for waves of different frequencies. This technique, called here the diffuse time tomography, is free of the intrinsic diffraction tomography limitations; the most important is the fact that it can be applied to strongly scattering structures.
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