Cross Correlation and Deconvolution of Noise Signals in Randomly Layered Media

It is known that cross correlation of waves generated by noise sources, propagating in an unknown medium, and recorded by a sensor array, can provide information about the medium. In this paper the medium is a three-dimensional small-scale randomly layered medium with slow macroscopic variations. The main objective is here to set forth a framework for analysis of cross correlations of waves generated by noise sources and propagating in such a medium, moreover, use this framework to design estimators for macroscale medium features. The noise sources are located at the bottom of a random medium slab and generate a random wave field that is scattered by the rapid random fluctuations of the medium and then recorded at the surface. Taking into account the pressure release boundary conditions at the surface, this situation corresponds to the so-called daylight configuration. The analysis is carried out in the asymptotic framework where the typical wavelength is small compared to the scale of the macroscopic variations of the background medium and large compared to the decoherence length of the random fluctuations of the medium. It is shown that the cross correlation of the waves recorded at the surface contains statistically stable information about the background medium.