Scattering enabled retrieval of Greenʹs functions from remotely incident wave packets using cross correlations

We analyze the “field-field” cross correlation associated with scattered coda waves, observed at a pair of distinct receivers, to obtain an estimate of the Greenʹs function between the receivers with an emphasis on high-frequency body waves. The scattered waves are generated in a slab with random medium fluctuations by an incident wave packet. Following the dyadic parabolic scaling of wave packets and considering appropriate scaling for the random fluctuations of the medium, we arrive at a description in terms of a system of Itô-Schrödinger diffusion models. Studying the Wigner distributions of the fields and expressing the cross correlation in terms of the Greenʹs function and the Wigner distribution, we can give a complete characterization of the cross correlation using a “blurring” transformation.