Time-series analysis of interferometry in diffusive systems

Abstract

Recovery of the Empirical Green’s Function (EGF) from cross correlation of time-series measured at two receiver locations, called interferometry, is a powerful idea in exploration geophysics. Interferometry enables subsurface imaging without the need for engineered or active sources. It also avoids difficulty of filtering noise signals from the controlled source signals. In theory, the method in lossy and diffusive systems requires large number of sources distributed in an infinite volume surrounding the receiver pair. However, the existence of such a situation is impossible to realize in practice. Hence, the question arise is that “What is the required number and distribution of sources to reconstruct EGF to a given error tolerance?” In this study, this question is investigated through numerical modeling of a double halfspace model. Time-series analysis of the EGF confirmed the previous findings in homogenous medium in which the width of source distribution needed to reconstruct EGF up to a desired time depends on the receiver separation and diffusivity of the medium. For inhomogeneous media, a suite of double halfspace models is examined in which receivers are located on either side of the interface in a 1D problem. It was shown that sources need to be further into the region with higher diffusivity than into low diffusivity region. Naturally, as a receiver pair is embedded sufficiently far into the high or low-D side, no sources are required from across the double halfspace boundary because, essentially, the problem is that for a wholespace. However, closer to the boundary at a given distance, h, a receiver pair in the high-D side will require sources from the low-D side of the system whereas a receiver pair in the low-D side will require no sources from the high-D side of the system.