Using SVD for improved interferometric Green's function retrieval

Seismic interferometry (SI) is a technique used to estimate the Green's function (GF) between two receiver locations, as if there were a source at one of the receiver locations. However, in many applications, the requirements to recover the exact GF are not satisfied and SI yields a poor estimate of the GF. For these non-ideal cases, we improve the interferometric GFs, by applying singular value decomposition (SVD) to the cross-correlations before stacking. The SVD approach preserves energy that is stationary in the cross-correlations, which is the energy that contributes most to the GF recovery, and attenuates non-stationary energy, which leads to artefacts in the interferometric GF. We apply this method to construct virtual shot gathers (for both synthetic and field data) and demonstrate how using SVD enhances physical arrivals in these gathers. We also find that SVD is robust with respect to weakly correlated random noise, allowing a better recovery of events from noisy data, in some cases recovering energy that would otherwise be completely lost in the noise and that the standard SI technique fails to recover