Using SVD for improved interferometric Green's function recovery

Seismic interferometry 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 locations. By crosscorrelating the recorded seismic signals at the two locations we generate a crosscorrelogram. Stacking the crosscorrelogram over sources generates an estimate of the inter-receiver GF. However, in most applications, the requirements to recover the exact GF are not satisfied and stacking the crosscorrelograms yields a poor estimate of the GF. For these non-ideal cases, we enhance the real events in the virtual shot gathers by applying Singular Value Decomposition (SVD) to the crosscorelograms before stacking. The SVD approach preserves energy that is stationary in the crosscorrelogram, thus enhancing energy from sources in stationary positions, which interfere constructively, and attenuating energy from non-stationary sources that interfere distructively. We apply this method to virtual gathers containing the virtual refraction artifact and find that using SVD enhances physical arrivals. We also find that SVD is quite robust in recovering physical arrivals from noisy data when these arrivals are obscured by or even lost in the noise in the standard seismic interferometry technique.