Microquake seismic interferometry with SVD enhanced Green's function recovery

Abstract

The conditions under which seismic interferometry (SI) leads to the exact Green’s function (GF) are rarely met in practice, resulting in errors in the recovered GF. To alleviate this problem, we employ additional information than what is typically used in SI. This information comes from the collection of crosscorrelated traces, one for each source for a pair of receivers, which we shall refer to as the crosscorrelogram. It is by stacking the crosscorrelogram in the source dimension that we obtain an interferometric GF. In general, this crosscorrelogram has both stationary energy that contributes to the estimated GF and non-stationary energy that does not. Stationary energy in the crosscorrelogram is characterized by linearity, coherency, low wavenumber, and thus nearly in-phase events along the source dimension. Non-stationary energy by contrast is characterized by non-linearity, incoherency, high wavenumber, and out-of-phase events along the source dimension. We exploit these differences to separate the two parts of the energy in the crosscorrelogram to obtain more accurate GF estimates for non-ideal cases. In order to perform this separation and extract more information from the crosscorrelograms we use the singular value decomposition (SVD). We find that SVD is able to enhance physical arrivals that are not properly recovered using standard stacking in SI and inmany cases to recover arrivals that would otherwise be obscured by noise. Here, we filter the crosscorrelograms by using a lower-rank approximation, computed with SVD by keeping only the largest singular values, to enhance events that are coherent across multiple sources, thus isolating this stationary energy that gives the primary contribution to the GF. We illustrate this method with synthetic results for both homogeneous and scattering media simulating a possible application in microseismic monitoring with downhole receivers.