Seismic interferometry for sparse data: SVD-enhanced Green´s function estimation

Seismic interferometry (SI) is a technique used to estimate the Green´s function (GF) between two receivers, as if there were a source at one of the receiver locations. The GF obtained in this way, the interferometric GF (IGF), is estimated here by crosscorrelating the signals from two receivers for many sources and averaging these crosscorrelations over sources. However, in many applications, the conditions needed to recover the exact GF are not met and thus the estimated IGF is inaccurate. For such cases, we improve the IGF by summing lower-rank approximations of the crosscorrelations obtained via the Singular Value Decomposition (SVD), instead of averaging the original crosscorrelations. SVD allows us to enhance low-rank, coherent signals; these are the signals needed to reconstruct the GF. We apply this method to a field dataset where seismic signals from active sources are transformed to simulate passive seismic recordings. In this data set we find that filtering with SVD allows for IGF recovery in cases where standard SI does not.