Sparsity-promoting least-squares interferometric migration for high-resolution passive source location

Abstract

Seismic source localization plays an important role in estimating the hypocenter of earthquakes and in monitoring hydraulic fracturing. Interferometric crosscorrelation migration (ICCM) is one of the most important waveform-based source location methods that produces a source image from interstation crosscorrelations without manual picking. However, the ICCM method suffers from blurring of the source image, especially for cases in which the acquisition aperture is limited, receivers are sparsely distributed, and the data signal-to-noise ratio is too low. As a result, it typically cannot resolve sources in close proximity to each other, whereas distinguishing them might be a desired feature when we want to follow the fracture evolution in space and time. One possible solution is by fitting a source distribution function to the observed interstation crosscorrelations by least-squares minimization, where the source distribution function is a source power-spectral density (PSD) defined as a function of frequency and spatial location. However, this least-squares interferometric crosscorrelation migration (LS-ICCM) approach provides limited resolution improvement compared to the ICCM method. To further improve the image resolution, we have adopted a sparsity-promoting interferometric crosscorrelation migration (SP-ICCM) method that negates the effects of unfocused sources during the inversion. This sparsity constraint is imposed on the source PSD in space to mitigate the loss of resolution that arises as a consequence of incomplete information, including limited aperture and discretization. The inverse problem involving this sparsity constraint can be solved relatively quickly with an iteratively reweighted least-squares algorithm. Using synthetic and field data tests, we demonstrate that our method is robust to noise and effective for closely spaced sources in complex geologic settings.