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In this paper we present a novel technique for micro-seismic localizationusing a group sparse penalization that is robust to the focal mechanism of thesource and requires only a velocity model of the stratigraphy rather than afull Green's function model of the earth's response. In this technique weconstruct a set of perfect delta detector responses, one for each detector inthe array, to a seismic event at a given location and impose a group sparsityacross the array. This scheme is independent of the moment tensor and exploitsthe time compactness of the incident seismic signal. Furthermore we present amethod for improving the inversion of the moment tensor and Green's functionwhen the geometry of seismic array is limited. In particular we demonstratethat both Tikhonov regularization and truncated SVD can improve the recovery ofthe moment tensor and be robust to noise. We evaluate our algorithm onsynthetic data and present error bounds for both estimation of the momenttensor as well as localization. Furthermore we discuss the estimated momenttensor accuracy as a function of both array geometry and fault orientation.

Complexity penalized hydraulic fracture localization and moment tensor estimation under limited model information