Simultaneous recovery of origin time, hypocentre location and seismic moment tensor using sparse representation theory

Using a proper parametrization, the source displacement field of a seismic event can be efficiently reconstructed by a redundant dictionary of Greens functions based on sparse representation theory. Then, by subjecting the pre-existing event records and pre-computed dictionary of Greens functions into a sparsity-promoting algorithm, it is possible to simultaneously evaluate the origin time, hypocentre coordinates and seismic moment tensor. The proposed method is applicable to single- or multiple-source scenarios and, with minor adjustments, can be a valuable tool for real-time, automatic monitoring systems. This study demonstrates the effectiveness and accuracy of the dictionary-based approach via (1) detection of microseismic events produced during the hydraulic fracturing of oil and gas wells and (2) inversion of a small-magnitude, regional earthquake (2002 June 18 in Caborn, Indiana) data. Our experiments based on numerical simulations and earthquake observations underscore the largely untapped potential of dictionary-based approaches and sparse representation theory in continuous source parameter recovery.