Full-waveform inversion for microseismic events using sparsity constraints

Full-waveform inversion (FWI) is a powerful tool that can be used to invert tiff microseismic event locations and the source signature because it can exploit the complete waveform information. We have developed an algorithm to invert for a spatio-temporal source function that encapsulates microseismic events with spatially localized or distributed locations and source signatures. The algorithm does not require assumptions to be made about the number or type of sources; however, it does require that the velocity model is close to the true subsurface velocity. We reformulate the conventional FWI algorithm based on the l(2)-norm data-misfit function by adding sparsity constraints using a sparsity promoting l(1)-norm as an additional regularization term to get more focused and less noise-sensitive event locations. The Orthant-Wise Limited-memory quasi-Newton algorithm is used to solve the optimization problem. It inherits the advantageous (fast convergence) properties of the limited memory BroydenFletcher-Goldfarb-Shanno method and can easily overcome the nondifferentiability of l(1)-norm at null positions. We determine the performance of the algorithm on noise-free and noisy synthetic data from the SEG/EAGE overthrust model.