Fast sparsity-promoting microseismic source estimation

Abstract

Microseismic events are generated during hydraulic fracturing of unconventional reservoirs and carry information on fracture locations and the origin times associated with these microseismic events. For drilling purposes and to prevent hazardous situations, we need to have accurate knowledge on the fracture locations as well as on their size and density. Because microseismic waves can travel far distances, microseismic data collected at the surface and/or in boreholes can help us to monitor hydraulic fracturing. While the so-called back propagation or time-reversal methods are able to focus recorded energy back onto the sources when a reasonable velocity model is available, these methods suffer from blurring especially in situations where the data acquisition suffers from lack of aperture, sparse sampling and noise. As a result, these methods typically cannot resolve sources in close proximity, a desired feature since we need this information if we want to follow the fracture evolution in space and time. In that situation, we need to estimate the locations and the associated source-time functions for closely spaced microseismic sources along the active fractures. To overcome the limitations of time-reversal methods, we propose a wave-equation based inversion approach where we invert for the complete source wavefield in both space and time. By promoting sparsity on the source wavefield in space, we negate the effects of non-radiating sources during the inversion and obtain high-resolution intensity plots and high-fidelity estimates for the source-time functions. We obtain these results relatively quickly by accelerating the linearized Bregman method with a dual formulation. Through experiments, we demonstrate that our method is computationally feasible, robust to noise and works for closely spaced sources with overlapping source-time functions in complex geological settings.