Accurate estimation of microseismic events (small earthquakes) generated during hydraulic fracturing of low permeability rocks such as shale enables important characterization of hydraulic fracture networks. Determining the orientation of the fracture is important in characterizing the effectiveness of the stimulation process. We consider the source as separable in time and space and invert for a complete description of the source in one of these two dimensions assuming the other is known. A change of variables applied to the velocity-stress form of the elastic-wave equation ensures that the system is self-adjoint. The inversion does not use any a priori assumptions about the form of the source, does not require a good starting guess for accurate source recovery, and is robust in the presence of noise. I will present realistic source estimation examples from coupled fluid flow and deformation modeling of a fracture.

This is joint work with Jordan Kaderli and Matt McChesney