Bayesian inversion of pressure diffusivity from microseismicity

We have considered the problem of using microseismic data to characterize the flow of injected fluid during hydraulic fracturing. We have developed a simple probabilistic physical model that directly ties the fluid pressure in the subsurface during the injection to observations of induced microseismicity. This tractable model includes key physical parameters that affect fluid pressure, rock failure, and seismic wave propagation. It is also amenable to a rigorous uncertainty quantification analysis of the forward model and the inversion. We have used this probabilistic rock failure model to invert for fluid pressure during injection from synthetically generated microseismicity and to quantify the uncertainty of this inversion. The results of our analysis can be used to assess the effectiveness of microseismic monitoring in a given experiment and even to suggest ways to improve the quality and value of monitoring.