Bayesian source-mechanism inversion for microearthquakes

Using a physics-based shear-tensile crack model, we develop a Bayesian approach to simultaneously calculate source mechanisms for a set of microearthquakes and rigorously quantify the uncertainties of model parameters. To that end, we use the normalized displacement amplitudes of direct P-waves as observations. The Bayesian inference employs Markov-chain Monte Carlo (McMC) sampling with parallel tempering and principal component diminishing adaption to ensure efficient sampling. The model-parameter uncertainties are quantified through a series of posterior distributions. In the inversion, we adopt new prior bounds for model parameters to reduce the number of modes within the marginal posterior distribution for strike and overcome the issue of half-Gaussian distribution for the dip of near-vertical faults. Finally, the effectiveness of the proposed algorithm is demonstrated through the application to three representative events in a passive seismic dataset acquired during a four-well hydraulic-fracture completion program west of Fox Creek, Alberta.