Bayesian inversion for source mechanisms of microearthquakes
Hongliang Zhang, Kristopher A. Innanen
We develop a Bayesian approach to simultaneously estimate source mechanisms for a set of microearthquakes, in which uncertainties of model parameters are vigorously quantified. To overcome limitations associated with the use of conventional moment-tensor inversion for low-magnitude events, we use a physically based shear-tensile crack model to characterize the seismic source in the inversion. The shear-tensile model consists of four parameters, strike, dip, rake and slope, to represent a superposition of a shear slip along the fault and a crack opening/closure. In the inversion, normalized displacement amplitudes of direct P-wave are used as observations. The Bayesian inference is employed via Markov-chain Monte Carlo (McMC) sampling with parallel tempering, and the principal component diminishing adaption is also used to ensure efficient sampling. In addition, to reduce the number of modes in 2D posterior marginals and avoid one-side distributed marginals for strike, new prior bounds are applied for strike (0 - 180) and dip (0 - 180). We apply the Bayesian inversion to a passive seismic dataset acquired during a four-well hydraulic-fracture completion program. For three representative events, uncertainties are quantified through posterior distributions of shear-tensile model parameters. The resulting source mechanisms are highly consistent results with a previous study, indicative of the effectiveness of the proposed algorithm.