A Bayesian probabilistic approach to estimate the focal mechanism of micro-earthquakes occurring at the Irpinia fault system, southern Italy.

We developed a Bayesian technique to infer the double-couple, focal mechanism parameters (strike, dip and slip angles) of an earthquake source. The method uses 3 independent datasets: P-wave peak amplitude and polarity and S-to-P amplitude ratio wherever it is available. The Bayesian technique works even in absence of one dataset and easily integrates any prior information about the region of study. The parameter space is explored thanks to an octree strategy. The method estimates the Posterior pdf, where the maximum likelihood parameter values (MAP model) both for the principal and auxiliary plane are chosen as the final fault mechanism solution. Furtherly, the uncertainties as the projections of the semi-axis of the 68% confidence ellipsoid centred on the MAP model are provided. The joint use of the three datasets allows to determine a solution even in the case of a limited number of stations that have recorded the event, which is the case for example for small magnitude earthquakes (M