Point-Source Inversion of Small and Moderate Earthquakes From P-wave Polarities and P/S Amplitude Ratios Within a Hierarchical Bayesian Framework: Implications for the Geysers Earthquakes

Characterizing seismic moment tensors of small- to moderate-magnitude earthquakes (i.e., 2.5<M<4.0) still represents a challenge in observational seismology. To address this problem, inversion methods based on fitting the first-motion polarity and/or the amplitude ratios of the recorded waves have been designed, and where possible, the full waveform inversions were also used. The inversions that include a combination of subsets of data are desirable, but the weighting of each subset is typically treated in an ad hoc manner. In order to circumvent this problem, here we develop a new method in a Bayesian framework, which apart from the model-parameter means and uncertainties, also relaxes the weighting scheme as a free hyper-parameter. We then rigorously test our proposed method for a range of representative focal mechanisms, each with a different level of noise. The proposed method constrains full moment-tensors better than the methods that employ only the first polarity, the amplitude ratio subsets of data or a combination of all subsets with fixed weightings. We apply our method to three representative events of different magnitudes from the Geysers, California geothermal field (the 26 April 2011; M_w 3.90, the 30 January 2010; M_w 3.61, and the 6 January 2012; M_w 2.75 earthquakes). While there are similarities with the previous results, two of the events require significantly smaller double-couple and higher positive isotropic components than previously estimated. This discrepancy in the obtained results has implications for the interpretation of physical mechanisms responsible for the seismicity in the Geysers. Overall, we demonstrate the efficiency of the proposed method, which opens a way to analyze small- to moderate-size events in different settings where the contribution of non-double-couple components in the seismic moment tensor is significant.