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

Abstract

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; Mw 3.90, the 30 January 2010; Mw 3.61, and the 6 January 2012; Mw 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.

Coal and Gas Outburst Affected by Law of Small Fault Instability during Working Face Advance

“…Due to the small fault structure of the mining face, even under low gas condition, coal and gas outbursts in the mining face are still frequent. By a statistic of the distribution rule of gas disasters in mining areas, it is found that the fault structure is closely related to the occurrence of the outburst [1][2][3][4]. According to relevant statistics, nearly 80% of coal and gas outburst accidents are caused by small faults [5,6], and these outburst accidents mostly occurred at coal roadway heading faces, followed by open-off cut, raise and dip, uncovering coal seam in the crosscut, mining face, and rock roadway heading face [7,8].…”

Locating Mine Microseismic Events in a 3D Velocity Model through the Gaussian Beam Reverse-Time Migration Technique

“…Oye and Roth [15] determined MS event locations through a grid search way of the neighborhood algorithm in [16], which still calls for a large amount of computation. In addition, genetic algorithm [17,18], particle swarm algorithm [1], simulated annealing algorithm [19], and Bayesian algorithm [20][21][22] have also been introduced for source location and achieved a higher inversion efficiency and better location accuracy. Furthermore, the combination between grid search algorithm and global optimization algorithm is also a potential solution to improve the efficiency and constraints on location results.…”

High-Accuracy Location of Microseismic Events in a Strong Inhomogeneous Mining Environment by Optimized Global Full Waveform Inversion

“…The origin time t 0 of an MS event can be regarded as an overall time-shift of all the recording waveforms. It can be eliminated in the data preprocessing step [11], then the M(x s )S (t − t 0 ) is shortened as S(t) for convenience and Equation (1) can be rewritten as Equation (2). The source-time function estimation strategy will be defined in Section 2.2.…”

“…Mine microseismic (MS) monitoring can effectively evaluate the risks of a mining area and optimize production plan, in which MS location is a fundamental indicator parameter to study the fracturing location of rock mass, understand crack extension law, focal mechanism inversion, and analyze characteristics of mining activities [1][2][3]. At present, ray tracing-based location methods based on travel time are generally used for MS location, in which the objective function is built by the difference between Appl.…”