Estimation of source parameters using a non-Gaussian probability density function in a Bayesian framework

Source parameters represent key factors in seismic hazard assessment and understanding source physics of earthquakes. In addition to conventional grid search approach to estimate source parameters, other approaches have been used recently. This study uses a Bayesian framework, the Markov Chain Monte Carlo method, to estimate source parameters including uncertainty assessment with inter-parameter correlations. The Bayesian calculation method requires to select a probability density function for estimating likelihood and the function can influence calculation reliability. While most studies use a normal distribution, we select an F -distribution due to its suitability for the data in ratio form. Using synthetic data and real observations from induced earthquakes in Oklahoma, we compare the calculation steps for spectral fitting and source parameter estimation using the two probability density functions. The sampling distribution and estimated parameters support the assumption that the F -distribution is well-suited for spectral ratio analysis. Results further show that a sampling distribution can effectively reveal trade-offs and uncertainty among parameters. Sampling distribution trends also reveal data quality criteria that can be used to refine results. Graphical Abstract