Induced Earthquake Source Characterization Using Multi-stage of Hamiltonian Monte Carlo Algorithm

Estimating earthquake parameters, including their uncertainty, requires probabilistic sampling or inversion using Bayesian algorithms. One such Bayesian algorithm known to be highly efficient is the Hamiltonian Monte Carlo (HMC) algorithm, and modifying the algorithm with an additional linearization step can further increase this efficiency. However, the modified HMC relies heavily on accurate prior information to effectively sample non-linear earthquake parameters (e.g., hypocenter and origin time). Furthermore, the ability of the modified HMC to estimate non-linear parameters diminishes with respect to the high degree of non-linearity that is inherent to some types of events, such as induced earthquakes. To address this, we adjust the modified HMC to be run in multiple stages, combined with pre-determined initial prior sets. We test this adjustment using synthetic and real data from an induced earthquake event in the Groningen gas field in the Netherlands. We start by obtaining an initial estimate of the prior information and use it to draw multiple initial prior sets. We then run the HMC for each initial prior set in multiple stages where the results from the current stage serve as the prior for the next stage. As the final step, we form the final posterior distributions by selecting results that give the best fit between the observed and modeled data. Within this approach, we estimate ten earthquake parameters those are the six components of a full moment tensor solution, the centroid (three coordinate components), and the earthquake's origin time (including the static time corrections for each recording station). After obtaining the final results, we compare our findings with those of an existing earthquake catalog and several other research results. Given the available fault map of Groningen's subsurface, we found that our results have a higher degree of correlation with respect to the major subsurface faults.