Hamiltonian Monte Carlo to Characterize Induced Earthquakes: Application to a M_L 3.4 Event in the Groningen Gas Field and the Role of Prior

The Hamiltonian Monte Carlo algorithm is known to be highly efficient when sampling high-dimensional model spaces due to Hamilton's equations guiding the sampling process. For weakly non-linear problems, linearizing the forward problem enhances this efficiency. This study integrates this linearization with geological prior knowledge for optimal results. We test this approach to estimate the source parameters of a 3.4 magnitude induced event that originated in the Groningen gas field in 2019. The source parameters are the event's centroid (three components), its moment tensor (six components), and its origin time. In terms of prior knowledge, we tested two sets of centroid priors. The first set exploits the known fault geometry of the Groningen gas field, whereas the second set is generated by placing initial centroid priors on a uniform horizontal grid at a depth of 3 km (the approximate depth of the gas reservoir). As for the forward problem linearization, we use an approach in which the linearization is run iteratively in tandem with updates of the centroid prior. We demonstrate that, in the absence of a sufficiently accurate initial centroid prior, the linearization of the forward model necessitates multiple initial centroid priors. Eventually, both prior sets yield similar posteriors. Most importantly, however, they agree with the geological knowledge of the area: the posterior peaks for model vectors containing a centroid near a major fault and a moment tensor that corresponds to normal faulting along a plane with a strike almost aligning with that of the major fault.