Spatiotemporal Modeling of Background Seismicity Using Gaussian Processes

The Epidemic Type Aftershock Sequence (ETAS) model, a widely used self-exciting, marked Hawkes process, has become a standard tool in statistical seismology. However, the standard ETAS formulation assumes a stationary background seismicity rate and therefore lacks the ability to capture the spatiotemporal structure of background seismicity. In this study, we extend the GP-ETAS model proposed by Molkenthin (2022) to incorporate a spatiotemporally varying background rate. We use nonparametric Gaussian process (GP) priors to describe spatiotemporal background seismicity and estimate them using a Bayesian inference framework with Markov chain Monte Carlo (MCMC) sampling techniques. We apply the extended GP-ETAS model to regions affected by Slow Slip Events (SSEs), which are known to generate stress changes that are both spatially and temporally heterogeneous, significantly influencing background seismicity patterns. The extended GP-ETAS model enables quantitative spatiotemporal analysis of SSE-driven variations in background seismicity.