Estimating Inhomogeneous Spatiotemporal Background Intensity Functions Using Graphical Dirichlet Processes

Abstract Enhancements in seismic monitoring instrumentation have been shown to have an impact on the number of observed earthquakes, since denser networks usually allow the recording of more events. However, phenomena such as strong earthquakes or aseismic transients, including slow slip events, may alter the seismicity rate. In the field of seismology, it is standard practice to model background seismicity as a Poisson process. Based on this idea, this work proposes a model that can incorporate the evolving spatial intensity of Poisson processes over time, which implies that temporal changes in background seismicity are included in the modeling. In recent years, novel methodologies have been developed for quantifying the uncertainty in the estimation of background seismicity in homogeneous cases using Bayesian nonparametric techniques. The present study develops a novel methodology based on graphical Dirichlet processes for incorporating spatial and temporal inhomogeneities in background seismicity. The proposed model is applied to study seismicity in southern Mexico, using recorded data from 2000 to 2015.