Estimating spatially varying event rates with a change point using Bayesian statistics: Application to induced seismicity

We describe a model to estimate event rates of a non-homogeneous spatio-temporal Poisson process. A Bayesian change point model is described to detect changes in temporal rates. The model is used to estimate whether a change in event rates occurred for a process at a given location, the time of change, and the event rates before and after the change. To estimate spatially varying rates, the space is divided into a grid and event rates are estimated using the change point model at each grid point. The spatial smoothing parameter for rate estimation is optimized using a likelihood comparison approach. An example is provided for earthquake occurrence in Oklahoma, where induced seismicity has caused a change in the frequency of earthquakes in some parts of the state. Seismicity rates estimated using this model are critical components for hazard assessment, which is used to estimate seismic risk to structures. Additionally, the time of change in seismicity can be used as a decision support tool by operators or regulators of activities that affect seismicity.