Coulomb Threshold Rate-and-State Model for Fault Reactivation: Application to induced seismicity at Groningen

A number of recent modeling studies of induced seismicity have used the rate-and-state friction model of Dieterich (1994) to account for the fact that earthquake nucleation is not instantaneous. Notably, the model assumes a population of seismic sources accelerating towards instability with a distribution of intial slip speeds such that they would produce earthquakes steadily in absence of any perturbation to the system. This assumption may not be valid in typical intra-plate settings where most examples of induced seismicity occur, since these regions have low stressing rates and initially low seismic activity. The goal of this paper is twofold. First, to derive a revised Coulomb rate-and-state model, which takes into account that seismic sources can be initially far from instability. Second, to apply and test this new model, called the Threshold rate-and-state model, on the induced seismicity of the Groningen gas field in the Netherlands. Stress changes are calculated based on a model of reservoir compaction (Smith et al. 2019) since the onset of gas production. We next compare the seismicity predicted by our threshold model and Dieterich (1994)'s model with the observations. The two models yields comparable spatial distributions of earthquakes in good agreement with the observations. We find however that the Threshold model provides a better fit to the observed time-varying seismicity rate than Dieterich (1994)'s model, and reproduces better the onset, peak, and decline of the observed seismicity rate. We compute the maximum magnitude expected for each model given the Gutenberg-Richter distribution and compare to the observations. We find that the Threshold model both shows better agreement with the observed maximum magnitude and provides results consistent with lack of observed seismicity prior to 1993. We carry out analysis of the model fit using a Chi-squared reduced statistics and find that the model fit is dramatically improved by smoothing the seismicity rate. We interpret this finding as possibly suggesting an influence of source interactions, or clustering, on a long time-scale of about 3-5 year.