A Simple Physics-Informed Stochastic Earthquake Simulator for Modeling Long-term Correlation in Seismic Activity

We present a simple physics-informed stochastic earthquake catalogue simulator to investigate the origin of long memory in seismic activity occurring on a single strongly connected fault system. While magnitudes are sampled according to a truncated Gutenberg-Richter law with exponential interevent time distribution, the model introduces an additional constraint aiming to reproduce a key physical phenomenon: whenever a threshold value for the average stress on fault is approached, the system becomes almost exponentially prone to spontaneous large-scale instability. We include this effect by forcing the occurrence of a new seismic event whenever an ideal, a priori assumed maximum value for the accumulated energy in crustal volume, i.e., strain and stress, is reached. The magnitude of the added earthquake is sampled from the same distribution of other events. Due to its occurrence, the mean interevent time decreases so that the clock of seismic activity speeds up until a large earthquake takes place provoking widespread stress drop; then, moving the system away from the upper threshold energy value. In the meanwhile, seismicity shows long-term persistence, i.e., a memory effect. We perform simulations and comparisons with both Poisson and ETAS catalogues proving that our model can better grasp the long-term trends of seismic activity on single faults highlighted in paleoseismic investigations and long-lasting parametric and seismic records; hence, in the future, allowing better mid- to long-term forecasts. Moreover, our model, although simple, is physically sound enabling connections between patterns in seismicity and the underlying process of energy accumulation in crustal volumes. It suggests, indeed, that long-term seismic clustering may arise because of persistent silent slip deficit on fault, so that regions featured by bursty small-to-moderate seismicity are more prone to nucleate persistent earthquake activity with the possibility of major shocks.