A physics-informed stochastic model for the long-term correlation of earthquakes

In this work, a simple physics-informed stochastic earthquake catalog simulator is presented for the modeling of long memory on a single fault (or crustal volume). The simulator combines the fundamental statistical laws of seismology (i.e., the Gutenberg-Richter law and the exponential distribution of inter-event times of spontaneous events) with two physical assumptions: 1) earthquake magnitudes are constrained by the amount of potential energy accumulated within the crustal volume at a given time, 2) existence of an upper boundary for stress on the fault. The consequence is a deviation from the conventional exponential inter-event distribution. We analyze a set of simulated catalogs to inspect long memory. Our results show that, depending on the relative proportion of energy accumulation and release, catalogs can exhibit complex patterns and long memory behavior. Despite its simplicity, our simulator can replicate the key features of seismic activity observed in real data, thus enabling a consistent physical interpretation.