Physics-informed numerical modeling of long-term memory correlation in seismic activity

The concept and awareness of fault long memory, or long-range dependence, in the seismic process has recently gained interest in recent years thanks to the increasing quality of earthquake cataloguescompleteness of earthquake data, which has progressively have allowed a better assessment of evaluating the level of correlation between the statistical features of seismicityearthquakes (e.g., Livina et al., 2005; Barani et al., 2021; Petrillo et al., 2022). Among them, unprecedented datasets have been key to and shed light on long-term earthquake clustering (e.g., Kagan and Jackson, 1991; Kagan and Jackson, 1999), one of the main manifestations of long memory behaviors. In the present work, we present a simple physics-informed stochastic earthquake catalogue simulator that allows the incorporation of long-term correlations in seismicity activity supposed to occurring within an isolated crustal volume with strongly interacting faultson a single strongly connected fault system (or crustal volume). While magnitudes are sampled according to a truncated Gutenberg-Richter law with exponential interevent time distribution, the model introduces an additional constraint, which is borrowed from Hurst’s model for water reservoirs (Hurst, 1951), aiming to reproduce a key physical phenomenon: whenever a threshold stress value on the fault is approached, the system becomes almost exponentially prone to spontaneous large-scale instability. We include this effect by forcing the occurrence of spontaneousa new seismic events whenever a given maximum value of the energy accumulated in the crustal volume (i.e., strain and stress) is reached: ti=t(i-1)+(Emax-E(i-1))/Er; i=1,…,n where Ei is the energy stored in the reservoir at the ith time step, and Er is the energy rate (i.e., loading rate). The previous condition implies an acceleration in seismic release and a consequent decrease in the mean interevent time. In other words, whenever the threshold energy is reached, the clock of the system speeds up until a very large earthquake occurs with a significant energy release, moving the systems towards a more stable physical configurationwith significant stress drop. Concurrently, seismicity shows persistent behavior (i.e., a memory effect). We perform simulations and comparisons with both Poisson- and ETAS-based 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, allowing better mid- to long-term forecasts in the future. Both the Poisson and ETAS models, indeed, have been proven unable to capture long-term correlations in seismic activity. Moreover, our model, although simple, is physically sound and allows connections between seismicity patterns and the underlying process of energy accumulation and release in crustal volumes. Indeed, it suggests 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 a consequent higher probability of occurrence of major shocks. When a very strong event occurs (with magnitude close to the maximum expected onemagnitude associated with the seismic reservoir), producing an abrupt change in the system due to a significant drop in the accumulated energy, the probability of another strong event in the near future is reduced. Although our simulator is quite simple (e.g., it cannot generate cascading interaction between usually poorly interacting fault patchess) and is not yet suitable for earthquake forecasting, it lays the groundwork for future developments in this direction. With further development, the model could complement existing approaches by capturing features of seismicity that models like the standard ETAS (Ogata, 1988) may overlook, especially in regions where long-term clustering is significant. References Livina V. N., Havlin S. and Bunde A.; 2005: Memory in the occurrence of earthquakes. Phys. Rev. Lett. 95(20), 208501. Barani S., Cristofaro L., Taroni M., Gil-Alana L. 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