Sandpile-based model for capturing magnitude distributions and spatiotemporal clustering and separation in regional earthquakes

Abstract

Abstract. We propose a cellular automata model for earthquake occurrences patterned after the sandpile model of selforganized criticality (SOC). By incorporating a single parameter describing the probability to target the most susceptible site, the model successfully reproduces the statistical signatures of seismicity. The energy distributions closely follow power-law probability density functions (PDFs) with a scaling exponent of around − 1.6, consistent with the expectations of the Gutenberg-Richter (GR) law, for a wide range of the targeted triggering probability values. Additionally, for targeted triggering probabilities within the range 0.004-0.007, we observe spatiotemporal distributions that show bimodal behavior, which is not observed previously for the original sandpile. For this critical range of values for the probability, model statistics show remarkable comparison with long-period empirical data from earthquakes from different seismogenic regions. The proposed model has key advantages, the foremost of which is the fact that it simultaneously captures the energy, space, and time statistics of earthquakes by just introducing a single parameter, while introducing minimal parameters in the simple rules of the sandpile. We believe that the critical targeting probability parameterizes the memory that is inherently present in earthquakegenerating regions.

Size Polydispersity Tunes Slip Avalanches of Granular Gouge

“…The empirical law is consistent with the power law distribution of energy release P(E) ∝ E −τ , where τ ¼ 1 þ 2 3 b. The exponent τ varies in a range depending on the considered earthquake catalog and region (Batac et al, 2017;Geller et al, 2015;Kagan, 2002;Marković & Gros, 2014;Nicolas et al, 2018). Understanding earthquake dynamics, especially the origin of scale-free statistics, remains a major issue in geophysics.…”

Avalanches in an extended Schelling model: an explanation of urban gentrification

“…Finally, we show the values of the fitted parameters in Table I, being x c the choosen size for the fitting (Appendix A). We can find α values in the range [−1.78, −0.98] previously reported in references [19][20][21][22][23], concerning self-organized criticality in different systems. Most of the processes that arise for these values of T are avalanches with similar parameter values and behaviours to those explained in the previous section (Sec.…”

The role of intervention mechanisms on a self-organized system: dynamics of a sandpile with site reinforcement

“…When updated sequentially, the Zhang sandpile produces scale-free statistics for avalanche areas [42]. Variants of this continuous-valued sandpile has been used to replicate the key characteristics of various complex systems [23,25].…”

“…The simplest model of SOC is the sandpile, a grid-based model that is inspired by the avalanches generated by an actual pile of sand [1]. Modifications to the sandpile model has resulted in simple discrete implementations that recover key signatures of earthquakes [23][24][25], landslides [5,26,27], forest fires [28,29], and rainfall [18,30], among others. Interestingly, while these modifications replicate many details of the system, the resulting distributions of avalanches continue to obey the same heavy-tailed (power-law) statistics [23,25].…”