Comparing the sandpile model with targeted triggering and the Olami-Feder-Christensen model as models of seismicity using recurrence network analysis

Abstract

Slowly driven sandpile models has found applications in modelling earthquakes due to the observed power law statistics in its magnitude distributions, like the behaviour of earthquakes. Adding a probability to target the most susceptible site in the grid, the sandpile model recovers even the spatio-temporal statistics of earthquake events. In this work, we compare the sandpile model with targeted triggering to the Olami-Feder-Christensen (OFC) model: a standard earthquake model that also exhibits self-organized criticality. The sandpile model captures the magnitude distributions of earthquake events at a value of targeted triggering probability p = [0.004,0.007]. The triggering probability value p = 1.0, showing that the most susceptible site is always triggered, follows the magnitude distribution of the OFC model. A comparison was done by constructing a record-breaking recurrence network for the events. Spatial and magnitude criteria set the temporally directed links between events across the entire record. Both the models recover power-law exponents comparable to those previously obtained for earthquake data, which is 1.0 for recurrence distance and recurrence time distributions, and 2.1 for the in-degree distributions for the farthest recurrence criteria. The sandpile model with targeted triggering exhibits a behaviour in between a slowly driven sandpile and the OFC model.