Realistic time correlations in sandpiles

TL;DR

This paper demonstrates that incorporating slow diffusive perturbations in sandpile models creates realistic temporal correlations, challenging previous dismissals of self-organized criticality's relevance to seismic activity.

Contribution

It introduces a sandpile automaton with diffusive perturbations that reproduces realistic earthquake waiting time distributions, linking spatial correlations to temporal activity.

Findings

Reproduces $1/f$ spectral behavior in sandpiles.

Shows slow diffusion of perturbations leads to realistic seismic correlations.

Challenges previous arguments against self-organized criticality in earthquakes.

Abstract

A ``sandpile'' cellular automaton achieves complex temporal correlations, like a $1/f$ spectrum, if the position where it is perturbed diffuses slowly rather than changing completely at random, showing that the spatial correlations of the driving are deeply related to the intermittent activity. Hence, recent arguments excluding the relevance of self-organized criticality in seismicity and in other contexts are inaccurate. As a toy model of single fault evolution, and despite of its simplicity, our automaton uniquely reproduces the scaling form of the broad distributions of waiting times between earthquakes.