Mapping the train model for earthquakes onto the stochastic sandpile model

TL;DR

This study maps a train model for earthquakes onto a stochastic sandpile model, revealing critical behavior dependent on grain shape and introducing a physically motivated randomness, with implications for understanding earthquake dynamics.

Contribution

It demonstrates a mapping between the earthquake train model and a stochastic sandpile model, including analysis of non-spherical grains and a new method for incorporating randomness.

Findings

Power-law distribution of avalanche sizes consistent with previous models

Critical behavior occurs only for grains with large aspect ratio

A new physically motivated method to introduce randomness

Abstract

We perform a computational study of a variant of the ``train'' model for earthquakes [PRA 46, 6288 (1992)], where we assume a static friction that is a stochastic function of position rather than being velocity dependent. The model consists of an array of blocks coupled by springs, with the forces between neighbouring blocks balanced by static friction. We calculate the probability, P(s), of the occurrence of avalanches with a size s or greater, finding that our results are consistent with the phenomenology and also with previous models which exhibit a power law over a wide range. We show that the train model may be mapped onto a stochastic sandpile model and study a variant of the latter for non-spherical grains. We show that, in this case, the model has critical behaviour only for grains with large aspect ratio, as was already shown in experiments with real ricepiles. We also demonstrate a way to introduce randomness in a physically motivated manner into the model.