Equivalence of the train model of earthquake and boundary driven Edwards-Wilkinson interface

TL;DR

This paper demonstrates that a discretized Burridge-Knopoff train model with random pinning exhibits avalanche and after-shock behaviors identical to the Edwards-Wilkinson interface model, revealing a deep connection between earthquake dynamics and interface depinning.

Contribution

It establishes the exact equivalence of avalanche dynamics and after-shock behavior between a discretized earthquake train model and the Edwards-Wilkinson interface model.

Findings

Avalanche size distribution follows a scale-free pattern.

After-shock behavior obeys Omori law.

Depinning velocity growth matches EW model exponents.

Abstract

A discretized version of the Burridge-Knopoff train model with (non-linear friction force replaced by) random pinning is studied in one and two dimensions. A scale free distribution of avalanches and the Omori law type behaviour for after-shocks are obtained. The avalanche dynamics of this model becomes precisely similar (identical exponent values) to the Edwards-Wilkinson (EW) model of interface propagation. It also allows the complimentary observation of depinning velocity growth (with exponent value identical with that for EW model) in this train model and Omori law behaviour of after-shock (depinning) avalanches in the EW model.