Eur. Phys. J. B 64, 139-146 (2008)
https://doi.org/10.1140/epjb/e2008-00279-5

Cell scale self-organisation in the OFC model for earthquake dynamics

Re-rupturing, memory loss and quantisation of strain

School of GeoSciences, Edinburgh University, EH9 3, JW Edinburgh, UK

Corresponding author: ^a mark.naylor@ed.ac.uk

Received: 26 January 2008
Revised: 11 June 2008
Published online: 16 July 2008

Abstract

We examine the cell scale self organising mechanisms in the Olami Feder Christensen (OFC) model that have the potential to generate critical behaviour. In particular we demonstrate how spatial organisation and quantisation of strain distributions occurs, why temporal strain fluctuations are minimised as the local strain conservation factor, β→ 1.0, and how the strain distributions are dependent upon the lattice geometry employed. The origin of the self-organising behaviour can be divided into two regimes; at low β where no re-rupturing of cells occurs and for higher β where the probability of re-rupturing becomes increasingly significant. The presence or absence of the re-rupturing mechanism leads to different system optimisations, tending from spatially well ordered strain domains at intermediate β to a spatially rough strain field but a temporally stationary, memory less strain distribution at β = 1. The construction of the Markov chain demonstrates that degeneracy of the transitions is a primary control on transition probabilities at β = 1. The stationary state occupation is controlled by transition degeneracy, local correlations and mean residence times.