Discrete Dynamics in Nature and Society
Volume 2 (1998), Issue 4, Pages 267-279

Simulation of earthquakes with cellular automata

P. G. Akishin,1,2,3 M. V. Altaisky,1,3,4 I. Antoniou,2,3,5 A. D. Budnik,1,2,3 and V. V. Ivanov1,2,3

1Laboratory of Computing Techniques and Automation, Joint Institute for Nuclear Research, Dubna 141980, Russia
2lnternational Solvay Institutes for Physics and Chemistry, CP-231, ULB, Campus Plaine, Bd. du Triomphe, Brussels 1050, Belgium
3European Commision, Joint Research Centre, Ispra (Va) 1-21020, Italy
4Space Research Institute RAS, Profsoyuznaya 84/32, Moscow 117810, Russia
5Theoretische Natuurkunde, Free University of Brussels, Brussels, Belgium

Received 20 April 1998

Copyright © 1998 P. G. Akishin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The relation between cellular automata (CA) models of earthquakes and the Burridge–Knopoff (BK) model is studied. It is shown that the CA proposed by P. Bak and C. Tang,although they have rather realistic power spectra, do not correspond to the BK model. We present a modification of the CA which establishes the correspondence with the BK model.An analytical method of studying the evolution of the BK-like CA is proposed. By this method a functional quadratic in stress release, which can be regarded as an analog of the event energy, is constructed. The distribution of seismic events with respect to this “energy” shows rather realistic behavior, even in two dimensions. Special attention is paid to two-dimensional automata; the physical restrictions on compression and shear stiffnesses are imposed.