Dynamics Phases and criticality in the Burridge-Knopoff
model of an earthquake fault.

Ian Clancy+, David Corcoran*

+Stokes Research Institute, University of Limerick 
*Department of Physics, University of Limerick

Abstract:

Bak, Tang and Wiesenfeld introduced the concept of
Self-Organised Criticality in which non-equilibrium
systems can attain a critical state without external
tuning. Such a phenomenon, Bak predicted, might explain
the abundance of fractals seen in nature. Self-Organised
Criticality is now widely held by many to explain the
scale invariance observed in the Gutenberg-Richter law for
earthquakes. In this talk, the results of a recent study
conducted at the University of Limerick are presented, in
which a previously establish model, the Burridge-Knopoff
model of an earthquake fault, has been derived, and the
criticality of the model explored. The Gutenberg-Richter
law is recovered, but interestingly, the system does not
self-organise to criticality, rather it must be tuned to
criticality. About the critical point one observes
differing dynamic phases, and spatio-temporal pattern
formation. Of wider interest, is that the study identifies
a potential pitfall of the cellular automata approach used
commonly in the study of complex systems. The
self-organisation to criticality predicted for earthquakes
and seen in well-established cellular automata earthquake
faults is most likely a result of the model assumptions.