State-variable friction for the Burridge-Knopoff model

This work shows the relationship of the state variable rock-friction law proposed by Dieterich to the Carlson and Langer friction law commonly used in the Burridge-Knopoff (BK) model of earthquakes. Further to this, the Dieterich law is modified to allow slip rates of zero magnitude yielding a three parameter friction law that is included in the BK system. Dynamic phases of small scale and large scale events are found with a transition surface in the parameter space. Near this transition surface the event size distribution follows a power law with an exponent that varies as the transition is approached contrasting with the invariant exponent observed using the Carlson and Langer friction. This variability of the power-law exponent is consistent with the range of exponents measured in real earthquake systems and is more selective than the range observed in the Olami-Feder-Christensen model.