A dynamical model for the stick-slip behaviour of faults
M Y Choi, Bernardo A. Huberman · Journal of Physics C Solid State Physics · 1984
The authors study a model of a fault by considering it as a dynamical array of asperities and show its formal analogy to probabilistic cellular automata. They use the fact that when the stress on a given asperity exceeds a critical value, it is transferred in a finite amount of time to its neighbouring ones. They also introduce conditional probabilities which allow for a dynamic description of the fault. In the limit of a broad stress distribution, they obtain exact solutions for the equations and show how initial distributions of failed asperities lead to stress propagation through the fault.