Dynamics of Tectonic Plates
  We suggest a model that describes a mutual dynamic of tectonic plates. The dynamic is a sort of stick-slip one which is modeled by a Markov random process. The process defines a microlevel of the dynamic. A macrolevel is obtained by a scaling limit which leads to a system of integro-differential equations which determines a kind of mean field systems. Conditions when Gutenberg-Richter empirical law are presented on the mean field level. These conditions are rather universal and do not depend on features of resistant forces. 
E. Pechersky, A. Pirogov, G. Sadowski and A. Yambartsev
math.PR cond-mat.stat-mech physics.geo-ph