Dynamics of Tectonic Plates

Abstract: 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.