Dynamics of Tectonic Plates E. Pechersky 1 S. Pirogov 1 , G. Sadowski 2 and A. Yambartsev 3 September 11, 2018 1 Dobrushin laboratory of Institute for Information Transmission Problems of Russian Academy of Sciences, 19, Bolshoj Karetny, Moscow, Russia. E-mail: pech@iitp.ru, pirogov@iitp.ru 2 Department of Mineralogy and Geotectonics, Institute of Geosciences University of S˜ ao Paulo Rua Prof. Guilherme Milward 246 S˜ ao Paulo, SP, Brazil, 05506-000 E-mail: sadowski@usp.br 3 Department of Statistics, Institute of Mathematics and Statistics, University of S˜ ao Paulo Rua do Mat˜ ao 1010, CEP 05508–090, S˜ ao Paulo SP, Brazil. E-mail: yambar@ime.usp.br Abstract We suggest a model that describes a mutual dynamics of tectonic plates. It is a sort of stick-slip dynamics modeled by a Markov random process. The process defines the dynamics on a micro-level. A macro- level is obtained by a scaling limit which leads to a system of integro- differential equations which determines a kind of mean field systems. The conditions when the Gutenberg-Richter empirical law holds are presented at the mean field level. Those conditions are rather universal and independent of the features of the resistant forces. 1 Introduction. Tectonic plate construction of the earth lithosphere is generally accepted and recently well described (for example, see [1, 3]). Moreover, the tectonic plates of another planets of the solar system, such as Mars and Venus, are a 1 arXiv:1405.5925v2 [math.PR] 10 Sep 2014