Dynamics of Tectonic Plates

TL;DR

This paper introduces a Markov process-based model for tectonic plate dynamics, deriving integro-differential equations at the macro level and identifying universal conditions for the Gutenberg-Richter law.

Contribution

It presents a novel micro-to-macro modeling framework for tectonic activity using stochastic processes and mean field equations, independent of resistant force specifics.

Findings

Derivation of integro-differential equations for tectonic dynamics

Universal conditions for Gutenberg-Richter law at macro level

Model captures stick-slip behavior 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.