Nonlinear Dynamical Models for Earthquakes and Frictional Sliding

Abstract

This paper describes two new approaches to understanding the nonlinear dynamics of earthquakes. These models are motivated by the inability to observe in nature effects associated with classical growth mechanisms for shear fractures. Moreover, friction experiments in the laboratory display a rate dependence through a series of state variables whose physical interpretation is unclear. Of the two nonclassical approaches examined here, the first is a field-theoretic extension of the classical Griffith-Gibbs nucleation approach. The second is a lattice automaton in which each site is characterized by threshold force below which the site is stable. Above the threshold, the site is in a state of metastable equilibrium, and will decay to a more stable state over a characteristic relaxation time. Qualitatively, the decay of each site is analogous to local barrier penetration, as understood from nucleation problems involving a Landau “double well” potential. However, the mathematical isomorphism for this analogy has not yet been made rigorous.