The Two-dimensional Nonlinear Burridge-Knopoff Model of Earthquakes

We present a two-dimensional spring-block model of earthquakes with the full nonlinear equations for the forces in terms of displacements. Correspondence of our linearized version to earlier models reveals in them inherently asymmetric elastic properties. Our model generalizes those models and allows an investigation of the effects of internal strains and vectorial forces. The former is found to be relevant to critical properties such as that described by the Gutenberg-Richter law, but the latter as well as nonlinearities up to second order in displacements are irrelevant.