Instability of a two‐dimensional dynamic spring‐slider model of an earthquake fault

We extend the 1‐D dynamic spring‐slider model proposed by Burridge & Knopoff (1967) to a 2‐D dynamic spring‐slider model in order to approximate fault dynamics. The model is mathematically described by a set of discrete equations. Some intrinsic properties of the model are studied in detail. When neither the coupling between a slider and the moving plate nor the friction force exists, the partial differential equations equivalent to the discrete ones are essentially the regular, linear wave equations. We carried out an analytical study by adding perturbations, with constant displacements, to a special solution of the related partial differential equations, with homogeneous friction. The results show that, when small perturbations are introduced into the system, the perturbations are amplified; that is, the system is unstable.