SCALING PROPERTIES OF A MODEL FOR RUPTURES IN AN ELASTIC MEDIUM

We generalize a model proposed by Xu et al for ruptures in an elastic medium subject to shear stress. This model is applied to the study of earthquakes. We restrict ourselves to one-dimensional discretizations of the region on which we focus and consider the effects of disorder, degree of stress release and degree of stress nonconservation (dissipa tion). The one-dimensional systems display power-law cumulative size-f requency distributions over a certain range of size. The power laws cu t off due to finite-size effects, i.e. the effects of the finite size of the system and the finite size of the basic unit of discretization. In addition, in the absence of disorder, there is a crossover region at small sizes and its origin is explained. The scaling properties in the absence of dissipation are characterized by exponents tau and nu a s well as by a function f dependent on the parameters of the model. ta u is associated with the cumulative size-frequency distribution in the thermodynamic limit, nu with the finite size of the system and f with the finite size of the basic unit of discretization. When stress diss ipation is introduced into the model, a characteristic earthquake size smaller than system size appears, in contrast with the case in which stress dissipation is absent.