Self-organized criticality and universality in a nonconservative earthquake model

We make an extensive numerical study of a two-dimensional nonconservative model proposed by Olami, Feder, and Christensen to describe earthquake behavior [Phys. Rev. Lett. 68, 1244 (1992)]. By analyzing the distribution of earthquake sizes using a multiscaling method, we find evidence that the model is critical, with no characteristic length scale other than the system size, in agreement with previous results. However, in contrast to previous claims, we find a convergence to universal behavior as the system size increases, over a range of values of the dissipation parameter α. We also find that both “free” and “open” boundary conditions tend to the same result. Our analysis indicates that, as L increases, the behavior slowly converges toward a power law distribution of earthquake sizes $P\left(s\right)\mathrm{}\sim s^{-\tau }$ with an exponent $\tau \simeq \mathrm{1.8.}$ The universal value of τ we find numerically agrees quantitatively with the empirical value $(\tau =B+1)$ associated with the Gutenberg-Richter law.