Some Common Features Between a Spring-Block Self-Organized Critical Model, Stick–Slip Experiments with Sandpapers and Actual Seismicity

Abstract

In this article we stand out that actual seismicity, stick–slip experiments with sandpapers and a self-organized critical (SOC) model (Olami et al. Phys Rev Lett 68(8):1233–1247, 1992) have some dynamical features in common. All the shared dynamic characteristics between these systems stem from the presence of friction as dominant phenomenon. As a matter of fact, the distribution of the number of events in terms of their sizes in actual seismicity and stick–slip experiments with sandpapers, which have the form of power laws, are clues about the self-organized critical nature of both two processes. These laws are of the Gutenberg–Richter type ($$\log \dot{N} = a - bM$$). Another relevant property of the mentioned SOC model is the negative correlation between the $$b$$ value and the $$\gamma$$ elastic ratio of the springs linking the blocks of this SOC system. As this $$\gamma$$ elastic ratio can be related with an aging effect, it is possible to incorporate a dependence on time of some features of the SOC system. Thus, we can describe aging effects over possible SOC systems such as actual subduction zones and weathering of sandpapers. We can also propose the way to incorporate the relative velocity between plates in a SOC model. With these ideas we can qualitatively reproduce the so-called Ruff–Kanamori diagram for subduction zones around the world.