Scaling laws in earthquake occurrence: Disorder, viscosity, and finite size effects in Olami-Feder-Christensen models

The influence of the brittle-ductile transition zone on aftershock and foreshock occurrence

Aftershock occurrence is characterized by scaling behaviors with quite universal exponents. At the same time, deviations from universality have been proposed as a tool to discriminate aftershocks from foreshocks. Here we show that the change in rheological behavior of the crust, from velocity weakening to velocity strengthening, represents a viable mechanism to explain statistical features of both aftershocks and foreshocks. More precisely, we present a model of the seismic fault described as a velocity weakening elastic layer coupled to a velocity strengthening visco-elastic layer. We show that the statistical properties of aftershocks in instrumental catalogs are recovered at a quantitative level, quite independently of the value of model parameters. We also find that large earthquakes are often anticipated by a preparatory phase characterized by the occurrence of foreshocks. Their magnitude distribution is significantly flatter than the aftershock one, in agreement with recent results for forecasting tools based on foreshocks.

Criticality of the nonconservative earthquake model on random spatial networks

We study the nonconservative earthquake model on random spatial networks. The spatial networks are composed of sites on a two-dimensional (2D) plane which are connected locally. Differently from a regular lattice, the locations of sites are modeled in the way that sites are randomly placed on the plane. Using the same connectivity degree as a 2D lattice, however, the spatial network cannot exhibit critical earthquake behavior. Mimicking long range energy transfer, the connection radius is increased and the connectivity degree of the spatial network is increased. Then we show that the model exhibits self-organized criticality. The mechanism of the structural effect is presented. The spatial network includes many modules when connectivity degree is very small. The effect of modular structure on the avalanche dynamics is to limit the spreading of avalanches in the whole network. When the connectivity degree is larger, the long range energy transfer can overcome the effect of local modularity and criticality can be reached.