Scaling laws of seismic events - A model with fractal geometry

Most models of earthquakes attempt to reproduce the observed scaling laws o f seismic events: the Gutenberg-Richter frequency magnitude distribution, b ut not the Omori law for aftershocks and the multifractal distribution of h ypocenters location. Many of these models are based on the idea of Self-Org anized Criticality (SOC). These are dynamic systems which organize themselv es into a transitional state and can reproduce the Gutenberg-Richter distri bution, but generally do not reproduce the space-time distribution. Here, w e suggest a model based on a fractal geometry: the two sides of a fault are modeled by means of a fractal surface. As a first step, one of them is sli pped of a random amount with periodic boundary conditions, then new contact points between the surfaces are found. The area surrounded by these points is assumed to be proportional to the area of the earthquake. The size dist ribution of events is in good agreement with the observed Gutenberg-Richter law and the local fluctuations of the b value are explained in terms of va riations of the fractal dimension of the surface. Also the multifractal dis tribution of earthquakes in space is well-reproduced with global properties not depending on the fractal dimension of the surface. However, we are not able to obtain something similar to the Omori law simply because we do not control the time evolution of the model.