Earthquake statistics and fractal faults

We introduce a self-affine asperity model (SAM) for the seismicity that mimics the fault friction by means of two fractional Brownian profiles that slide one over the other. An earthquake occurs when there is an overlap of the two profiles representing the two fault faces and its energy is assumed proportional to the overlap surface. The SAM exhibits the Gutenberg-Richter law with an exponent \ensuremath{\beta} related to the roughness index of the profiles. Apart from being analytically treatable, the model exhibits a nontrivial clustering in the spatiotemporal distribution of epicenters that strongly resembles the experimentally observed one. A generalized and more realistic version of the model exhibits the Omori scaling for the distribution of the aftershocks. The SAM lies in a different perspective with respect to usual models for seismicity. In this case, in fact, the critical behavior is not self-organized but stems from the fractal geometry of the faults, which, in its turn, is supposed to arise as a consequence of geological processes on very long time scales with respect to the seismic dynamics. Our approach is distinguished by the explicit introduction of the fault geometry as an active element of this complex phenomenology.