  We introduce a Self-affine Asperity Model (SAM) for the seismicity that
mimics the fault friction by means of two fractional Brownian profiles (fBm)
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 $\beta$ related to the roughness index of the profiles. Apart
from being analytically treatable, the model exhibits a non-trivial clustering
in the spatio-temporal 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 behaviour is not Self-Organized
but stems from the fractal geometry of the faults, which, on its turn, is
supposed to arise as a consequence of geological processes on very long time
scales with respect to the seismic dynamics. The explicit introduction of the
fault geometry, as an active element of this complex phenomenology, represents
the real novelty of our approach.
