Applications of fractal geometry and renormalization group to the Italian seismic activity

In the past two decades, Fractal Geometry developed as a new and powerful mathematical tool able to model a wide class of complex natural systems. Particularly, when joined with renormalization techniques, Fractal Geometry represents the natural and synthetic way to characterize the so-called self-organized processes, emphasizing their universality and the scaling laws arising at the critical points. Nevertheless, the choice of the most relevant seismic parameter is often not trivial, as in the case of Italian seismicity, where magnitude must be replaced by the seismic energy release, in order to obtain unambiguous multifractal spectra. Moreover, to model the stick-slip phenomenon, it is useful to consider the contact mechanics of self-affine rough faults. A numerical model provides the exact distribution of normal and tangential forces at any rough surface. The Renormalization Group technique represents the theoretical framework able to explain the multifractal distribution of contact micro-forces obtained numerically. As a consequence, the experimentally detected multifractal release of seismic energy derives directly from the mechanical work of a multifractal distribution of forces during the slip event.