**
Parisi and Frisch [1985] and Halsey et al.[1986] have introduced
the extended concept of scale invariance, called multifractality,
motivated by hydrodynamic turbulence and fractal growth processes
respectively. Use of the multifractal spectrum as a metric to
characterize complex systems is now routinely used in many fields
to describe hierarchical structures in space and time. However,
the origin of multifractality is rarely identified. This is
certainly true for earthquakes for which the possible existence of
multifractality is still debated.
**

**We have introduced a physically-based ``multifractal stress
activation'' model of earthquake interaction and triggering based
on two simple ingredients: (i) a seismic rupture results from
thermally activated processes giving an exponential dependence on
the local stress (Khurkov law); (ii) the stress relaxation has a
long memory. The interplay between these two physical processes
are shown to lead to a multifractal organization of seismicity in
the shape of a remarkable magnitude-dependence of the exponent p
of the Omori law for aftershocks, which we observe quantitatively
in real catalogs. The general mechanism for multifractality found
here has also been found in other fields, such as in financial
markets.
**

- G. Ouillon and D. Sornette
*Magnitude-Dependent Omori Law: Theory and Empirical Study,*J. Geophys. Res. (2005) (http://arXiv.org/abs/cond-mat/0407208) - D. Sornette and G. Ouillon
*Multifractal Scaling of Thermally-Activated Rupture Processes,*Phys. Rev. Lett. 94, 038501 (2005) (http://arXiv.org/abs/physics/0407053)

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