Parisi and Frisch  and Halsey et al. 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.
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