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Mulifractal phase transitions: the origin of self-organized criticality in earthquakes
1Department of Physics, McGill University, 3600 University Street, Montréal (Québec), H3A 2T8, Canada
2Laboratoire de Météorologie Dynamique (CNRS), Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France
Abstract. Fractal and occasionally multifractal behaviour has been invoked to characterize (independently of their magnitude) the spatial distribution of seismic epicenters, whereas more recently, the frequency distribution of magnitudes (irrespective of their spatial location) has been considered as a manifestation of Self-Organized Criticality (SOC). In this paper we relate these two aspects on rather general grounds, (i.e. in a model independent way), and further show that this involves a non-classical SOC. We consider the multifractal characteristics of the projection of the space-time seismic process onto the horizontal plane whose values are defined by the measured ground displacements, we show that it satisfies the requirements for a first order multifractal phase transition and by implication for a non-classical SOC. We emphasize the important consequences of the stochastic alternative to the classical (deterministic) SOC.
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Citation: Hooge, C., Lovejoy, S., Schertzer, D., Pecknold, S., Malouin, J.-F., and Schmitt, F.: Mulifractal phase transitions: the origin of self-organized criticality in earthquakes, Nonlin. Processes Geophys., 1, 191-197, 1994. Bibtex EndNote Reference Manager
