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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 1, issue 2/3
Nonlin. Processes Geophys., 1, 191-197, 1994
https://doi.org/10.5194/npg-1-191-1994
© Author(s) 1994. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

Special issue: Including papers presented at the EGS Richardson - AGU Chapman...

Nonlin. Processes Geophys., 1, 191-197, 1994
https://doi.org/10.5194/npg-1-191-1994
© Author(s) 1994. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  30 Sep 1994

30 Sep 1994

Mulifractal phase transitions: the origin of self-organized criticality in earthquakes

C. Hooge1, S. Lovejoy1, D. Schertzer2, S. Pecknold1, J.-F. Malouin1, and F. Schmitt2 C. Hooge et al.
  • 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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