Multifractal phase transitions: The origin of self-organized criticality in earthquakes

Abstract

Fractal and occasionally multifractal behaviour has been invoked to characterize (independently of their magnitude) the spatial distribution of seismic cpicenters, whereas more recently, the frequency distriibution of magnitudes (irrespective of their spatial locaition) 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 multifracital 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 this stochastic alternative to the classical (deterriiinistic) SOC. © European Geophysical Society 1994.