POWER-LAWS AND APPLICATIONS TO EARTHQUAKE POPULATIONS

In this paper we study the rooted tree model applying the concepts of probability to obtain results of importance in understanding power-law distributions in pure populations and also in an ensemble of pure pop ulations. The well-known Gutenberg-Richter relation, which is an empir ical relation providing the number of earthquakes whose magnitude exce eds a given value, is shown to be an asymptotic form of survivor funct ion of earthquake magnitudes. The implications of this model are brief ly discussed in relation to other branches of sciences where power-law distributions are encountered.