Models of generation of power laws of distribution in the processes of seismicity and in formation of oil fields and ore deposits

Geophysical Center, Russian Academy of Sciences, Moscow, Russia

Abstract

[1]  A feature indicative of non-equilibrium dynamic system is a fulfillment of a power law of distribution. We consider a number of simple models of generation of power-law distributions in seismic processes and in the processes of mineral deposits formation. As for seismicity, it is shown that deterministic earthquake prediction does not appear to be possible within the used model, whereas a probabilistic prognosis is feasible. Thus it seems possible to reconcile the well-known theoretical concept of unpredictability of earthquakes with the actual existence of algorithms realizing a non-trivial prognosis of strong earthquakes. As for processes of mineral deposits formation, models are discussed that permit to explain a generation of a power-law distribution of a number of large hydrocarbon and ore deposits from the stock values. A new interpretation is proposed of relatively less (than could be expected from the extrapolation of a power distribution law) number of deposits with relatively smaller stock values.

Received 19 January 2008; accepted 27 April 2008; published 26 June 2008.

Keywords: Power laws, dynamic systems, earthquake prognosis, deposit size distribution.

Index Terms: 0545 Computational Geophysics: Modeling; 3245 Mathematical Geophysics: Probabilistic forecasting; 3265 Mathematical Geophysics: Stochastic processes; 3665 Mineralogy and Petrology: Mineral occurrences and deposits; 4415 Nonlinear Geophysics: Cascades; 4468 Nonlinear Geophysics: Probability distributions, heavy and fat-tailed; 7223 Seismology: Earthquake interaction, forecasting, and prediction.

Citation: Rodkin, M. V., A. D. Gvishiani, and L. M. Labuntsova (2008), Models of generation of power laws of distribution in the processes of seismicity and in formation of oil fields and ore deposits, Russ. J. Earth Sci., 10, ES5004, doi:10.2205/2007ES000282.