RUSSIAN JOURNAL OF EARTH SCIENCES VOL. 10, ES5004, doi:10.2205/2007ES000282, 2008

Conclusion

[38]  Several simple statistical variants of origin of empirical power distribution typical of earthquake statistics (Gutenberg-Richter law) and of the distribution of a number of mineral deposits in relation to the amount of reserves are examined. To interpret the origin of a power-law distribution in seismology and in the statistics of hydrocarbon deposits the model of generation of such distribution in result of a number of processes of avalanche-like relaxation of meta-stable states is suggested. To simulate processes of ore deposit formation we consider as a basic variant a model based on the assumption of a power-law distribution of intensity of fluid and magmatic flows feeding the deposits.

[39]  For the case of examination of earthquakes statistics, it is shown that the effects commonly treated as precursor anomalies may occur in a model with independent events; thus it can occur in the case when precursor effects strictly speaking are impossible. The appearance of such anomalies is caused by correlation of probability of strong event occurrence with change in the regime of a weak seismicity. Treating such features as precursor anomalies is not correct because such anomalies occur not only before strong events but also during some time after them.

[40]  The obtained result allows us to propose a variant bringing to agreement the two major alternative approaches to earthquake prognosis problem. According to the first of them [Geller et al., 1997; Wyss et al., 1997; and others], seismicity is believed to be unpredictable in principle. According to the second [Kosobokov, 2005; Shebalin, 2006; Sobolev, 1993; Sobolev and Ponomarev, 2003; Zavialov, 2006; and others], a definite prognostic behavior in a number of effects that allow to accomplish a statistically non-trivial prognosis of strong earthquakes does take place. The random character of seismic process and even the absence of earthquake preparation process as well as the possibility of obtaining of a non-trivial statistical prognosis of strong earthquakes are retained in the described-above model. Note that this approach is a further development of concepts of limited possibilities of the theory and practice of earthquake prediction. [Dubois and Gvishiani, 1998; Gvishiani and Dubois, 2002; Gvishiani and Gurvich, 1992; and others].

[41]  As for the problem of explaining of empirically observed distribution of deposits number in relation to their stock values the model is proposed that explains the fulfillment of the power law distribution of a number of large deposits both at the stage of formation and at the stage of degradation of deposits. Besides, this model leads to a conclusion that the number of deposits with small volume of reserves is considerably less than it follows from an extrapolation of the power law distribution. This conclusion is in a good agreement with empirical results. This deviation is commonly treated as a consequence of relatively smaller probability of revealing of smaller deposits. From the used model it may be assumed that the actual number of medium-size and small earthquakes is relatively smaller as well. Note that this conclusion appears to be significant for the strategy of geological prospecting in old and new mining areas.


RJES

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.

Copyright 2008 by the Russian Journal of Earth Sciences

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