Russian Journal of Earth Sciences Russian Journal of Earth Sciences Russian Journal of Earth Sciences 1681-1208 46973 ОРИГИНАЛЬНЫЕ СТАТЬИ ORIGINAL ARTICLES ОРИГИНАЛЬНЫЕ СТАТЬИ Models of generation of power laws of distribution in the processes of seismicity and in formation of oil fields and ore deposits Models of generation of power laws of distribution in the processes of seismicity and in formation of oil fields and ore deposits Rodkin M V Rodkin M V Gvishiani A D Gvishiani A D Labuntsova L M Labuntsova L M Geophysical Center, Russian Academy of Sciences, Moscow, Russia ru Geophysical Center, Russian Academy of Sciences, Moscow, Russia ru Geophysical Center, Russian Academy of Sciences, Moscow, Russia ru Geophysical Center, Russian Academy of Sciences, Moscow, Russia ru Geophysical Center, Russian Academy of Sciences, Moscow, Russia ru Geophysical Center, Russian Academy of Sciences, Moscow, Russia ru 10 5 1 9 10 11 2021 https://rjes.ru/en/nauka/article/46973/view

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.

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.

 Power laws dynamic systems earthquake prognosis deposit size distribution. Power laws dynamic systems earthquake prognosis deposit size distribution.

Arnold, Priroda, no. 4, 1998. Arnold, Priroda, no. 4, 1998. Bak, Phys. Rev. Lett., v. 59, no. 4, 1987., doi: 10.1103/PhysRevLett.59.381 Bak, Phys. Rev. Lett., v. 59, no. 4, 1987., doi: 10.1103/PhysRevLett.59.381 Bak, Phys. Rev. A., v. 38, 1988., doi: 10.1103/PhysRevA.38.364 Bak, Phys. Rev. A., v. 38, 1988., doi: 10.1103/PhysRevA.38.364 Burshtein, Geologia i geofizika, v. 47, no. 9, 2006. Burshtein, Geologia i geofizika, v. 47, no. 9, 2006. Czechowski, Geophys. J. Int., v. 144, 2001., doi: 10.1046/j.1365-246x.2001.00318.x Czechowski, Geophys. J. Int., v. 144, 2001., doi: 10.1046/j.1365-246x.2001.00318.x Czechowski, Geophys. J. Int., v. 154, 2003., doi: 10.1046/j.1365-246X.2003.01994.x Czechowski, Geophys. J. Int., v. 154, 2003., doi: 10.1046/j.1365-246X.2003.01994.x Dubois, Dynamic Systems and Dynamic Classification Problems in Geophysical Applications, 1998. Dubois, Dynamic Systems and Dynamic Classification Problems in Geophysical Applications, 1998. Embrechts, Modelling Extremal Events, 1997. Embrechts, Modelling Extremal Events, 1997. Frolov, Carbonatite and Kimberlite, 2005. Frolov, Carbonatite and Kimberlite, 2005. Geller, Science, v. 275, 1997., doi: 10.1126/science.275.5306.1616 Geller, Science, v. 275, 1997., doi: 10.1126/science.275.5306.1616 Golitsyn, Vychislitelnaya Seismologia, v. 32, 2001. Golitsyn, Vychislitelnaya Seismologia, v. 32, 2001. Grigorian, DAN SSSR, v. 299, no. 6, 1988. Grigorian, DAN SSSR, v. 299, no. 6, 1988. Gvishiani, Artificial Intelligence and Dynamic Systems for Geophysical Applications, 2002. Gvishiani, Artificial Intelligence and Dynamic Systems for Geophysical Applications, 2002. Gvishiani, Dynamic Tasks of Classification and Convex Programming in Applications, 1992. Gvishiani, Dynamic Tasks of Classification and Convex Programming in Applications, 1992. Ito, J. Geophys. Res., v. 95, 1990., doi: 10.1029/JB095iB05p06853 Ito, J. Geophys. Res., v. 95, 1990., doi: 10.1029/JB095iB05p06853 Klimontovich, Statistical Theory of Open Systems, 1995. Klimontovich, Statistical Theory of Open Systems, 1995. Kontorovich, Geologia i Geofizika, no. 11, 1985. Kontorovich, Geologia i Geofizika, no. 11, 1985. Kosobokov, Vychislitelnaya Seismologia, v. 36, no. 1, 2005. Kosobokov, Vychislitelnaya Seismologia, v. 36, no. 1, 2005. Laverov, Large and Super-Large Mineral Deposits, Location Regularities and Conditions of Formation, 2004. Laverov, Large and Super-Large Mineral Deposits, Location Regularities and Conditions of Formation, 2004. Laverov, Largest Mineral Deposits of the World, 2006. Laverov, Largest Mineral Deposits of the World, 2006. Ma, Modern Theory of Critical Phenomena, 1980. Ma, Modern Theory of Critical Phenomena, 1980. Mandelbrot, The Fractal Geometry of Nature, 1982. Mandelbrot, The Fractal Geometry of Nature, 1982. Muslimov, Natural Science Series, v. 147, no. 1, 2005. Muslimov, Natural Science Series, v. 147, no. 1, 2005. Muslimov, Hydrocarbon Potential of the Basement of Young and Ancient Platforms, 2006. Muslimov, Hydrocarbon Potential of the Basement of Young and Ancient Platforms, 2006. Pisarenko, Vychislitelnaya Seismologia, issue 38, 2007. Pisarenko, Vychislitelnaya Seismologia, issue 38, 2007. Rodkin, Geoecologia, no. 4, 2001. Rodkin, Geoecologia, no. 4, 2001. Rodkin, Towards the Creation of the General Theory of Oil and Gas Presence in the Earth's Interior, Book 2, 2002. Rodkin, Towards the Creation of the General Theory of Oil and Gas Presence in the Earth's Interior, Book 2, 2002. Rodkin, Alternative to the Criticality Hypothesis? XXVIII General Assembly of ESC, CD-ROM compilation of full papers, 1-6 September, 2002. Rodkin, Alternative to the Criticality Hypothesis? XXVIII General Assembly of ESC, CD-ROM compilation of full papers, 1-6 September, 2002. Rodkin, The Genesis of Hydrocarbon Fluids and Deposits, 2006. Rodkin, The Genesis of Hydrocarbon Fluids and Deposits, 2006. Romaniuk, Large and Super-Large Useful Mineral Ore Deposits, Global Regularities of Location, vol. 1, 2007. Romaniuk, Large and Super-Large Useful Mineral Ore Deposits, Global Regularities of Location, vol. 1, 2007. Rundle, Pure Appl. Geophys., v. 157, 2000., doi: 10.1007/PL00001079 Rundle, Pure Appl. Geophys., v. 157, 2000., doi: 10.1007/PL00001079 Sadovskiy, Discrete Characteristics of Geophysical Environment, 1989. Sadovskiy, Discrete Characteristics of Geophysical Environment, 1989. Shebalin, Vychislitelnaya Seismologia, v. 37, 2006. Shebalin, Vychislitelnaya Seismologia, v. 37, 2006. Sobolev, Principles of Earthquake Prediction, 1993. Sobolev, Principles of Earthquake Prediction, 1993. Sobolev, Earthquake Physics and Precursors, 2003. Sobolev, Earthquake Physics and Precursors, 2003. Sornette, Critical Phenomena in Natural Sciences, 2000. Sornette, Critical Phenomena in Natural Sciences, 2000. Sornette, Geophys. Res. Lett., v. 30, no. 3, 2003., doi: 10.1029/2002GL015043 Sornette, Geophys. Res. Lett., v. 30, no. 3, 2003., doi: 10.1029/2002GL015043 Turcotte, Fractals and Chaos in Geology and Geophysics, 1997. Turcotte, Fractals and Chaos in Geology and Geophysics, 1997. Tyupkin, Fizika Zemli, no. 8, 2002. Tyupkin, Fizika Zemli, no. 8, 2002. Tyupkin, Tectonophysics, v. 431, no. 1--4, 2007., doi: 10.1016/j.tecto.2006.04.022 Tyupkin, Tectonophysics, v. 431, no. 1--4, 2007., doi: 10.1016/j.tecto.2006.04.022 Tyupkin, EPSL, v. 230, 2005., doi: 10.1016/j.epsl.2004.10.037 Tyupkin, EPSL, v. 230, 2005., doi: 10.1016/j.epsl.2004.10.037 Wyss, Science, v. 278, 1997., doi: 10.1126/science.278.5337.487 Wyss, Science, v. 278, 1997., doi: 10.1126/science.278.5337.487 Zaliapin, Computation Seismology, v. 33, 2002. Zaliapin, Computation Seismology, v. 33, 2002. Zavialov, Middle-Term Prediction of Earthquakes, Principles, Methods, Realization, 2006. Zavialov, Middle-Term Prediction of Earthquakes, Principles, Methods, Realization, 2006. Zotov, Transmagmatic Fluids in Magmatism and Ore Formation, 1989. Zotov, Transmagmatic Fluids in Magmatism and Ore Formation, 1989.