Russian Journal of Earth Sciences Russian Journal of Earth Sciences Russian Journal of Earth Sciences 1681-1208 46500 10.2205/2019ES000697 ОРИГИНАЛЬНЫЕ СТАТЬИ ORIGINAL ARTICLES ОРИГИНАЛЬНЫЕ СТАТЬИ An introduction to geophysical distributions An introduction to geophysical distributions Лушников Алексей Алексеевич Lushnikov Alexey Alexeevich rjes@wdcb.ru

доктор физико-математических наук;

doctor of physical and mathematical sciences;

 https://orcid.org/0000-0002-3171-5768 Богоутдинов Шамиль Рафекович Bogoutdinov Shamil Rafekovich shm@gcras.ru Geophysical Center of the Russian Academy of Sciences (GC RAS) ru Geophysical Center of the Russian Academy of Sciences (GC RAS) ru Геофизический центр РАН Россия Geophysical Center RAS Russian Federation Институт физики Земли им. О. Ю. Шмидта РАН Россия Schmidt institute of physics of the Earth of the RAS Russian Federation 19 6 29 10 2021 https://rjes.ru/en/nauka/article/46500/view

This paper reviews the methods of treating the results of geophysical observations typically met in various geophysical studies. The main emphasize is given to the sets of data on the phenomena undergone the actions of random factors. These data are normally described by the distributions depending on the nature of the processes. Among them the magnitude of earthquakes, the diameters of moon craters, the intensity of solar flares, population of cities, size of aerosol and hydrosol particles, eddies in turbulent water, the strengths of tornadoes and hurricanes and many other things. Irrespective of the causes for their randomness these manifestations of planetary activity are characterized by few distribution functions like Gauss distribution, lognormal distribution, gamma distribution, and algebraic distributions. Each of these distributions contains empirical parameters the values of which depend on the concrete nature of the process. Especially interesting are so called "thick" distributions with the algebraic tails. Possible parametrizations of these distributions are discussed.

This paper reviews the methods of treating the results of geophysical observations typically met in various geophysical studies. The main emphasize is given to the sets of data on the phenomena undergone the actions of random factors. These data are normally described by the distributions depending on the nature of the processes. Among them the magnitude of earthquakes, the diameters of moon craters, the intensity of solar flares, population of cities, size of aerosol and hydrosol particles, eddies in turbulent water, the strengths of tornadoes and hurricanes and many other things. Irrespective of the causes for their randomness these manifestations of planetary activity are characterized by few distribution functions like Gauss distribution, lognormal distribution, gamma distribution, and algebraic distributions. Each of these distributions contains empirical parameters the values of which depend on the concrete nature of the process. Especially interesting are so called "thick" distributions with the algebraic tails. Possible parametrizations of these distributions are discussed.

 Random geophysical processes distributions master equation parametrization of distributions Random geophysical processes distributions master equation parametrization of distributions This work was carried out within the project of the fundamental research program of RAS Presidium No. 2 with financial support by the Ministry of Science and Higher Education of the Russian Federation.

Adams, P. J., J. H. Seinfeld (2002) , Predicting global aerosol size distribution in general circulation models, J. Geophys. Res., 107, no. D19, p. 4370, https://doi.org/10.1029/2001JD001010. Adams, P. J., J. H. Seinfeld (2002) , Predicting global aerosol size distribution in general circulation models, J. Geophys. Res., 107, no. D19, p. 4370, https://doi.org/10.1029/2001JD001010. Bailey, N. T. J. (1964) , The Elements of Stochastic Processes, With Applications to Natural Sciences, 130 pp., John Wiley & Sons, Inc., New York-London-Sydney. Bailey, N. T. J. (1964) , The Elements of Stochastic Processes, With Applications to Natural Sciences, 130 pp., John Wiley & Sons, Inc., New York-London-Sydney. Barrett, J. C., C. F. Clement (1991) , Aerosol concentrations from a burst of nucleation, J. Aerosol Sci., 22, p. 327-335, https://doi.org/10.1016/S0021-8502(05)80010-2. Barrett, J. C., C. F. Clement (1991) , Aerosol concentrations from a burst of nucleation, J. Aerosol Sci., 22, p. 327-335, https://doi.org/10.1016/S0021-8502(05)80010-2. Ding, R., J. Li (2007) , Nonlinear finite-time Lyapunov exponent and predictability, Phys. Lett. A, 364, p. 396-400, https://doi.org/10.1016/j.physleta.2006.11.094. Ding, R., J. Li (2007) , Nonlinear finite-time Lyapunov exponent and predictability, Phys. Lett. A, 364, p. 396-400, https://doi.org/10.1016/j.physleta.2006.11.094. Eckmann, J.-P., D. Ruelle (1985) , Ergodic theory of chaos and strange attractors, Rev. Modern Phys., 57, p. 617-656, https://doi.org/10.1103/RevModPhys.57.617. Eckmann, J.-P., D. Ruelle (1985) , Ergodic theory of chaos and strange attractors, Rev. Modern Phys., 57, p. 617-656, https://doi.org/10.1103/RevModPhys.57.617. Friedlander, S. K. (2000) , Smoke, Dust and Haze: Fundamentals of Aerosol Dynamics (2nd Edition), Oxford University Press, Oxford. Friedlander, S. K. (2000) , Smoke, Dust and Haze: Fundamentals of Aerosol Dynamics (2nd Edition), Oxford University Press, Oxford. Golubkov, G. V., M. G. Golubkov, G. K. Ivanov (2010) , Rydberg states of atoms and molecules in a field of neutral particles, The Atmosphere and Ionosphere: Dynamics, Processes and Monitoring, Bychkov V. L., Golubkov G. V. and Nikitin A. I. (eds.), p. 1-67, Springer, New York, https://doi.org/10.1007/978-90-481-3212-6_1. Golubkov, G. V., M. G. Golubkov, G. K. Ivanov (2010) , Rydberg states of atoms and molecules in a field of neutral particles, The Atmosphere and Ionosphere: Dynamics, Processes and Monitoring, Bychkov V. L., Golubkov G. V. and Nikitin A. I. (eds.), p. 1-67, Springer, New York, https://doi.org/10.1007/978-90-481-3212-6_1. Golubkov, G. V., M. G. Golubkov, M. I. Manzhelii, et al. (2014) , Optical quantum properties of GPS signal propagation medium - D layer, The Atmosphere and Ionosphere: Elementary Processes, Monitoring, and Ball Lightning, Bychkov V. L., Golubkov G. V. and Nikitin A. I. (eds.), p. 1-68, Springer, New York. Golubkov, G. V., M. G. Golubkov, M. I. Manzhelii, et al. (2014) , Optical quantum properties of GPS signal propagation medium - D layer, The Atmosphere and Ionosphere: Elementary Processes, Monitoring, and Ball Lightning, Bychkov V. L., Golubkov G. V. and Nikitin A. I. (eds.), p. 1-68, Springer, New York. Janson, R., K. Rozman, A. Karlsson, H.-C. Hansson (2001) , Biogenic emission and gaseous precursor to forest aerosols, Tellus, 53B, p. 423-440, https://doi.org/10.3402/tellusb.v53i4.16615. Janson, R., K. Rozman, A. Karlsson, H.-C. Hansson (2001) , Biogenic emission and gaseous precursor to forest aerosols, Tellus, 53B, p. 423-440, https://doi.org/10.3402/tellusb.v53i4.16615. Julanov, Yu. V., A. A. Lushnikov, I. A. Nevskii (1983) , Statistics of particle counting in highly concentrated disperse systems, DAN SSSR, 270, p. 1140. Julanov, Yu. V., A. A. Lushnikov, I. A. Nevskii (1983) , Statistics of particle counting in highly concentrated disperse systems, DAN SSSR, 270, p. 1140. Julanov, Yu. V., A. A. Lushnikov, I. A. Nevskii (1984) , Statistics of Multiple Counting in Aerosol Counters, J. Aerosol Sci., 15, p. 69-79, https://doi.org/10.1016/0021-8502(84)90057-0. Julanov, Yu. V., A. A. Lushnikov, I. A. Nevskii (1984) , Statistics of Multiple Counting in Aerosol Counters, J. Aerosol Sci., 15, p. 69-79, https://doi.org/10.1016/0021-8502(84)90057-0. Julanov, Yu. V., A. A. Lushnikov, I. A. Nevskii (1986) , Statistics of Multiple Counting II. Concentration Counters, J. Aerosol Sci., 17, p. 87-93, https://doi.org/10.1016/0021-8502(86)90010-8. Julanov, Yu. V., A. A. Lushnikov, I. A. Nevskii (1986) , Statistics of Multiple Counting II. Concentration Counters, J. Aerosol Sci., 17, p. 87-93, https://doi.org/10.1016/0021-8502(86)90010-8. Klyatskin, V. I. (2005) , Stochastic Equations through the Eye of the Physicist: Basic Concepts, Exact Results and Asymptotic Approximations, 556 pp., Elsevier, Amsterdam, https://doi.org/10.1016/B978-0-444-51797-5.X5000-X. Klyatskin, V. I. (2005) , Stochastic Equations through the Eye of the Physicist: Basic Concepts, Exact Results and Asymptotic Approximations, 556 pp., Elsevier, Amsterdam, https://doi.org/10.1016/B978-0-444-51797-5.X5000-X. Leyvraz, F. (2003) , Scaling theory and exactly solved models in the kinetics of irreversible aggregation, Phys. Rep., 383, p. 95-212, https://doi.org/10.1016/S0370-1573(03)00241-2. Leyvraz, F. (2003) , Scaling theory and exactly solved models in the kinetics of irreversible aggregation, Phys. Rep., 383, p. 95-212, https://doi.org/10.1016/S0370-1573(03)00241-2. Lushnikov, A. A., J. S. Bhatt, I. J. Ford (2003) , Stochastic approach to chemical kinetics in ultrafine aerosols, J. Aerosol Sci., 34, p. 1117-1133, https://doi.org/10.1016/S0021-8502(03)00082-X. Lushnikov, A. A., J. S. Bhatt, I. J. Ford (2003) , Stochastic approach to chemical kinetics in ultrafine aerosols, J. Aerosol Sci., 34, p. 1117-1133, https://doi.org/10.1016/S0021-8502(03)00082-X. Lushnikov, A. A., A. S. Kagan (2016) , A linear model of population dynamics, Int. J. Mod. Phys. B, 30, no. 15, p. 1541008, https://doi.org/10.1142/S0217979215410088. Lushnikov, A. A., A. S. Kagan (2016) , A linear model of population dynamics, Int. J. Mod. Phys. B, 30, no. 15, p. 1541008, https://doi.org/10.1142/S0217979215410088. Mazo, R. M. (2002) , Brownian Motion: Fluctuations, Dynamics, and Applications, Oxford University Press, Oxford. Mazo, R. M. (2002) , Brownian Motion: Fluctuations, Dynamics, and Applications, Oxford University Press, Oxford. McKibben, M. A. (2011) , Discovering Evolution Equations with Applications: Volume 2. Stochastic Equations, 463 pp., Chapman & Hall/CRC, New York. McKibben, M. A. (2011) , Discovering Evolution Equations with Applications: Volume 2. Stochastic Equations, 463 pp., Chapman & Hall/CRC, New York. Michael, A. J. (2012) , Fundamental questions of earthquake statistics, source behavior, and the estimation of earthquake probabilities from possible foreshocks, Bulletin of the Seismological Society of America, 102, no. 6, p. 2547, https://doi.org/10.1785/0120090184. Michael, A. J. (2012) , Fundamental questions of earthquake statistics, source behavior, and the estimation of earthquake probabilities from possible foreshocks, Bulletin of the Seismological Society of America, 102, no. 6, p. 2547, https://doi.org/10.1785/0120090184. Pruppacher, H. R., J. D. Klett (2006) , Microphysics of clouds and precipitation, Kluwer Academic, New York. Pruppacher, H. R., J. D. Klett (2006) , Microphysics of clouds and precipitation, Kluwer Academic, New York. Schmeltzer, J., G. R'opke, R. Mahnke (1999) , Aggregation Phenomena in Complex Systems, Wiley-VCH, Weinbeim. Schmeltzer, J., G. R'opke, R. Mahnke (1999) , Aggregation Phenomena in Complex Systems, Wiley-VCH, Weinbeim. Seinfeld, J. H. (2008) , Climate Change, Review of Chemical Engineering, 24, no. 1, p. 1-65, https://doi.org/10.1515/REVCE.2008.24.1.1. Seinfeld, J. H. (2008) , Climate Change, Review of Chemical Engineering, 24, no. 1, p. 1-65, https://doi.org/10.1515/REVCE.2008.24.1.1. Seinfeld, J. H., S. N. Pandis (1998) , Atmospheric Chemistry and Physics, John Wiley & Sons, Inc., New York. Seinfeld, J. H., S. N. Pandis (1998) , Atmospheric Chemistry and Physics, John Wiley & Sons, Inc., New York. Van Kampen, N. G. (2007) , Stochastic Processes in Physics and Chemistry, 464 pp., Elsevier, Amsterdam. Van Kampen, N. G. (2007) , Stochastic Processes in Physics and Chemistry, 464 pp., Elsevier, Amsterdam. Zagaynov, V. A., A. A. Lushnikov, O. N. Nikitin, et al. (1989) , Background aerosol over lake of Baikal, DAN SSSR, 308, p. 1087. Zagaynov, V. A., A. A. Lushnikov, O. N. Nikitin, et al. (1989) , Background aerosol over lake of Baikal, DAN SSSR, 308, p. 1087.