Russian Federation
Schmidt institute of physics of the Earth of the RAS
Moscow, Russian Federation
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
1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. Friedlander, S. K. (2000) , Smoke, Dust and Haze: Fundamentals of Aerosol Dynamics (2nd Edition), Oxford University Press, Oxford.
7. 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.
8. 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.
9. 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.
10. Julanov, Yu. V., A. A. Lushnikov, I. A. Nevskii (1983) , Statistics of particle counting in highly concentrated disperse systems, DAN SSSR, 270, p. 1140.
11. 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.
12. 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.
13. 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.
14. 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.
15. 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.
16. 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.
17. Mazo, R. M. (2002) , Brownian Motion: Fluctuations, Dynamics, and Applications, Oxford University Press, Oxford.
18. McKibben, M. A. (2011) , Discovering Evolution Equations with Applications: Volume 2. Stochastic Equations, 463 pp., Chapman & Hall/CRC, New York.
19. 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.
20. Pruppacher, H. R., J. D. Klett (2006) , Microphysics of clouds and precipitation, Kluwer Academic, New York.
21. Schmeltzer, J., G. R'opke, R. Mahnke (1999) , Aggregation Phenomena in Complex Systems, Wiley-VCH, Weinbeim.
22. 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.
23. Seinfeld, J. H., S. N. Pandis (1998) , Atmospheric Chemistry and Physics, John Wiley & Sons, Inc., New York.
24. Van Kampen, N. G. (2007) , Stochastic Processes in Physics and Chemistry, 464 pp., Elsevier, Amsterdam.
25. Zagaynov, V. A., A. A. Lushnikov, O. N. Nikitin, et al. (1989) , Background aerosol over lake of Baikal, DAN SSSR, 308, p. 1087.