Mathematical and computer modeling of seismic processes based on a soliton approach
DOI:
https://doi.org/10.15587/2312-8372.2015.41151Keywords:
soliton, solitary wave, earthquake, dynamic systemAbstract
In this paper we consider a mathematical model of seismic process, taking into account the role of solitary waves as a shocks "trigger". Methods of forecasting are based on evaluating trajectories of individual solitons and clarification of shocks probability. We allocate among the entire set of shocks individual subsets caused by the same soliton and construct of hypothetical trajectory of the solitons. The probability of a shock can be verified taking into account the soliton components of seismic process. The information system for the analysis of soliton component seismic processes was developed. We show the effectiveness of soliton approach and the possibility of its application to the analysis of seismic processes in several regions of the Earth by using this information system.
References
- Kozák, J., Šílený, J. (1985, January). Seismic events with non-shear component: I. Shallow earthquakes with a possible tensile source component. Pure and Applied Geophysics PAGEOPH, Vol. 123, № 1, 1–15. doi:10.1007/bf00877045
- Ogata, Y. (1988, March). Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes. Journal of the American Statistical Association, Vol. 83, № 401, 9–27. doi:10.1080/01621459.1988.10478560
- Utsu, T. (1999). Representation and Analysis of the Earthquake Size Distribution: A Historical Review and Some New Approaches. Seismicity Patterns, their Statistical Significance and Physical Meaning. Springer Science + Business Media, 509–535. doi:10.1007/978-3-0348-8677-2_15
- Utsu, T., Seki, A. (1954-1955). A Relation between the Area of After-shock Region and the Energy of Main-shock. Journal of the Seismological Society of Japan, 2nd ser., Vol. 7, No. 4, 233-240.
- Lomnitz, C., Nava, F. A. (1983). The Predictive Value of Seismic Gaps. Bulletin of the Seismological Society of America, Vol. 73, № 6A, 1815-1824.
- Vere-Jones, D., Ben-Zion, Y., Zúñiga, R. (2005). Statistical Seismology. Pageoph Topical Volumes. Springer Science + Business Media, 1023–1026.doi:10.1007/3-7643-7375-x_1
- Vere-Jones, D. (2008, March 1). Some models and procedures for space-time point processes. Environmental and Ecological Statistics, Vol. 16, № 2, 173–195. doi:10.1007/s10651-007-0086-0
- Kendall, D. G. (1949). Stochastic Processes and Population Growth. Journal of the Royal Statistical Society. Series B (Methodological), Vol. 11, No. 2, 230-282.
- Hawkes, A. G., Adamopoulos, L. (1973). Cluster Models for Earthquakes–Regional Comparisons. Bulletin of the International Statistical Institute, 45, Book 3, 454-461.
- Akaike, H., Ozaki, T., Ishiguro, M., Ogata, Y., Kitagawa, G., Tamura, Y. H., Arahata, E., Katsura, K., Tamura, Y. (1984). Time Series Analysis and Control Program Package. TIMSAC-84. Tokyo: The Institute of Statistical Mathematics. Available: http://rpackages.ianhowson.com/cran/timsac/man/timsac-package.html
- Turbal, Yu. V. (2013). Matematychna model seismichnoho protsesu, shcho vrakhovuie povilni vidokremleni khvyli deformatsii. Visnyk Kremenchutskoho natsionalnoho universytetu imeni Mykhaila Ostrohradskoho, 4 (81), 88-93.
- Bomba, A. Ya., Turbal, Yu. V. (2014). Metody analiza dannyh i prognozirovanie traektorii uedinennyh voln. Problemy upravleniia i informatiki, 3, 12-22.
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Copyright (c) 2016 Андрій Ярославович Бомба, Юрій Васильович Турбал, Маріанна Юріївна Турбал, Олена Віталіївна Радовенюк
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