Vestnik КRAUNC. Fiz.-Mat. nauki. 2024. vol. 46. no. 1. P. 89-102. ISSN 2079-6641

Research Article
Full text in Russian
MSC 60G22, 37M10, 33E12

Contents of this issue

Read Russian Version

Application of the Hereditarian Criticality Model to the Study of the Characteristics of the Seismic Process of the Kuril-Kamchatka Island Arc Subduction Zone

O. V. Sheremetyeva^\ast, B. M. Shevtsov^\ast

Institute of Cosmophysical Research and Radio Wave Propagation, FEB RAS, 684034 Kamchatka region, Elizovskiy district, Paratunka, Mirnaya str., 7, Russia

Abstract. The article presents the results of statistical processing of data from the earthquake catalog of the KBGSRAS for the period from 1 January 1962 to 31 December 2002 for the Kuril-Kamchatka island arc subduction zone (area 46◦–62◦ N, 158◦–174◦ E) within the framework of the earlier presented by the authors hereditarian criticality model. The compound power-law Poisson process in fractional time representation is considered as a model. The use of this model assumes quasi-stationary and quasi-homogeneous regime of the seismic process averaged over time and space during long-term observation. The study of the instability of this process over time is carried out using critical indices, which are determined by the numerical characteristics of the process and depend on the parameter b of the Gutenberg-Richter law. Based on the catalog data, the parameters of the seismic process were found by linear and nonlinear regression: the coefficient b and the exponent of the Caputo fractional derivative ν, by averaging over the magnitude interval in which the power law distribution of recurrence frequencies of events is performed. The significance of the obtained value of the Gutenberg-Richter law parameter b is estimated. Critical indices have been calculated, according to the values of which, and in comparison with the hereditarity parameter ν, the state of the seismic process in the period under consideration is determined.

Key words: fractional Poisson process, quasi-stationary regime, quasi-homogeneous regime, seismic process, Gutenberg-Rihter law, first-passage time, Mittag-Leffler’s function, approximation, statistical model, fractional model.

Received: 03.02.2024; Revised: 05.03.2024; Accepted: 06.03.2024; First online: 07.03.2024

For citation. Sheremetyeva O. V., Shevtsov B. M. Application of the hereditarian criticality model to the study of the characteristics of the seismic process of the Kuril-Kamchatka Island arc subduction zone. Vestnik KRAUNC. Fiz.-mat. nauki. 2024, 46: 1, 89-102. EDN: GYGBQZ.

Funding. The work was supported by IKIR FEB RAS State Task (subject registration No. 124012300245-2).

Competing interests. There are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.

^\astCorrespondence: E-mail:,

The content is published under the terms of the Creative Commons Attribution 4.0 International License

© Sheremetyeva O. V., Shevtsov B. M., 2024

© Institute of Cosmophysical Research and Radio Wave Propagation, 2024 (original layout, design, compilation)


  1. Shevtsov B., Sheremetyeva O. Fractional Criticality Theory and Its Application in Seismology, Fractal Fract., 2023, vol. 7, no. 890, pp. 1–12. DOI: 10.3390/fractalfract7120890
  2. Shevtsov B., Sheremetyeva O. Power-Law Compound and Fractional Poisson Process in the Theory of Anomalous Phenomena. In: Dmitriev A., Lichtenberger J., Mandrikova O., Nahayo E. (eds) Solar-Terrestrial Relations and Physics of Earthquake Precursors. STRPEP 2023. Springer Proceedings in Earth and Environmental Sciences. Springer, Cham, 2023, pp. 266–275. DOI: 10.1007/978-3-031-50248-4_27
  3. Janossy L., Renyi A., Aczel J. On composed Poisson distributions, I. Acta Math. Acad. Sci. Hungar., 1950, no. 1, pp. 209–224.
  4. Adelson R. M. Compound Poisson distributions, Oper. Res. Quart., 1966, vol. 17, pp. 73–75.
  5. Antonio Di Crescenzo, Barbara Martinucci, Alessandra Meoli A fractional counting process and its connection with the Poisson process, ALEA Lat. Am. J. Probab. Math. Stat., 2016, no. 13, pp. 291–307. DOI: 10.30757/ALEA.v13-12
  6. Beghin L., Macci C. Multivariate fractional Poisson processes and compound sums, Adv. in Appl. Probab., 2016, vol. 48, no. 3. DOI: 10.1017/apr.2016.23 author
  7. Kataria K. K., Khandakar M. Convoluted Fractional Poisson Process, ALEA, Lat. Am. J. Probab. Math. Stat., 2021, no. 18, pp. 1241–1265. DOI: 10.30757/ALEA.v18-46
  8. Khandakar M., Kataria K. K. Some Compound Fractional Poisson Processes, Fractal Fract., 2023, vol. 7, no. 15.
  9. Gutenberg B., Richter C. F. Frequency of Earthquakes in California, Bulletin of the Seismological Society of America, 1944, vol. 34, pp. 185–188.
  10. Kanamori Hiroo The Energy Release in Great Earthquakes, J. of Geophysical Research, 1977, vol. 82, no. 20, pp. 2981–2987.
  11. The Geophysical Service of the Russian Academy of Sciences. Available online:
  12. Gmurman N. Sh. Teoriya veroyatnostej i matematicheskaya statistika: Ucheb. posobie dlya vuzov. – 9-e izd., ster [Probability theory and mathematical statistics: Textbook for universities]. M.: Vy‘ssh. shk., 2003, 479pp. (In Russian).
  13. Kremer N. SH. Teoriya veroyatnostej i matematicheskaya statistika: Uchebnik dlya vuzov [Probability theory and mathematical statistics: Textbook for universities]. M.: YUNITIDANA, 2004, 573pp. (In Russian).
  14. Shevtsov B., Sheremetyeva O. Fractional models of seismoacoustic and electromagnetic activity, E3S Web Conf., 2017, vol. 20, no. 02013, pp. 1–8. DOI: 10.1051/e3sconf/20172002013
  15. Sheremetyeva O., Shevtsov B. Fractional Model of the Deformation Process, Fractal Fract., 2022, vol. 6, no. 372, pp. 1–12. DOI: 10.3390/fractalfract6070372

Information about authors

Sheremetyeva Olga Vladimirovna – PhD (Tech.), Research Scientist, Laboratory of Physical Process Modeling, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, Paratunka, Kamchatka, Russia, ORCID 0000-0001-9417-9731.

Shevtsov Boris Mikhaylovich – D. Sci. (Phys. & Math.), Professor, Chief Scientific Officer, Laboratory of Electromagnetic Radiation, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, Paratunka, Kamchatka, Russia, ORCID 0000-0003-0625-0361.