Geodesic
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. Fiziko-matematičeskie nauki, Tome 46 (2024) no. 1, pp. 89-101 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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$^\circ$–62$^\circ$ N, 158$^\circ$–174$^\circ$ 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 $\nu$, 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 $\nu$, the state of the seismic process in the period under consideration is determined.
Mots-clés : fractional Poisson process
Keywords: quasi-stationary regime, quasi-homogeneous regime, seismic process, Gutenberg-Rihter law, first-passage time, Mittag-Leffler's function, approximation, statistical model, fractional model. 
@article{VKAM_2024_46_1_a4,
     author = {O. V. Sheremetyeva and B. M. Shevtsov},
     title = {Application of the hereditarian criticality model to the study of the characteristics of the seismic process of the {Kuril-Kamchatka} island {Arc} subduction zone},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {89--101},
     year = {2024},
     volume = {46},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2024_46_1_a4/}
}
TY  - JOUR
AU  - O. V. Sheremetyeva
AU  - B. M. Shevtsov
TI  - Application of the hereditarian criticality model to the study of the characteristics of the seismic process of the Kuril-Kamchatka island Arc subduction zone
JO  - Vestnik KRAUNC. Fiziko-matematičeskie nauki
PY  - 2024
SP  - 89
EP  - 101
VL  - 46
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VKAM_2024_46_1_a4/
LA  - ru
ID  - VKAM_2024_46_1_a4
ER  - 
%0 Journal Article
%A O. V. Sheremetyeva
%A B. M. Shevtsov
%T Application of the hereditarian criticality model to the study of the characteristics of the seismic process of the Kuril-Kamchatka island Arc subduction zone
%J Vestnik KRAUNC. Fiziko-matematičeskie nauki
%D 2024
%P 89-101
%V 46
%N 1
%U http://geodesic.mathdoc.fr/item/VKAM_2024_46_1_a4/
%G ru
%F VKAM_2024_46_1_a4
O. V. Sheremetyeva; B. M. Shevtsov. 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. Fiziko-matematičeskie nauki, Tome 46 (2024) no. 1, pp. 89-101. http://geodesic.mathdoc.fr/item/VKAM_2024_46_1_a4/

[1] Shevtsov B., Sheremetyeva O., “Fractional Criticality Theory and Its Application in Seismology”, Fractal Fract., 7:890 (2023), 1–12 DOI: 10.3390/fractalfract7120890

[2] Shevtsov B., Sheremetyeva O., “Power-Law Compound and Fractional Poisson Process in the Theory of Anomalous Phenomena”, Solar-Terrestrial Relations and Physics of Earthquake Precursors. STRPEP 2023, Springer Proceedings in Earth and Environmental Sciences, Springer, Cham, 2023, 266–275 DOI: 10.1007/978-3-031-50248-4_27 | DOI

[3] Janossy L., Renyi A., Aczel J., “On composed Poisson distributions”, I. Acta Math. Acad. Sci. Hungar., 1950, no. 1, 209–224 | DOI | MR | Zbl

[4] Adelson R. M., “Compound Poisson distributions”, Oper. Res. Quart., 17 (1966), 73–75 | DOI

[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, 291–307 DOI: 10.30757/ALEA.v13-12 | MR | Zbl

[6] Beghin L., Macci C., “Multivariate fractional Poisson processes and compound sums”, Adv. in Appl. Probab., 48:3 author (2016) DOI: 10.1017/apr.2016.23 | DOI | MR | Zbl

[7] Kataria K. K., Khandakar M., “Convoluted Fractional Poisson Process”, ALEA, Lat. Am. J. Probab. Math. Stat., 2021, no. 18, 1241–1265 DOI: 10.30757/ALEA.v18-46 | DOI | MR | Zbl

[8] Khandakar M., Kataria K. K., “Some Compound Fractional Poisson Processes”, Fractal Fract., 7:15 (2023) DOI: 10.3390/fractalfract7010015

[9] Gutenberg B., Richter C. F., “Frequency of Earthquakes in California”, Bulletin of the Seismological Society of America, 34 (1944), 185–188 | DOI

[10] Kanamori Hiroo, “The Energy Release in Great Earthquakes”, J. of Geophysical Research, 82:20 (1977), 2981–2987 | DOI

[11] The Geophysical Service of the Russian Academy of Sciences. Available online: http://www.gsras.ru/new/eng/catalog/

[12] Gmurman N. Sh., Teoriya veroyatnostei i matematicheskaya statistika: Ucheb. posobie dlya vuzov. – 9-e izd., ster, Vyssh. shk., M., 2003, 479 pp. | MR

[13] Kremer N. Sh., Teoriya veroyatnostei i matematicheskaya statistika: Uchebnik dlya vuzov. – 2-e izd., pererab. i dop., YuNITI-DANA, M., 2004, 573 pp.

[14] Shevtsov B., Sheremetyeva O., “Fractional models of seismoacoustic and electromagnetic activity”, E3S Web Conf., 20:02013 (2017), 1–8 DOI: 10.1051/e3sconf/20172002013

[15] Sheremetyeva O., Shevtsov B., “Fractional Model of the Deformation Process”, Fractal Fract., 6:372 (2022), 1–12 DOI: 10.3390/fractalfract6070372