Vestnik KRAUNC. Fiz.-Mat. Nauki. 2022. vol. 40. no. 3. pp. 137–152. ISSN 2079-6641

Contents of this issue

Read Russian Version US Flag

MSC 60G22, 37M10, 60J80, 33E12

Research Article

Approximation of the waiting times distribution laws for foreshocks based on a fractional model of deformation activity

O. V. Sheremetyeva, B. M. Shevtsov

Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, 684034, Paratunka, Mirnaya str., 7, Russia
E-mail: sheremeteva@ikir.ru

The article discusses two algorithms for constructing sequences of foreshocks associated with the main event of a given energy, based on the statistical model of the deformation process previously developed by the authors. Catalog of the Kamchatka Branch of the Geophysical Survey of Russia Academy of Sciences for the period from 1 January 1962 to 31 December 2002 for the Kuril-Kamchatka island arc subduction zone is used for research (area 46◦–62◦ N, 158◦–174◦ E) [28]. The method of «epochs» is applied to the sequences of foreshocks to obtain an empirical cumulative distribution function (eCDF) P∗(τ) of relative frequency of foreshocks occurrence depending on the time before the mainshock. Based on the fractional model of the deformation process developed by the authors, the empirical cumulative distribution function P∗(τ) of foreshocks waiting time are approximated by the Mittag-Leffler function and the exponential function. It is shown that the accuracy of the approximation by the Mittag-Leffler function is higher than the exponential one. A comparative analysis of three parameters of approximating functions for the empirical distributions obtained from the results of two algorithms for constructing sequences of foreshocks is carried out. Based on the obtained values of the parameters of the Mittag-Leffler function, the deformation process in the considered region can be considered non-stationary and close to the standard Poisson process.

Key words: foreshocks, approximation, fractional Poisson process, Mittag-Leffler function, non-local effect, non-stationarity, statistical model, fractional model

DOI: 10.26117/2079-6641-2022-40-3-137-152

Original article submitted: 12.10.2022

Revision submitted: 29.10.2022

For citation. Sheremetyeva O. V., Shevtsov B. M. Approximation of the waiting times distribution laws for foreshocks based on a fractional model of deformation activity. Vestnik KRAUNC. Fiz.-mat. nauki. 2022, 40: 3, 137-152. DOI: 10.26117/2079-6641-2022-40-3-137-152

Competing interests. The authors declare that 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.

Funding. The work was carried out within the framework of the state assignment on the topic «Physical processes in the system of near space and geospheres under solar and lithospheric influences» (No. AAAA-A21-121011290003-0).

The content is published under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/deed.ru)

© Sheremetyeva O. V., Shevtsov B. M., 2022

References

  1. Mogi K. Active periods in the world’s shieft seismic belts, Tectonophysics, 1974, 22, 265-282.
  2. Kagan Y., Knopoff L. Earthquake risk prediction as a stochastic process, Phys. Earth Planet. Inter., 1977, 14, 97-108.
  3. Bak P., Christensen K., Danon L., Scanlon T. Unified scaling law for earthquakes, Phys. Rev. Lett., 2002, 88:17, 178501-1-178501-4.
  4. Keilis-Borok V. I., Soloviev A. A. Nonlinear Dynamics of the Lithosphere and Earthquake Prediction. Springer-Verlag, Berlin-Heidelberg, 2003, 337.
  5. Gutenberg B., Richter C. F. Seismicity of the Earth, Geol. Soc. Am. Bull., 1944, 34, 185-188.
  6. Utsu T., Ogata Y., Matsu’ura R. S. The centenary of the Omori formula for a decay law of aftershocks activity, J. Phys. Earth, 1995, 43, 1-33.
  7. Pisarenko V. F., Rodkin M. V. Declustering of Seismicity Flow: Statistical Analysis, Izv. Phys. Solid Earth, 2019, no. 55, pp. 733-745. DOI: 10.31857/S0002-33372019538-52
  8. Zaliapin I., Gabrielov A., Keilis-Borok V., Wong H. Clustering Analysis of Seismicity and Aftershock Identification, Phys. Rev. Lett., 2008, 101, 018501.
  9. Zaliapin I., Ben-Zion Y. Earthquake declustering using the nearest-neighbor approach in space-time-magnitude domain, Journal of Geophysical Research: Solid Earth, 2020, 125, 1-33. DOI: 10.1029/2018JB017120
  10. Manna S. S. Two-state model of self-organized criticality, J. Phys. A.: Math. Gen., 1991, 125, L363-L369. DOI: 10.1088/0305-4470/24/7/009
  11. Shebalin P. N. Chains of epicenters as an indicator of increasing radius of correlation of seismicity before strong earthquakes, Vulkanologiya i Seysmologiya [Volcanology and Seismology], 2005, 1, 3-15. (In Russian)
  12. Shebalin P. N. Methodology for forecasting strong earthquakes with a waiting period of less than a year, Algoritmy prognoza zemletryaseniy. Vychislitel’naya seysmologiya, 2006, 37, 5-180. (In Russian)
  13. Shevtsov B. M., Sagitova R. N. Statistical analysis of seismic processes on the basis of the diffusion approach, Doklady Earth Sciences, 2009, 426:1, 642-644. (In Russian)
  14. Shevtsov B. M., Sagitova R. N. A diffusion approach to the statistical analysis of Kamchatka Seismicity, Journal of Volcanology and Seismology, 2012. 6:2, 116-125.
  15. Shebalin P. N., Narteau C. Depth Dependent Stress Revealed by Aftershocks, Nat. Commun., 2017, 8, 1317-1318. DOI: 10.1038/s41467-017-01446-y
  16. Shebalin P. N., Narteau C., Baranov S. V. Earthquake Productivity Law, Geophys. J. Int., 2020, 222, 1264-1269. DOI: 10.1093/gji/ggaa252
  17. Baiesi M., Paczuski M. Complex networks of earthquakes and aftershocks, Nonlinear Processes in Geophysics, 2005, 12, 1-11.
  18. Davy P., Sornette A., Sornette D. Some consequences of a proposed fractal nature of continental faulting, Nature, 1990, no. 348, pp. 56-58.
  19. Kagan Y. Y., Knopoff L. Spatial distribution of earthquakes: The two-point correlation function, Geophys. J. Roy. Astr. Soc., 1980, 62, 303-320.
  20. Saichev A. I., Zaslavsky G. M. Fractional kinetic equations: solutions and applications, Chaos, 1997, 7:4, 753-764.
  21. Kagan Y.Y. Observational evidence for earthquakes as nonlinear dynamic process, Physica D., 1994, 77, 160-192.
  22. Metzler R., Klafter J. The random walk’s guide to anomalous diffusion: a fractional dynamics approach, Physics Reports, 2000, 339, 1-77.
  23. Carbone V., Sorriso-Valvo L., Harabaglia P., Guerra I. Unified scaling law for waiting times between seismic events, Europhys. Lett., 2005, 71:6, 1036-1042. DOI: 10.1209/epl/i2005-10185-0
  24. Turcotte D. Fractals and chaos in geology and geophysics. 2nd ed., Cambridge University Press: Cambridge, London, 1997, 221 pp.
  25. Shevtsov B. M., Sheremetyeva O. V. Fractional models of seismoacoustic and electromagnetic activity, E3S Web of Conferences: Solar-Terrestrial Relations and Physics of Earthquake Precursors, 2017, 20, 02013. DOI: 10.1051/e3sconf/20172002013
  26. Sheremetyeva O. V., Shevtsov B. M. Fractional Model of the Deformation Process, Fractal& Fract., 2022, 6, 372. DOI: 10.3390/fractalfract6070372
  27. Sheremetyeva O. V. Power-law patterns in sequences of statistically related events preceding to the main event, Vestnik KRAUNC. Fiz.-Mat. Nauki, 2020, vol. 33, no. 4, pp. 102-109. DOI: 10.26117/2079-6641-2020-33-4-102-109 (In Russian).
  28. The Geophysical Service of the Russian Academy of Sciences. Available online: http://www.gsras.ru/new/eng/catalog/
  29. Fedotov S. A. O zakonomernostyakh raspredeleniya sil’nykh zemletryaseniy Kamchatki, Kuril’skikh ostrovov i severo-vostochnoy Yaponii. Pr. IPE of the USSR Academy of Sciences [Tr. IFZAN SSSR]. Moscow, Nauka, 1968, 121-150. (In Russian).
  30. Dobrovolsky I. R., Zubkov S. I., Myachkin V. I. Estimation of the size of earthquake preparation zones, Pageoph., 1979, 117, 1025-1044.
  31. Popova A. V., Sheremetyeva O. V., Sagitova R. N. Analysis of the data sampling parameters Global CMT Catalog to build a statistical model of the seismic process by the example of the subduction zone of the Kuril-Kamchatka island arc, Vestnik KRAUNC. Fiz.-Mat. Nauki, 2012, 5(2), 23-32. DOI: 10.18454/2079-6641-2012-5-2-23-32 (In Russian).
  32. Davis J. C. Statistics and data analysis in geology. N-Y, J. Wiley & Sons. Inc., 1986, 267

Sheremetyeva Olga Vladimirovna – Ph.D. (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.), 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.

Read articleDownload article