Evaluation of the self-similarity of earthquake epicenters field in the Baikal region

Object of research. The mathematical apparatus of the theory of fractals and the algorithms developed within its framework are used to assess the statistical self-similarity of the fields of epicenter earthquakes in the Baikal region.

Materials and methods. The solution is implemented on numerical models and at three hierarchical levels of the lithosphere of the region. A modified method for determining the fractal dimension is applied, when the scaling data are approximated uniformly for territories of various shapes and sizes, subject to the maximum coefficient of pair linear correlation of the function lnN = f(lnr). Numerical implementations of epicentral field models in the form of a “Koch snowflake” and “Sierpinski carpet” confirmed the advantage of the method in conditions of limited data arrays used.

Results. Seismicity reflects the process of fault formation in the lithosphere, and the use of the modified method allows one to obtain more accurate parameters of the state of the fault structure of the lithosphere from the field of epicenters of earthquakes in the Baikal region. The main influence on the assessment of the indicator is provided by two interrelated factors: the growth of instrumental data over time and the geometry of the distribution of earthquake epicenters over the territory. Using the maximum correlation coefficient to estimate the self-similarity of the field of epicenters of earthquakes in the Baikal region allows us to significantly refine the magnitude of the self-similarity index - the difference between the self-similarity index (D₀ ≈ 1.70) and the cell dimension (D₀ ≈ 1.58) significantly exceeds three standard deviations.

Findings. The applied method has a particular advantage with a small amount of initial data and can significantly improve the assessment of the self-similarity index in conditions of a limited duration of instrumental monitoring of earthquakes. In the absence of reliable data on the deep structure of the fault-block geomedium, the approach used and the results obtained contribute to the understanding of modern geodynamics and seismotectonics of the lithosphere of the Baikal region by analyzing the fault structure of the territories through the fractal dimension of the earthquake epicenter fields. In practical terms, information on monitoring the state of the fault structure of the lithosphere according to earthquake data can be used to characterize the seismic situation and the danger in industrial and civil construction areas.

1. Katalog zemletryasenii Pribaikal’ya [Catalogue of Baikal region earthquakes]. http://www.seis-bykl.ru/

2. Klyuchevskii A.V. (2007) Stresses and seismicity at the present stage of evolution of the Baikal rift zone lithosphere. Izv. Phys. Solid Earth, 43(12), 992-1004. DOI:10.1134/S1069351307120026

3. Klyuchevskii A.V., Dem’yanovich V.M., Bayar G. (2005) Large earthquakes in the Baikal region and Mongolia: Recurrence time and probability. Russ. Geol. Geophys, 46(7), 731-745.

4. Klyuchevskii A.V., Dem’yanovich V.M., Dzhurik V.I. (2009) Hierarchy of earthquakes in the Baikal rift system: implication for lithospheric stress. Russ. Geol. Geo-phys, 50(3), 206-213. D0I:10.1016/j.rgg.2008.06.023

5. Klyuchevskii A.V., Zuev F.L. (2006) Investigation of seismicity dynamics in the Baikal region. Dokl. Earth Sci., 409(5), 831-835. DOI:10.1134/S1028334X06050345

6. Klyuchevskii A.V., Zuev F.L. (2007) Structure of the epicenter field of earthquakes in the Baikal region. Dokl. Earth Sci., 415(2), 944-949. DOI:10.1134/S1028334X07060268

7. Klyuchevskii A.V., Zuev F.L. (2011) Fractal assessments of seismic process in the Baikal region lithosphere. Lito-sfera (1), 143-149. (In Russian)

8. Klyuchevskii A.V., Zuev F.L., Klyuchevskaya A.A. (2017) Patent na izobretenie № 2625627. Sposob opredeleniya pokazatelya samopodobiya polya epitsentrov zemle-tryasenii. Zayavka № 2016102935. Prioritet izobreteniya 28yanvarya 2016 g. Zaregistrirovano v Gosudarstvennom reestre izobretenii Rossiiskoi Federatsii 17 iyulya 2017 g. [Patent for invention No. 2625627. Method for determining the self-similarity index of the earthquake epicenter field. Application No. 2016102935. Priority of the invention on January 28, 2016. Registered in the State Register of Inventions of the Russian Federation on July 17, 2017]. (In Russian)

9. Mandelbrot B.B. (1982) The Fractal Geometry of Nature. W.H. Freeman and Co, N. Y., 468 pp.

10. Novaya global’naya tektonika. (1974) [The new global tectonics]. Moskow, Mir Publ., 472 p. (In Russian)

11. Sadovsky M.A. (1979) Natural lumpiness of rocks. Dokl. Akad. Nauk SSSR, 247(4), 829-831. (In Russian)

12. Sadovsky M.F., Bolkhovitinov L.G., Pisarenko V.F. (1987) Deformirovanie geofizicheskoi sredy i seismicheskii protsess [Deformation of the geophysical environment and seismic process]. Moskow, Nauka Publ., 101 p. (In Russian)

13. Solonenko A.V., Shteiman E.A. (1994) Self-similarity of seismicity in the Baikal rift. Dokl. Earth Sci., 337(2), 253-257.

14. Sadovsky M.A., Golubeva T.V., Pisarenko V.F., Shnir-man M.G. (1984) Characteristic dimensions of rock and hierarchical properties of seismicity. Izv. Phys. Solid Earth, 20, 87-95.

15. Scholz C.H. (2002) The mechanics of earthquakes and faulting. Cambridge: University Press, 470 p.

16. Sherman S.I., Gladkov A.S. (1999) Fractals in studies of faulting and seismicity in the Baikal rift zone. Tectono-physics, 308, 133-142.

17. Turcotte D.L., Malamud B.D. (2002) Earthquakes as a complex system. International Handbook of Earthquake and Engineering Seismology. (Eds. W.H.K. Lee, H. Kanamo-ri, P.C. Jennings, C. Kisslinger). Academic Press. Amsterdam, Boston, N. Y., Tokyo. P. A, 209-227.

18. Zuev F.L., Klyuchevskii A.V. (2015) Computation aspects of seismicity self-similarity characteristics. Vestn. Irk. Univ, 98(3), 71-75. (In Russian)