Fractal analysis of the seismicity of the territory of Azerbaijan
Keywords:Azerbaijan’s seismicity, Gutenberg—Richter magnitude-frequency relationship, b-value, fractal dimension, earthquake distribution
The article examines the distribution of earthquakes occurred in Azerbaijan and the adjacent territories during the instrumental period (1902¾2018) by investigating the self-similarity and fractal properties of the seismicity of the region. Most parts of the territory of Azerbaijan are considered to be seismically active, and seismic events with a wide range of magnitudes (3 ≤ М < 7.3) have been registered in Azerbaijan during the instrumental period. Earthquake distribution has been analysed by means of the fractal theory, which is based on such notions as the detection of statistical self-similarity in the process under study and its quantitative assessment. The composite catalogue serves as a basis for the research and covers the time span of 1902—2018. It has been compiled with the help of seismic data from the Republican Seismic Survey Center of the Azerbaijan National Academy of Sciences and earthquake catalogues of various international seismological centres.
As a result, for the distribution of earthquakes registered in the territory of Azerbaijan the fractal dimensions (the quantitative indicators of self-similarity) of earthquake energy distribution and epicentre distribution have been calculated. The fractal dimension of earthquake epicentre distribution (De) is 1.63, whereas the average value of fractal dimension of energy distribution (d) for Azerbaijani seismic events equals 0.54.
Also, using the data from the composite catalogue, the Gutenberg—Richter magnitude-frequency relationship and the b-value for the earthquakes of Azerbaijan and the adjacent territories have been estimated. The statistical relationships between the calculated fractal dimensions of the earthquake energy and epicentre distribution (d and De, respectively) have also been examined.
Agamirzoev, R.A. (1987). Seismotectonics of the Azerbaijan part of the Greater Caucasus. Baku: Elm, 124 p. (in Russian).
Zakharov, V.S. (2008). Characteristics of self-similarity of seismicity of networks of active faults of Eurasia. Electronic scientific publication «GEOrazrez», (1), 20 (in Russian).
Kasahara, K. (1985). Mechanics earthquakes. Moscow: Mir, 264 p. (in Russian).
Riznichenko, Yu.V. Problems of seismology: selected works. Moscow: Nauka, 408 p. (in Russian).
Sherman, C.I., & Gladkov, A.C. (1999). Analysis of the actual fracture and seismic dimensions in the Baikal rift zone. Geologiya i geofizika, 40, 28—35 (in Russian).
Aki, K. (1981). A probabilistic synthesis of precursory phenomena. In D.W. Simpson, & P.G. Richards (Eds.), Earthquake Prediction: An International Review (pp. 566—574). AGU. Washington, DC.
Angulo-Brown, F., Ramн(?)rez-Guzmб(?)n, A.H., Yй(?)pez, E., Rudolf-Navarro, A., & Pavн(?)a-Miller, C.G. (1998). Fractal geometry and seismicity in the Mexican subduction zone. Geofisica Internacional, 37(1), 29—33.
Bеth, M. (1981). Earthquake Magnitude — Recent Research and Current Trends. Earth Science Reviews, 17(4), 315—398. https://doi.org/10.1016/0012-8252(81)90014-3.
Caneva, A., & Smirnov, V. (2004). Using the fractal dimension of earthquake distributions and the slope of the recurrence curve to forecast earthquakes in Colombia. Earth Sciences Research Journal, 8(1), 3—9.
Falconer, K. (1990). Fractal Geometry: Mathematical Foundations and Applications. New York: Wiley, 398 p.
Gutenberg, B., & Richter, C.F. (1944). Frequency of earthquakes in California. Bulletin of the Seismological Society of America, 34, 164—176
Han, Q., Carpinteri, A., Lacidogna, G., & Xu, J. (2015). Fractal analysis and yule statistics for seismic prediction based on 2009 L'Aquila earthquake in Italy. Arabian Journal of Geosciences, 8, 2457—2465. https://doi.org/10.1007/s12517-014-1386-y.
Kadirov, F.A., Gadirov, A.G., Babayev, G.R., Agayeva, S.T., Mammadov, S.K., Garagezova, N.R., & Safarov, R.T. (2013). Seismic zoning of the southern slope of Greater Caucasus from the fractal parameters of the earthquakes, stress state, and GPS velocities. Izvestiya, Physics of the Solid Earth, 49, 554—562. https://doi.org/10.1134/S1069351313040046.
Kagan, Y. (2007). Earthquake spatial distribution: the correlation dimension. Geophysical Journal Internationa, 168(3), 1175—1194. https://doi.org/10.1111/j.1365-246X.2006.03251.x.
Kanamori, H., & Anderson, D. (1975). Theoretical basis of some empirical relations in seismology. Bulletin of the Seismological Society of America, 65, 1073—1096.
Mandelbrot, B.B. (1982). The fractal geometry of nature. San Francisco: Freeman, 480 p.
Öztürk, S. (2015). A study on the correlations between seismotectonic b-value and Dc-value, and seismic quiescence Z-value in the Western Anatolian region of Turkey. Austrian Journal of Earth Sciences, 108(2), 172—184. doi: 10.17738/ajes.2015.0019.
Richter, C. (1958). Elementary seismology. San Franсisco, Calif.: Freeman, 768 p.
Robertson, M.C., Sammis, C.G., Sahimi, M., & Martin, A.J. (1995). Fractal analysis of three dimensional spatial distributions of earthquakes with a percolation interpretation. Journal of Geophysical Research, 100(B1), 609—620. https://doi.org/10.1029/94JB02463.
Sander, E., Sander, L.M., & Ziff, R.F. (1994). Fractals and fractal correlations. Computers in Physics, 8, 420—425. https://doi.org/10.1063/1.168501.
Scholz, C.H. (1968). Microfracturing and the inelastic deformation of rock in compression. Journal of Geophysical Research, 73(4), 1417—1432. https://doi.org/10.1029/JB073i004p01417.
Smalley, R.F., Chatelain, J.L., Turcotte, D.L., & Prevot, R. (1087). A fractal approach to the clustering of earthquakes— applications to the seismicity of the New Hebrides. Bulletin of the Seismological Society of America, 77(4), 1368—1381.
Turcotte, D.L. (1997). Fractals and Chaos in Geology and Geophysics. Second edition. Cambridge University Press, 398 p.
Volant, P., & Grasso, J.R. (1994). The finite extension of fractal geometry and power law distribution of shallow earthquakes: a geomechanical effect. Journal of Geophysical Research, 99(B11), 21879—21889. https://doi.org/10.1029/94JB01176.
Wiemer, S., McNutt, S.R., & Wyss, M. (1998). Temporal and three dimensional spatial analysis of the frequency-magnitude distribution near Long Valley Caldera. California. Geophysical Journal International, 134(2), 409—421. https://doi.org/10.1046/j.1365-246x.1998.00561.x.
Wyss, M. (1973). Towards a physical understanding of the earthquake frequency distribution. Geophysical Journal of the Royal Astronomical Society, 31(4), 341—359. https://doi.org/10.1111/j.1365-246X.1973.tb06506.x.
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