Fractal dimension and earthquake frequency-magnitude distribution in the North of Central-East Iran Blocks (NCEIB)

Document Type : Research Paper


1 Department of Geology, Faculty of Earth Sciences, University of Birjand, Birjand, Iran

2 Research institute for Earth sciences, Geological Survey of Iran


The Gutenberg–Richter parameters (a and b), fractal dimension (DC), and relationships between these parameters are calculated for different regions of the North of Central-East Iran Blocks (NCEIB). The whole examined area (between 34°-36° N and 55°-61° E) is divided into 55 equal square grids. Both the a and b values for the frequency-magnitude distribution (FMD) and the fractal dimension (DC) are investigated simultaneously from 55 equal square grids. By using the completeness earthquake dataset for earthquakes of the instrumental period from 1976 to 2015, it is concluded that calculated values of a, b and DC imply variations of seismotectonic stress.The most vulnerable regions for occurrence of the large earthquakes in the NCEIB considering the computed lowest b-values and the highest DC -values. The relationships among DC -b and DC - (a/b) are used to classify the level of earthquake hazards for individual seismic source zones, in which the calibration curves illustrate a positive correlation among the DC and b values and also a positive
correlation among the DC and a/b ratios having similar regression coefficients (R2 = 0.80 to 0.87) for both regressions. It is observed that the relationship among a/b and DC may be used for evaluation of seismicity and earthquake hazard assessment because of the high value for correlation coefficients and limited scattering of the calculated parameters


Article Title [فارسی]

توزیع پارامترهای بزرگا-فراوانی وبعد فرکتال زلزله ها در شمال بلوک های ایران مرکزی وخاور ایران

Authors [فارسی]

  • ناصر قیاص آبادی 1
  • محمد مهدی خطیب 1
  • حمید نظری 2
  • محمد رضا هیهات 1
Abstract [فارسی]

پارامترهای گوتنبرگ-ریشتر (aو b)، بعد فرکتال (DC)، و روابط بین این پارامترها برای مناطق مختلف شمال بلوک های ایران مرکزی و خاور ایران (NCEIB). با استفاده از مجموعه داده کامل زلزله ببین دوره زمانی 1976-2015محاسبه شده است، مقادیر محاسبه شده از پارامترهایa، b و DC دلالت برتغییرات تنش لرزه ای در منطقه دارد. براین اساس مناطق آسیب پذیر برای وقوع زمین لرزه های بزرگ در NCEIB با توجه به مناطقی با کمترین ارزش b وبیشترین مقدار ​​DC مشخص شده است. ازروابط بین b- DC ،DC و (a / b) برای طبقه بندی سطح خطرات زلزله برای مناطق چشمه لرزه استفاده شده است، که در آن منحنی های کالیبراسیون نشان همبستگی مثبت میان ارزش DC و b و همچنین همبستگی مثبت میان DC و یک نسبت a/ b براساس ضرایب رگرسیون مشابه (R2 = 0.80-0.87) برای هر دو رگرسیون دارد. مشاهدات نشان می دهد که روابط a / b و DC می تواند برای ارزیابی لرزه خیزی و خطر زلزله در منطقه به دلیل ارزش بالا برای ضریب همبستگی و پراکندگی محدودی از پارامترهای محاسبه استفاده شود.

Keywords [فارسی]

  • لرزه خیزی
  • پارامترهای توزیع بزرگا-فراوانی
  • بعد فراکتال زمین لرزه ای
  • شمال بلوک های ایران مرکزی
Agard, P., Omrani, J., Jolivet, J., Whiterurch, H., Vrielynck, B., Spakman, W., Monie, P., Meyer, B., Wortel, R., 2011. Zagros orogeny: a subduction-dominated process. Geological Magazine, 148: 692–725.
Aghanabati, A., 2004. Geology of Iran. Tehran, Geological Survey of Iran, 586 p. (in Persian).
Aki, K., 1981. A probabilistic synthesis of precursory phenomena. In: Simpson, D.W., Richards, P.G. (Eds.), Earthquake prediction: an international review, Maurice Ewing Set, vol. 4. AGU, Washington, DC, 566–574.
Alavi, M., 1991. Tectonic map of the Middle East (1:2900, 000). Geological Survey of Iran, Tehran.
Alavi-Naini, M., Vaezi-Pour, M. J., Alavi Tehrani, N., Behrouzi, A., Kholghi. M. H., 1992. Torbat-e Heidariyeh, in Geological Map of Iran, sheet K-5, scale 1:250,000, Geol. Surv. Of Iran, Tehran.
Allen, M., Jackson, J., Walker, R., 2004. Late Cenozoic reorganization of the Arabia-Eurasia collision and the comparison of short-term and long-term deformation rates. Tectonics, 23, TC2008. doi: 10.1029/2003TC001530.
Allen, M., Blanc, E.J.P., Walker, R., Jackson, J., Talebian, M., Ghassemi, M.R., 2006. Contrasting styles of convergence in the Arabia-Eurasia collision: Why escape tectonics does not occur in Iran. Geological Society of America Special Paper, 409: 579–89.
Ambraseys, N., Melville, C., 1982. A History of Persian Earthquakes, Cambridge Univ. Press, Cambridge, U. K, 240 p.
Baker, C., Jackson, J., Priestley, K., 1993. Earthquakes on the Kazerun Line in the Zagros Mountains of Iran: strike-slip faulting within a fold-and-thrust belt. Geo-phys. J. Int., 115 (1): 41–61.
Bayrak, Y., Yılmaztürk, A., Öztürk, S., 2002. Lateral variations of the modal (a/b) values for the different regions of the world. Journal of Geodynamics 34: 653–666.
Bayrak, Y., Bayrak, E., 2011. An evaluation of earthquake hazard potential for different regions in Western Anatolia using the historical and instrumental earthquake data. Pure Appl Geophys 169: 1859–1873.
Bayrak, Y., Bayrak, E., 2012. Regional variations and correlations of Gutenberg–Richter parameters and fractal dimension for the different seismogenic zones in Western Anatolia. J Asian Earth Sci. 58: 98–107.
Barton, D.J., Foulger, G.R., Henderson, J.R., Julian, B.R. 1999. Frequency-magnitude statistics and spatial correlation dimensions of earthquakes at Long Valley Caldera, California. Geophysical Journal International, 138: 563–570.
Berberian, M., Yeats, R.S., 1999. Patterns of historical earthquake ruptures in the Iranian Plateau. Bull. Seismol. Soc. Am., 89: 120–139.
Blenkinsop, T.G., 1994. The fractal distribution of gold deposits. In: Kruhl, J.H. (ed.), Fractals and Dynamic Systems in Geosciences. Kruhl, J.H. (ed.), Fractals and Dynamic Systems in Geosciences. Springer, Berlin, 247–258.
Blenkinsop, T.G., Sanderson, D.J., 1999. Are gold deposits in the crust fractals? A study of gold mines in the Zimbabwe craton. In: McCaffrey, K.J.W., Lonergan, L., and Wilkinson, J.J. (ed.), Fractures, Fluid Flow and Mineralization. Geological Society Special Publication, 155: 141–151.
Bott, M. H. P., 1959. The mechanisms of oblique slip faulting. Geol. Mag. 96: 109–117.
Caceres, D., Kulhanek, O., 2000. Seismic hazard of Honduras, Nat. Hazards, 22: 49–69.
Farbod, Y., Bellier, O., Shabanian, E., Abbassi, M.R., 2011. Geomorphic and structural Variations along the Doruneh Fault System (central Iran). Tectonics 30, TC6014.
Fattahi, M., Walker, R.T., Khatib, M.M., Dolati, A., Bahroudi, A., 2007.  Slip-rate estimate and past earthquakes on the Doruneh fault, eastern Iran. Geophys. J. Int., 168, 691–709. doi:10.1111/j.1365-246X. 2006.03248. X.
Frohlich, C., Davis, S., 1993. Teleseismic b-Values: Or, Much Abouth 1.0. Journal of Geophysical Research 98: 631–644.
Gillespie, P.A., Howard, C.B., Walsh, J.J., Watterson, J., 1993. Measurement and characterisation of spatial distributions of fractures. Tectonophysics, 226: 113–141.
Guo, Z., Ogata, Y., 1995. Correlation between characteristic parameters of aftershock distributions in time, space, and magnitude. Geophysical Research Letters, 22: 993–996.
Gutenberg, B., Richter, C.F., 1944. Frequency of earthquakes in California. Bulletin of the Seismological Society of America, 34: 185–188.
Hanks, T.C., Kanamori, H., 1979. A moment-magnitude scale, J. Geophys. Res., 84: 2348–2350.
Henderson, J.R., Barton, D.J., Foulger, G.R., 1999. Fractal clustering of induced seismicity in the Geysers geothermal area, California. Geophysical Journal International 139: 317–324.
Hessami, K., Jamali, F., Tabassi, H., 2003. Map of Major Active Faults of Iran, Ministry of Science, Research and Tecnology, International Institute of Earthquake Engineering and Seismology (IIEES), Tehran, Iran.
Hirata, T., 1989. Fractal dimension of fault system in Japan: Fractal structure in rock fracture geometry at various scales. Pure and Applied Geophysics.
Huber, H., 1977. North Central Iran and North East Iran, in Geological Map of Iran, sheets 2 and 3, scale 1:1,000,000, Nati. Iranian Oil Co., Tehran.
Jackson, J., Mckenzie, D., 1984. Active tectonics of the Alpine-Himalayan Belt between western Turkey and Pakistan. Geophysical Journal of the Royal Astronomical Society, 77: 185–264.
Jackson, J., Haines, A., Holt, A., 1995. The accommodation of the Arabia–Eurasia plate
Convergence in Iran. Journal of Geophysical Research, 100: 15205–15219.
Jackson, J., Priestley, K., Allen, M., Berberian, M., 2002. Active tectonics of the South Caspian Basin. Geophys. J. Int., 148: 214–245.
Javadi, H. R., Ghassemi, M. R., Shahpasandzadeh, M., Guest, B., Esterabi Ashtiani, M., Yassaghi, A., Kouhpeyma, M., 2013. History of faulting on the Doruneh Fault System: Implications for the kinematic changes of the Central Iranian Microplate, Geol. Mag., doi: 10.1017/ S0016756812000751.
King, G.C.P., Nabelek, J., 1985. Role of fault bends in the initiation and termination of earthquake rupture, Science, 228, 984–987, doi: 10.1126/ science.228.4702.984.
Legrand, D., 2002. Fractal dimensions of small, intermediate, and large earthquakes. Bulletin of the Seismological Society of America 92, 3318–3320.
Lopez- Casado, C., Sanz de Galdano, C., Delgado, J., Peinado, M.A., 1995. The b parameter in the Betic Cordillera, Rif and nearbysectors. Relations with the tectonics of the region. Tectonophysics, 248: 277–292.
Manakou, M.V., Tsapanos, T.M., 2000. Seismicity and seismic hazard parameters evaluation in the island of crete and surrounding area inferred from mixed data files. Tectonophysics, 321: 157–178.
Mandal, P., Rastogi, B.K., 2005. Self-organized fractal seismicity and b value of aftershocks of the 2001 Bhuj earthquake in Kutch (India). Pure and Applied Geophysic, 162: 53–72.
Mandal, P., Mabawonku, A.O., Dimri, V.P., 2005. Self-organized fractal seismicity of reservoir triggered earthquakes in the Koyna-Warna seismic zone, western India. Pure and Applied Geophysics, 162: 73–90.
McKenzie, D., 1972. Active tectonics of the Mediterranean region. Geophys. J. R. Astron. Soc., 30: 109–185.
McNally, K.C., 1989. Earthquakes and seismicity. In: James, D.E., (Eds.), The Encyclopedia of Solid Earth. Geophysics, 308–315.
Miyamura, S., 1962. Magnitude–frequency relations and its bearing to geotectonics. Proc. Jpn. Acad. 38: 27–30.
Mogi, K., 1962. Magnitude-frequency relationship for elastic shocks accompanying fractures of various materials and some related problems in earthquakes. Bulletin of the Earthquake Research Institute University of Tokyo, 40: 831–883.
Mogi, K., 1967. Earthquakes and Fractures. Tectonophysics 5: 35–55.
Mouthereau, F., Lacombe, O., Vergés, J., 2012. Building the Zagros collisional orogen: timing, strain distribution and the dynamics of Arabia/Eurasia plate convergence. Tectonophysics, 532–535: 27–60.
Naimi-Ghassabian, N., Khatib, M.M., Nazari, H., Heyhat, M.R., 2015. Present-day tectonic regime and stress patterns from the formal inversion of focal mechanism data, in the North of Central-East Iran Blocks, Journal of African Earth Sciences, 111: 113–126.
Öncel, A.O., Main, I., Alptekin, Ö. Cowie, P., 1996. Temporal variations in the fractal properties of seismicity in the north Anatolian fault zone between 31_E and 41_E. Pure Applied Geophysics, 147: 147–159.
Öncel, A.O., Wilson, T., 2002. Space-time correlations of seismotectonic parameter and examples from Japan and Turkey preceding the izmit earthquake. Bulletin Seismological Society of America, 92: 339–350.
Öncel, A.O., Wilson, T., 2004. Correlation of seismotectonic variables and GPS strain measurements in western Turkey. Journal of Geophysical Research-American Geophysical Union, 109 (B11306): 1–13.
Pacheco, J.F., Scholz, C., Sykes, L., 1992. Changes in frequency–size relationship from small to large earthquakes. Nature, 355: 71–73.
Pascua, M.A.R., Devicente, G., Calvo, J.P., Perezlopez, R., 2003. Similarities between recent seismic activity and paleoseismites during the late Miocene in the external Betic Chain (Spain)-relationship by b value and the fractal dimension Journal of Structural Geology, 25: 749–763.
Pailoplee, S., Channarong, P., Chutakositkanon, V., 2013. Earthquake activities in the Thailand-Laos-Myanmar border region: a statistical approach. Terr Atmos Ocean Sci 24(Part II): 721–730.
Poroohan, N., Teimournegad, K., 2010. An analysis of correlations of seismotectonic parameter and fractal dimension preceding Roudbar-Tarom earthquake (northwest of Iran). Int Conf Geology Seismology, 148–154.
Scholz, C.H., 1968. The frequency–magnitude relation of microfracturing in rock and its relation to earthquakes. Bulletin of Seismological Society of America, 58: 399–415.
Shabanian, E., Siame, L., Bellier, O., Benedetti, L., Abbassi, M.R., 2009a. Quaternary slip-rates along the north-eastern boundary of the Arabia-Eurasia collision zone (Kopeh Dagh Mountains, north-east Iran). Geophys. J. Int., 178: 1055–1077
Shabanian, E., Bellier, O., Siame, L., Arnaud, N., Abbassi, M.R., Cochemé, J.J., 2009b. New tectonic configuration in NE Iran: Active strike-slip faulting between the Kopeh Dagh and Binalud mountains. Tectonics, 28, TC5002, doi: 10.1029/2008TC002444.
Tchalenko, J., Berberian, M., Behzadi, H., 1973. Geomorphic and seismic evidence for recent activity on the Doruneh fault, Iran. Tectonophysics, 19: 333–341.
Turcotte, D.L., 1986. Fractal model for crustal deformation. Tectonophysics 132: 261–269.
Turcotte, D.L., 1992. Fractals and Chaos in Geology and Geophysics. Cambridge University Press, Cambridge, 221 p.
Vernant, P., Nilforoushan, F., Chery, J., Bayer, R., Diamour, Y., Masson, F., Nankoli, H., Ritz, F., Sedighi, M., Tavakolim, F., 2004a. Deciphering oblique shortening of central Alborz in Iran using geodetic data. Earth Planet. Sci. Lett., 223(1–2): 177–185.
Vernant, P., Nilforoushan, F., Hatzfeld, D., Abbassi, M.R., Vigny, C., Masson, F., Nankali, H., Martinod, J., Ashtiani, A., Bayer, R., Tavakolim, F., Chéry, J., 2004b. Present-day crustal deformation and plate kinematics in the Middle East constrained by GPS measurements in Iran and northern Oman. Geophysical Journal International, 157: 381–398.
Udias, A., Mezcua, J., 1997. Fundamentos de Geofisica. Alianza Universidad Textos Paper no. 476.
Walker, R., Jackson, J., 2004. Active tectonics and Late Cenozoic strain distribution in central and eastern Iran. Tectonics, 23, TC5010, doi: 10.1029/2003TC001529.
Walsh, J.J., Watterson, J., 1993. Fractal analysis of fracture patterns using the standard box-counting technique: valid and invalid methodologies. Journal of Structural Geology, 15: 1509–1512.
Wang, J.H., 1991. A note on the correlation between b-value and fractal dimension from synthetic seismicity, Terrest. Atmospheric and Oceanic Sciences 2: 317–329.
Wang, J.H., Lee, C.W., 1996. Multifractal measures of earthquakes in west Taiwan. Pure and Applied Geophysics, 146: 131–145.
Wiemer, S., 2001. A software package to analyze seismicity: ZMAP. Seismological Research Letters 72: 373–382
Wiemer, S., Wyss, M., 1997. Mapping the frequency–magnitude distribution in asperities: an improved technique to calculate recurrence times. Journal of Geophysical Research 102: 15115–15128.
Wyss, M., Sammis, C.G., Nadeau, R.M., Wiemer, S., 2004. Fractal dimension and bvalue on creeping and locked patches of the San Andreas fault near Parkfield, California. Bulletin of Seismological Society of America, 94: 410–421
Zamani, B., Angelier, J., Zamani, A., 2008. State of stress induced by plate convergence and stress partitioning in northeastern Iran, as indicated by focal mechanisms of earthquakes. J. Geodyn. 45: 120–132. doi:10.1016/j.jog.2007.07.003.
Yadav, R.B.S., Papadimitriou, E.E., Karakostas, V.G., Rastogi, B.K., Shanker, D., Chopra, S., Singh, A.P., Kumar, S., 2011. The 2007 Talala, Saurashtra, western India earthquake sequence. Tectonic implications and seismicity triggering. Journal of Asian Earth Sciences, 40 (1): 303–314.
Yadav, R.B.S., Gahalaut, V.K., Chopra, S., Shan, B., 2012. Tectonic implications and seismicity triggering during the 2008 Baluchistan, Pakistan Earthquake Sequence. Journal of Asian Earth Sciences, 45 (2): 167–178.