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Testing a scaling law for the earthquake recurrence time distributions

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Abstract

The earthquake recurrence time distribution in a given space-time window is being studied, using earthquake catalogues from different seismic regions (Southern California, Canada, and Central Asia). The quality of the available catalogues, taking into account the completeness of the magnitude, is examined. Based on the analysis of the catalogues, it was determined that the probability densities of the earthquake recurrence times can be described by a universal gamma distribution, in which the time is normalized with the mean rate of occurrence. The results show a deviation from the gamma distribution at the short interevent times, suggesting the existence of clustering. This holds from worldwide to local scales and for quite different tectonic environments.

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References

  • Bak, P., K. Christensen, L. Danon, and T. Scanlon (2002), Unified scaling law for earthquakes, Phys. Rev. Lett. 88,17, 178501, DOI: 10.1103/PhysRevLet.88.178501.

    Article  Google Scholar 

  • Bottiglieri, M., L. de Arcangelis, C. Godano, and E. Lippiello (2010), Multiple-time scaling and universal behavior of the earthquake interevent time distribution, Phys. Rev. Lett. 104,15, 158501, DOI: 10.1103/PhysRevLett. 104.158501.

    Article  Google Scholar 

  • Christoskov, L., and R. Lazarov (1981), A method for estimating the seismological catalogues representativeness and its application to the central part of the Balkan region, Bulg. Geophys. J. 8,3, 66–76 (in Bulgarian).

    Google Scholar 

  • Corral, A. (2003), Local distributions and rate fluctuations in a unified scaling law for earthquakes, Phys. Rev. E 68,3, 035102(R), DOI: 10.1103/PhysRevE.68.035102.

    Article  Google Scholar 

  • Corral, A. (2004a), Long-term clustering, scaling, and universality in the temporal occurrence of earthquakes, Phys. Rev. Lett. 92,10, 108501, DOI: 10.1103/PhysRevLett.92.108501.

    Article  Google Scholar 

  • Corral, A. (2004b), Universal local versus unified global scaling laws in the statistics of seismicity, Physica A 340, 590–597, DOI: 10.1016/j.physa.2004.05.010.

    Article  Google Scholar 

  • Corral, A. (2005a), Mixing of rescaled data and Bayesian inference for earthquake recurrence times, Nonlin. Processes Geophys. 12,1, 89–100, DOI: 10.5194/npg-12-89-2005.

    Article  Google Scholar 

  • Corral, A. (2005b), Time-decreasing hazard and increasing time until the next earthquake, Phys. Rev. E 71,1, 017101, DOI: 10.1103/PhysRevE.71.017101.

    Article  Google Scholar 

  • Corral, A. (2005c), Renormalization-group transformations and correlations of seismicity, Phys. Rev. Lett. 95,2, 028501; DOI: 10.1103/PhysRevLett.95.028501.

    Article  Google Scholar 

  • Corral, A. (2006), Statistical features of earthquake temporal occurrence, Lect. Notes Phys. 705, 191–221, DOI: 10.1007/3-540-35375-5_8.

    Article  Google Scholar 

  • Corral, A. (2009), Statistical tests for scaling in the inter-event times of earthquakes in California, Int. J. Mod. Phys. B 23,28–29, 5570–5582, DOI: 10.1142/S0217979209063869.

    Article  Google Scholar 

  • Davidsen, J., and C. Goltz (2004), Are seismic waiting time distributions universal?, Geophys. Res. Lett. 31, L21612, DOI: 10.1029/2004GL020892.

    Article  Google Scholar 

  • Ellsworth, W.L., M.V. Matthews, R.M. Nadeau, S.P. Nishenko, P.A. Reasenberg, and R.W. Simpson (1999), A physically-based earthquake recurrence model for estimation of long-term earthquake probabilities, U.S. Geological Survey Open-File Report 99-522.

  • Gardner, J.K., and L. Knopoff (1974), Is the sequence of earthquakes in Southern California, with aftershocks removed, Poissonian?, Bull. Seimol. Soc. Am. 64,5, 1363–1367.

    Google Scholar 

  • Gutenberg, B., and C.F. Richter (1965), Seismicity of the Earth, Hafner Pub., New York.

    Google Scholar 

  • Hainzl, S., F. Scherbaum, and C. Beauval (2006), Estimating background activity based on interevent-time distribution, Bull. Seismol. Soc. Am. 96,1, 313–320, DOI: 10.1785/0120050053.

    Article  Google Scholar 

  • Kagan, Y.Y. (1994), Observational evidence for earthquakes as a nonlinear dynamic process, Physica D 77,1–3, 160–192, DOI: 10.1016/0167-2789(94)90132-5.

    Article  Google Scholar 

  • Kagan, Y.Y. (1997), Statistical aspects of Parkfield earthquake sequence and Parkfield prediction experiment, Tectonophysics 270,3–4, 207–219, DOI: 10.1016/S0040-1951(96)00210-7.

    Article  Google Scholar 

  • Kagan, Y.Y., and D.D. Jackson (1995), New seismic gap hypothesis: Five years after, J. Geophys. Res. 100,B3, 3943–3959, DOI: 10.1029/94JB03014.

    Article  Google Scholar 

  • Knopoff, L. (1997), Scale invariance of earthquakes. In: B. Dubrulle, F. Graner, and D. Sornette (eds.), Scale Invariance and Beyond, Springer-Verlag, Berlin, 159–172.

    Google Scholar 

  • Molchan, G. (2005), Interevent time distribution in seismicity: A theoretical approach, Pure Appl. Geophys. 162,6–7, 1135–1150, DOI: 10.1007/s00024-004-2664-5.

    Article  Google Scholar 

  • Murray, J., and P. Segall (2002), Testing time-predictable earthquake recurrence by direct measurement of strain accumulation and release, Nature 419, 287–291, DOI: 10.1038/nature00984.

    Article  Google Scholar 

  • Prozorov, A.G., and A.M. Dziewonski (1982), A method of studying variations in the clustering property of earthquakes: Application to the analysis of global seismicity, J. Geophys. Res. 87,B4, 2829–2839, DOI: 10.1029/JB087iB04 p02829.

    Article  Google Scholar 

  • Reasenberg, P. (1985), Second-order moment of Central California seismicity, 1969–1982, J. Geophys. Res. 90,B7, 5479–5495, DOI: 10.1029/JB090iB07 p05479.

    Article  Google Scholar 

  • Reasenberg, P.A., and L.M. Jones (1989), Earthquake hazard after a mainshock in California, Science 243,4895, 1173–1176, DOI: 10.1126/science.243.4895.1173.

    Article  Google Scholar 

  • Saichev, A., and D. Sornette (2006), “Universal” distribution of interearthquake times explained, Phys. Rev. Lett. 97,7, 078501, DOI: 10.1103/PhysRevLett.97.078501.

    Article  Google Scholar 

  • Saichev, A., and D. Sornette (2007), Theory of earthquake recurrence times, J. Geophys. Res. 112, B04313, DOI: 10.1029/2006JB004536.

    Article  Google Scholar 

  • Schwartz, D.P., and K.J. Coppersmith (1984), Fault behavior and characteristic earthquakes: Examples from the Wasatch and San Andreas fault zones, J. Geophys. Res. 89,B7, 5681–5698, DOI: 10.1029/JB089iB07p05681.

    Article  Google Scholar 

  • Shcherbakov, R., G. Yakovlev, D.L. Turcotte, and J.B. Rundle (2005), Model for the distribution of aftershock interoccurrence times, Phys. Rev. Lett. 95,21, 218501, DOI: 10.1103/PhysRevLett.95.218501.

    Article  Google Scholar 

  • Shearer, P., E. Hauksson, and G. Lin (2005), Southern California hypocenter relocation with waveform cross-correlation, Part 2: Results using source-specific station terms and cluster analysis, Bull. Seismol. Soc. Am. 95,3, 904–915, DOI: 10.1785/0120040168.

    Article  Google Scholar 

  • Sieh, K. (1996), The repetition of large-earthquake ruptures, Proc. Natl. Acad. Sci. USA 93,9, 3764–3771, DOI: 10.1073/pnas.93.9.3764.

    Article  Google Scholar 

  • Sornette, D., S. Utkin, and A. Saichev (2008), Solution of the nonlinear theory and tests of earthquake recurrence times, Phys. Rev. E 77,6, 066109, DOI: 10.1103/PhysRevE.77.066109.

    Article  Google Scholar 

  • Stein, R.S. (2002), Parkfield’s unfulfilled promise, Nature 419, 257–258, DOI: 10.1038/419257a.

    Article  Google Scholar 

  • Touati, S., M. Naylor, and I.G. Main (2009), Origin and nonuniversality of the earthquake interevent time distribution, Phys. Rev. Lett. 102,16, 168501, DOI: 10.1103/PhysRevLett.102.168501.

    Article  Google Scholar 

  • Turcotte, D.L. (1997), Fractals and Chaos in Geology and Geophysics, 2nd ed., Cambridge University Press, Cambridge, 398 pp.

    Google Scholar 

  • Udias, A., and J. Rice (1975), Statistical analysis of microearthquake activity near San Andreas geophysical observatory, Hollister, California, Bull. Seismol. Soc. Am. 65,4, 809–827.

    Google Scholar 

  • Utsu, T. (1984), Estimation of parameters for recurrence models of earthquakes, Bull. Earthq. Res. Inst. Univ. Tokyo 59, 53–66.

    Google Scholar 

  • Utsu, T. (2002), Statistical features of seismicity. In: W.H.K. Lee, H. Kanamori, P.C. Jennings, and C. Kisslinger (eds.), International Handbook of Earthquake and Engineering Seismology, Part A, Elsevier, New York, 719–732, DOI: 10.1016/S0074-6142(02)80246-7.

    Chapter  Google Scholar 

  • Utsu, T., Y. Ogata, and R.S. Matsu’ura (1995), The centenary of the Omori formula for a decay law of aftershock activity, J. Phys. Earth 43,1, 1–33, DOI: 10.4294/jpe1952.43.1.

    Article  Google Scholar 

  • Wang, J.-H., and C.-H. Kuo (1998), On the frequency distribution of interoccurrence times of earthquakes, J. Seismol. 2,4, 351–358, DOI: 10.1023/A: 1009774819512.

    Article  Google Scholar 

  • Wiemer, S. (2001), A software package to analyze seismicity: ZMAP, Seismol. Res. Lett. 72,3, 373–382, DOI: 10.1785/gssrl.72.3.373.

    Article  Google Scholar 

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Correspondence to Elisaveta Marekova.

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Marekova, E. Testing a scaling law for the earthquake recurrence time distributions. Acta Geophys. 60, 858–873 (2012). https://doi.org/10.2478/s11600-012-0007-y

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