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Chile2015: Lévy Flight and Long-Range Correlation Analysis of Earthquake Magnitudes in Chile

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Abstract

The stochastic Truncated Lévy Flight model and detrended fluctuation analysis (DFA) are used to investigate the temporal distribution of earthquake magnitudes in Chile. We show that Lévy Flight is appropriated for modeling the time series of the magnitudes of the earthquakes. Furthermore, DFA shows that these events present memory effects, suggesting that the magnitude of impeding earthquakes depends on the magnitude of previous earthquakes. Based on this dependency, we use a non-linear regression to estimate the magnitude of the 2015, M8.3 Illapel earthquake based on the magnitudes of the previous events.

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References

  • Aggarwal S.K., L. Michele, P.K. Khanc, B.K. Rastogi, and L. Telesca (2015), Multifractal detrended fluctuation analysis of magnitude series of seismicity of Kachchh region, Western India, Physica A, 426, pp. 56–62.

  • Ausloos, M. and K. Ivanova (2000), Introducing False EUR and False EUR Exchange Rates, Physica A, 286, pp. 353–366.

  • Barthelemy, P., J. Bertolotti and D.S. Wiersma (2008), A Lévy flight for light, Nature, 453, doi:10.1038/nature06948.

  • Bartumeus, F., M.G. Da Luz, G. M. Viswanathan, and J. Catalan (2005), Animal search strategies: A quantitative random-walk analysis, Ecology, 86, pp. 3078–3087.

  • Brockmann, D., L. Hufnagel and T. Geisel (2006), The scaling laws of human travel, Nature, 439, pp. 462–465.

  • Bruno, R., L. Sorriso-Valvo, V. Carbone and B. Bavassano (2004), A possible truncated-Lévy flight statistics recovered from interplanetary solar-wind velocity and magnetic-field fluctuations, Europhys, Lett., 66(1), pp. 146-152.

  • Buldyrev S.V., A.L. Goldberger, S. Havlin, R.N. Mantegna, M.E. Matsa, C.K. Peng, M. Simons, H.E. Stanley (1995), Long-Range Correlation Properties of Coding and Noncoding DNA Sequences: GenBank Analysis, Phys. Rev. E, 51, pp. 5084–5091.

  • Cizeau, P., Y.H. Liu, M. Meyer, C.K. Peng and H.E. Stanley (1997), Volatility Distribution in the S-P500 Stock Index, Physica A, 245, pp. 441–445.

  • Contoyiannis Y.F. and K. Eftaxias (2008), Tsallis and Lévy statistics on the preparation of an earthquake, Nonlin, Processes Geophys., 15, pp. 379–388.

  • Flores-Mrqueza, E.L., A. Ramrez-Rojasb and L. Telesca (2015), Multifractal detrended fluctuation analysis of earthquake magnitude series of Mexican South Pacific Region, Applied Mathematics and Computation, 265, pp. 1106–1114.

  • Humphries, N.E., N. Queiroz, J. Dyer, et al. (2010), Environmental context explains Lévy and Brownian movement patterns of marine predators, Nature, 465, pp. 1066–1069.

  • Ivanova, K., and M. Ausloos (1999), Application of the Detrended Fluctuation Analysis (DFA) method for describing cloud breaking, Physica A, 274, pp. 349–354.

  • Kantelhardt, J.W., R. Berkovits, S. Havlin, A. Bunde (1999), Are the phases in the Anderson model long-range correlated?, Physica A, 266, pp. 461–464.

  • Khintchine A.Y. and P. Lvy (1936), Sur les lois stables, C. R. Acad. Sci. Paris, 202, pp. 374.

  • Koponen, I. (1995), Analytic approach to the problem of convergence of truncated Lévy flights towards the Gaussian stochastic process, Phys. Rev. E, 52, pp. 1197.

  • Koscienly-Bunde, E., A. Bunde, S. Havlin, H.E. Roman, Y. Goldreich and H. J. Schellnhuber (1998.a), Indication of universal persistence law governing atmospheric variability, Phys. Rev. Lett., 81, pp. 729–732.

  • Koscienly-Bunde, E., H.E. Roman, A. Bunde, S. Havlin and H. J.Schellnhuber (1998.b), Long-range power-law correlations in local daily temperature fluctuations, Phil. Mag. B, 77, pp. 1331–1339.

  • Lennartz, S., V.N. Livina, A. Bunde and S. Havlin (2008), Long-term memory in earthquakes and the distribution of interoccurrence times, EPL, 81, pp. 6900.

  • Lévy, P. (1925), Calcul des probabilits, Gauthier-Villars, Paris.

  • Liu, Y.H., P. Cizeau, M. Meyer, C.K. Peng and H.E. Stanley (1997), Quantification of Correlations in Economic Time Series, Physica A, 245, pp. 437–440.

  • Lomnitz, C. (2004), Major earthquakes of Chile: A historical survey, 1535–1960, Seismol. Res. Lett., 75(3), pp. 368–378.

  • Mantegna, R.N. and H.E. Stanley (1994), Stochastic Process with Ultra-Slow Convergence to a Gaussian: The Truncated Lévy Flight, Phys. Rev. Lett., 73, pp. 2946–2949.

  • Mariani, M.C. and Y. Liu (2007), Normalized truncated Lévy walks applied to the study of financial indices, Physica A , 377, pp. 590–598.

  • Mariani, M.C., I. Florescu, I. SenGupta, M.P. Beccar-Varela, P. Bezdek and L. Serpa (2013), Lévy model and scale invariance properties applied to Geophysics, Physica A, 392, pp. 824–839.

  • Mariani, M.C., O.K. Tweneboah, H. Gonzalez-Huizar, L.F. Serpa (2016), Stochastic differential equations of earthquakes series, Pure Appl Geophys, doi:10.1007/s00024-016-1292-1.

  • Peng, C.K., J. Mietus, J.M. Hausdorff, S. Havlin, H.E. Stanley, A.L. Goldberger (1993), Long-Range Anticorrelations and Non-Gaussian Behavior of the Heartbeat, Phys. Rev. Lett. 70, pp. 1343–1346.

  • Peng, C.K., S.V. Buldyrev, S. Havlin, M. Simons, H.E. Stanley, A.L. Goldberger (1994), Mosaic organization of DNA nucleotides, Phys. Rev. E 49, pp. 1685–1689.

  • Peng, C.K., S. Havlin, H.E. Stanley, and A.L. Goldberger (1995), Quantification of Scaling Exponents and Crossover Phenomena in Nonstationary Heartbeat Time Series, Proc. NATO Dynamical Disease Conference, Chaos, 5, pp. 82–87.

  • Posadas, A., J. Morales, F. Vidal, O. Sotolongo-Costa and J.C. Antoranz (2002), Continuous time random walks and south Spain seismic series, Journal of Seismology, 6, pp. 61–67.

  • Rhea, S., G. Hayes, A. Villaseor, K.P. Furlong, A.C. Tarr, and H.M. Benz (2010), Seismicity of the Earth 1900–2007, Nazca Plate and South America, U.S. Geological Survey Open-File Report 2010-1083-E

  • Sotolongo-Costa, O., J.C. Antoranz, A. Posadas, F. Vidal, A. Vazquez (2000), Lévy Flight and Earthquakes, Geophy. Res. Lett., 27(13), pp. 1965–1968.

  • Sims, D.W., E.J. Southall, N.E. Humphries, G.C. Hays, Bradshaw, Corey J. A., et al. (2008), Scaling laws of marine predator search behavior, Nature, 451, pp. 1098–1102.

  • Talkner, P. and R. O. Weber (2000), Power spectrum and detrended fluctuation analysis: Application to daily temperatures, Phys. Rev. E, 62, pp. 150–160.

  • Telesca, L., V. Cuomo and V. Lapenna (2001), Depth-dependent Time-clustering Behavior in Seismicity of Southern California, Geophys, Res. Lett., 28(22), pp. 4323–4326.

  • Telesca, L. and M. Macchiato (2004), Time-scaling properties of the Umbria-Marche 1997–1998 seismic crisis, investigated by the detrended fluctuation analysis of interevent time series, Chaos, Solitones and Fractals, 19, pp. 377–385.

  • Telesca, L., V. Cuomo, V. Lapenna and Macchiato (2004.a), Detrended fluctuation analysis of the spatial variability of the temporal distribution of Southern California seismicity, Chaos, Solitones and Fractals, 21, pp. 335–342.

  • Telesca L., V. Lappenna, M. Lovallo and M. Macchiato (2004.b), Long-range time-correlation properties of seismic sequences, Chaos, Solitones and Fractals, 21, pp. 387–393.

  • Vigny, C., A. Socquet, J.C. Ruegg, M. Metois, R. Madariaga, S. Morvan, R. Lacassin, J. Campos, D. Carrizo, M. Bejar-Pizarro, S. Barrientos and R. Armijo (2011), The 2010 Mw 8.8 Maule Megathrust Earthquake of Central Chile, Monitored by GPS, Science, 332, pp. 1417–1421.S

  • Vandewalle, N., M. Ausloos, M. Houssa, P.W. Mertens, M.M. Heyns (1999), Non-Gaussian behavior and anticorrelations in ultrathin gate oxides after soft breakdown, Appl. Phys. Lett., 74, pp. 1579–1581.

  • Yin, J., H. Yang, H. Yao, and H. Weng (2016), Coseismic radiation and stress drop during the 2015 Mw 8.3 Illapel, Chile megathrust earthquake, Geophys. Res. Lett., 43, 1520–1528, doi:10.1002/2015GL067381.

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Acknowledgments

Earthquake data used in this study were provided by the Incorporated Research Institutions for Seismology, Data Management Center (IRIS DMC).

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX, 79902, USA

    Maria P. Beccar-Varela, Maria C. Mariani & Osei K. Tweneboah

  2. Department of Geological Sciences, University of Texas at El Paso, El Paso, TX, 79902, USA

    Hector Gonzalez-Huizar & Laura F. Serpa

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  1. Maria P. Beccar-Varela
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  2. Hector Gonzalez-Huizar
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  3. Maria C. Mariani
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  4. Laura F. Serpa
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  5. Osei K. Tweneboah
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Correspondence to Hector Gonzalez-Huizar.

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Beccar-Varela, M.P., Gonzalez-Huizar, H., Mariani, M.C. et al. Chile2015: Lévy Flight and Long-Range Correlation Analysis of Earthquake Magnitudes in Chile. Pure Appl. Geophys. 173, 2257–2266 (2016). https://doi.org/10.1007/s00024-016-1334-8

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