Natural Hazards and Earth System Science www.nat-hazards-earth-syst-sci.net 1561-8633 1684-9981 9 6 2009 10.5194/nhess-9-1953-2009 http://www.nat-hazards-earth-syst-sci.net/9/1953/2009/ http://www.nat-hazards-earth-syst-sci.net/9/1953/2009/nhess-9-1953-2009.html http://www.nat-hazards-earth-syst-sci.net/9/1953/2009/nhess-9-1953-2009.pdf 1953 1971 2009-11-25 Unfolding the procedure of characterizing recorded ultra low frequency, kHZ and MHz electromagetic anomalies prior to the L'Aquila earthquake as pre-seismic ones – Part 1 K. Eftaxias ceftax@phys.uoa.gr L. Athanasopoulou G. Balasis M. Kalimeri S. Nikolopoulos Y. Contoyiannis J. Kopanas G. Antonopoulos C. Nomicos Section of Solid State Physics, Department of Physics, Univ. of Athens, Panepistimiopolis, Zografos, 15784, Athens, Greece Institute for Space Applications and Remote Sensing, National Observatory of Athens, Metaxa and Vas. Pavlou, Penteli, 15236, Athens, Greece Centre de Recherchede l'ICM, INSERM UMRS 975 – CNRS UMR 7225, Hopital de la Pitie-Salpetriere, Paris, France Department of Electronics, Technological Educational Institute of Athens, Ag. Spyridonos, Egaleo, 12210, Athens, Greece Ultra low frequency, kHz and MHz electromagnetic (EM) anomalies were recorded prior to the L'Aquila catastrophic earthquake that occurred on 6 April 2009. The main aims of this paper are threefold: (i) suggest a procedure for the designation of detected EM anomalies as seismogenic ones. We do not expect to be able to provide a succinct and solid definition of a pre-seismic EM emission. Instead, we aim, through a multidisciplinary analysis, to provide the elements of a definition. (ii) Link the detected MHz and kHz EM anomalies with equivalent last stages of the earthquake preparation process. (iii) Put forward physically meaningful arguments for quantifying the time to global failure and the identification of distinguishing features beyond which the evolution towards global failure becomes irreversible. We emphasize that we try to specify not only whether a single EM anomaly is pre-seismic in itself, but also whether a combination of kHz, MHz, and ULF EM anomalies can be characterized as pre-seismic. The entire procedure unfolds in two consecutive parts. Here in Part 1 we focus on the detected kHz EM anomaly, which play a crucial role in our approach to these challenges. We try to discriminate clearly this anomaly from background noise. For this purpose, we analyze the data successively in terms of various concepts of entropy and information theory including, Shannon <i>n</i>-block entropy, conditional entropy, entropy of the source, Kolmogorov-Sinai entropy, <i>T</i>-entropy, approximate entropy, fractal spectral analysis, R/S analysis and detrended fluctuation analysis. We argue that this analysis reliably distinguishes the candidate kHz EM precursor from the noise: the launch of anomalies from the normal state is combined by a simultaneous appearance of a significantly higher level of organization, and persistency. This finding indicates that the process in which the anomalies are rooted is governed by a positive feedback mechanism. This mechanism induces a non-equilibrium process, i.e., a catastrophic event. This conclusion is supported by the fact that the two crucial signatures included in the kHz EM precursor are also hidden in other quite different, complex catastrophic events as predicted by the theory of complex systems. However, our view is that such an analysis by itself cannot establish a kHz EM anomaly as a precursor. It likely offers necessary but not sufficient criteria in order to recognize an anomaly as pre-seismic. In Part 2 we aim to provide sufficient criteria: the fracture process is characterized by fundamental universally valid scaling relationships which should be reflected in a real fracto-electromagnetic activity. Moreover, we aim to answer the following two key questions: (i) How can we link an individual EM precursor with a distinctive stage of the EQ preparation process; and (ii) How can we identify precursory symptoms in EM observations that indicate that the occurrence of the EQ is unavoidable. Andersen, J., Sornette, D., and Leung, K.: Tricritical behaviour in iupture Induced by disorder, Phys. Rev. Lett., 78, 2140–2143, 1997. de Arcangelis, L., Godano, C., Lippiello, E., and Nicodemi, M.: Universality in Solar Flare and Earthquake Occurrence, Phys. Rev. Lett., 96, 051102/1–4, 2006. Bahat, D., Rabinovitch, A., and Frid, V.: Tensile fracturing in rocks: Tectonofractographic and Electromagnetic Radiation Methods, Springer Verlag, Berlin, 570~pp., 2005. %Balasis, G., Daglis, I., Kapiris, P., Mandea, M., Vassiliadis, D., and Eftaxias, K.: From pre-storm activity to magnetic storms: a transition described in terms of fractal dynamics, Ann. Geophys., 24, 3557-3567, 2006. Balasis, G., Daglis, I., Papadimitriou, C., Kalimeri, M., Anastasiadis, A., and Eftaxias, K.: Dynamical complexity in Dst time series using non-extensive Tsallis entropy, Geophys. Res. Lett., 35, L14102, doi:10.1029/2008GL034743, 2008. Balasis, G. and Eftaxias, K.: A study of non-extensivity in the Earth’s magnetosphere, European Physical Journal, 174, 219-—225, 2009a. Balasis, G., Daglis, I., Papadimitriou, C., Kalimeri, M., Anastasiadis, A., and Eftaxias, K.: Investigating dynamical complexity in the magnetosphere using various entropy measures, J. Geophys. Res., 114, A00D06 (13~pp.), doi:10.1029/2008JA014035, 2009b. Bar-Yan, Y.: Dynamics of complex systems, Addison-Wesley, Reading, Massachusetts, 849~pp, 1997. %Biagi, P., Castellana, L., Maggipinto, T., Loiacono, D., Schiavulli, L., Ligonzo, T., Fiore, M., Suciu, E., and Ermini, A.: A pre seismic radio anomaly revealed in the area where the Abruzzo earthquake (M=6.3) occurred on 6 April 2009, Nat. Hazards Earth Syst. Sci., 9, 1551–1556, 2009. Bowman, D., Ouillon, G., Sammis, C., Sornette, A., and Sornette, D.: An observational test of the critical earthquake concept, J. Geophys. Res., 103, 24359-24372, 1998. Contoyiannis, Y. and Diakonos, F.: Criticality and intermittency in the order parameter space, Phys. Lett. A, 268, 286–272, 2000. Contoyiannis, Y., Diakonos, F., and Malakis, A.: Intermittent dynamics of critical fluctuations, Phys. Rev. Lett., 89, 35701–35704, 2002. Contoyiannis, Y., Kapiris, P., and Eftaxias, K.: Monitoring of a preseismic phase from its electromagnetic precursors, Physical Review E, 71, 061123/1–14, 2005. %Contoyiannis, Y. and Eftaxias, K.: Tsallis, Levy statistics in the preparation of an earthquake, Nonlinear Processes in Geophysics, 15, 379-388, 2008. Daglis, I.: The storm-time ring current, Space Sci. Rev., 98, 323–363, 2001. Daglis, I., Kozyra, J., Kamide, Y., Vassiliadis, D., Sharma, A., Liemohn, M., Gonzalez, W., Tsurutani, B., and Lu, G.: Intense space storms: Critical issues and open disputes, J. Geophys. Res., 108, 1208, doi:10.1029/2002JA009722, 2003. Ebeling, W. and Nicolis, G.: Word frequency and entropy of symbolic sequences: A dynamical Perspective, Chaos, Solitons & Fractals, 2, 635–650, 1992. Ebeling, W.:Prediction and entropy of nonlinear dynamical systems and symbolic sequences with LRO, Physica D, 109, 42-52, 1997. Ebeling, W., Steuer, R., Titchener, M.: Partition-based entropies of deterministic and stochastic maps, Stochastics and Dynamics, 1, 45-61, 2001. Ebeling, W.: Entropies and predictability of nonlinear processes and time series, P.M.A. Sloot et al., (Eds): ICCS 2002, LNCS, 1209-1217, 2002 Eftaxias, K., Kapiris, P., Dologlou, E., Kopanas, J., Bogris, N., Antonopoulos, G., Peratzakis, A., and Hadjicontis, V.: EM anomalies before the Kozani earthquake: A study of their behaviour through laboratory experiments, Geophys. Res. Lett., 29, 69/1-69/4, 2002. Eftaxias, K., Frangos, P., Kapiris, P., Polygiannakis, J., Kopanas, J., Peratzakis, A., Skountzos, P., and Jaggard, D.: Review and a Model of Pre-Seismic electromagnetic emissions in terms of fractal electrodynamics, Fractals, 12, 243-273, 2004. Eftaxias, K., Kapiris, P., Balasis, G., Peratzakis, A., Karamanos, K., Kopanas, J., Antonopoulos, G., and Nomicos, K.: A Unified Approach to Catastrophic Events: From the Normal State to Geological or Biological Shock in Terms of Spectral Fractal and Nonlinear Analysis, Natural Hazards and Earth System Sciences, 6, 205-228, 2006. Eftaxias, K., Sgrigna, V., and Chelidze, T.: Mechanical and Electromagnetic Phenomena Accompanying Preseismic Deformation: from Laboratory to Geophysical Scale, Tectonophysics, 431, 1–301, 2007a. Eftaxias, K., Panin, V., and Deryugin Y.: Evolution EM-signals before earthquake and during laboratory test of rocks, Tectonophysics, 431, 273–300, 2007b. Eftaxias K.: Footprints of nonextensive Tsallis statistics, selfaffinity and universality in the preparation of the L'Aquila earthquake hidden in a pre-seismic EM emission, Physica A, 389, 133-140, 2009a. K. Eftaxias, K., Balasis, G., Papadimitriou, C., Contoyiannis, Y., Athanasopoulou, L., Kalimeri, M., Nikolopoulos., S., Kopanas, J., Antonopoulos, G., Nomicos, C.: Unfolding the procedure of characterizing recorded ultra low frequency, kHZ and MHz electromagnetic anomalies prior to the L'Aquila earthquake as pre-seismic ones. Part~2 (submitted) 2009b. Fukuda, K., Nunes, L., and Stanley, H.: Similarities between communication dynamics in the Internet and the automatic nervous system, Europhysics Letters, 62, 189-195, 2003. Gershenzon, N. and Bambakidis, G.: Modelling of seismoelectromagnetic phenomena, Russ. J. Earth Sci., 3, 247-275, 2001. Grassberger, P., and Procaccia, I.: Characterization of strange attractors, 50, 346-349, 1983. Gluzman, S., and Sornette, D.: Self-consistent theory of rupture by progressive diffuse damage, Phys. Rev. E., 63, 066129 (1-11), 2001. Graben, P., and Kurths, J.: Detecting subthreshold events in noisy data by symbolic dynamics, Phys. Rev. Lett., 90, 100602 (1-4), 2003. Hansen, A., and Schmittbuhl, J.: Origin of the universal roughness exponent of brittle fracture surfaces: stress-weighted percolation in the damage zone, Phys. Rev. Lett., 90, 45 504–45 507, 2003. Hao, B-L.: Elementary symbolic dynamics and chaos in dissipative systems, World Scientific, 476pp, 1989. Hao, B-L.: Symbolic dynamics and characterization of complexity, Physica D, 51, 161-176, 1991. Hayakawa, M. and Fujinawa, Y.: Electromagnetic Phenomena Related to Earthquake Prediction, Terrapub, Tokyo, 1994. Hayakawa, M.: Atmospheric and Ionospheric Electromagnetic Phenomena Associated with Earthquakes, Terrapub, Tokyo, 1999. Hayakawa, M. and Molchanov, O.: Seismo Electromagnetics, Terrapub, Tokyo, 2002. Henegham, C. and McDarby, G.: Establishing the relation between detrended fluctuation analysis and power spectral density analysis foe stochastic processes, Phys. Rev. E, 62, 6103-6110, 2000. Herrmann, H. J., and Roux, S.: Statistical Physics for the Fracture of Disordered Media, Elsevier, Amsterdam, 1990. Herz, A. and Hopfield, J.: Earthquake cycles and neural reverberations: Collective oscillations in systems with pulse-coupled threshold elements, Phys. Rev. Lett., 75, 1222–1225, 1995. Hopfield, J.: Neurons, dynamics and computation, Physics Today, 40, 40–46, 1994. Huang, J. and Turcotte, D.: Fractal distributions of stress and strength and variations of b value, Earth Planet. Sci. Lett., 91, 223–230, 1988. Hurst, H.: Long term storage capacity of reservoirs, Trans. Am. Soc. Civ. Eng., 116, 770–808, 1951. Johansen, A., and Sornette, D.: Critical ruptures, European Physics Journal B, 18, 163-181, 2000. Kalimeri, M., Papadimitriou, C., and Eftaxias, K.: Dynamical complexity detection in pre-seismic emissions using nonadditive Tsallis entropy, Physica A, 387, 1161-1172, 2008. Kapiris, P., Eftaxias, K., and Chelidze, T.: The electromagnetic signature of prefracture criticality in heterogeneous media, Phys. Rev. Lett., 92, 065702/1-4, 2004. Kapiris, P., Polygiannakis, J., Li, X., Yao X. and Eftaxias, K.: Similarities in precursory features in seismic shocks and epileptic seizures, Europhysics Letters 69, 657-663, 2005. Karamanos, K. and Nicolis, G.: Symbolic Dynamics and Entropy Analysis of Feigenbaum Limit Sets, Chaos, Solitons & Fractals, 10(7), 1135-1150, 1999. Karamanos, K.: From symbolic dynamics to a digital approach: Chaos and Transcendence, Lect. Notes in Phys., 550, 357-371, 2000. Karamanos, K.: Entropy analysis of substitutive sequences revisited, J. Phys. A: Math. Gen., 34, 9231-9241, 2001. Karamanos, K., Dakopoulos, D., Aloupis, K., Peratzakis, A., Athanasopoulou, L., Nikolopoulos, S., Kapiris, P., and Eftaxias, K.: Study of pre-seismic electromagnetic signals in terms of complexity, Physical Review E, 74, 016104-1/21, 2006. Khinchin A. I.: Mathematical Foundations of Information Theory, Dover, New York 1957. Kitchens, B.: Symbolic Dynamics, One-Sided, Two-Sided and Countable State Markov Shifts, Springer, 252 p.p., 1998. Koulouras,G., Balasis, G., Kiourktsidis, I., Nannos, E., Kontakos, K., Stonham, J., Ruzhin, Y., Eftaxias, K., Kavouras, D., Nomikos, K.: Discrimination between preseismic electromagnetic anomalies and solar activity effects, Physica Scripta, 79, 45901 (12pp), 2009. Kurths, J., Voss, A., Saparin, P., Witt, A., Kleiner, H., and Wessel., N.: Quantitative analysis of heart rate variability, Chaos, 5, 88-94, 1995. Lopez, J. and Schmittbuhl, J.: Anomalous scaling of fracture surfaces, Phys. Rev. E, 57, 6405–6408, 1998. Latora, V., and Baranger, M., Kolmogorov-Sinai Entropy Rate versus Physical Entropy, Phys. Rev. Lett., 82, 520 – 523, 1999. Maslov, S., Paczuski, M., and Bak, P.: Avalanches and 1/f Noise in Evolution and Growth Models, Phys. Rev. Lett., 73, 2162, 1994. Morgounov, V., Relaxation creep model of impending earthquake, Annali di Geofisica, 44(2), 369-381, 2001. Muto, J., Nagahama, H., Miura, T., and Arakawa, I.:Frictional discharge at fault asperities: origin of fractal seismo-electromagnetic radiation, Tectonophysics, 431, 113-122, 2007. Osorio, I., Frei, M., Sornette, D., Milton, J., Lai, Y.: Epileptic Seizures: Quakes of the brain?, arXiv:0712.3929v1 (2007). Papadimitriou, C., Kalimeri, M. and Eftaxias, K.: Nonextensivity and universality in the earthquake preparation process, Phys. Rev. E., 77, 036101/1–14, 2008. Peng, C., Mietus, J., Hausdorff, J., Havlin, S., Stanley, H., and Goldberger.: Phys. Rev. Lett., 70, 1343-1346, 1993. Peng, C., Havlin, S., Stanley, H., and Goldberger, A.: Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat timeseries, Chaos, 5, 82–87, 1995. Picoli, S., Mendes, R., Malacarne, L., Papa, A.: Similarities between the dynamics of geomagnetic signal and heartbeat intervals, Europhysics Letters, 80, 50006/1—6, 2007. Pincus, S.: Approximate Entropy: A Complexity Measure for Biologic Time series Data, Proceedings of IEEE 17th Annual Northeast Bioengineering Conference, pp. 35–36, New York: IEE Press, 1991. Pincus, S., and Keefe, D.: Quantification of hormone pulsatility via an approximate entropy algorithm, Am. J. Physiol. (Endocrinol Metab) 262, E741-E754, 1992. Pincus, S., and Goldberger, A.: Physiological time-series analysis: what does regularity quantify? Am. J. Physiol. 266, H1643 – H1656, 1994. Pincus, S., and Singer, B.: Randomness and degree of irregularity , Proc. Natl. Acad. Sci. USA, 93, 2083-2088, 1996. Ponomarev, A., Zavyalov, A., Smirnov, V., and Lockner, D.: Physical modelling of the formation and evolution of seismically active fault zones, Tectonophysics, 277, 57-81, 1997. Ponson, L., Bonamy, D., and Bouchaud, E.: Two-dimensional scaling properties of experimental fracture surfaces, Phys. Rev. Lett., 96(3), 035506, doi:10.1103/PhysRevLett.96.035506, 2006. Rozhnoi, A., Solovieva, M., Molchanov, O., Schwingenschuh, K., Boudjada, M., Biagi, P., Maggipinto, T., Castellana, L: VLF signal precursor of L'Aquila earthquake. JRA3/EMDAF kick-off meeting (2009). Rundle, J., Tiampo, K., Klein, W., and Martins, J. S.: Selforganization in leaky threshold systems: the influence of nearmean field dynamics and its implications for EQ, neurology, and forecasting, PNAS, 99, 2514–2521, 2002. Sammis, C., and Sornette, D.: Positive feedback, memory, and the predictability of EQ, PNAS, 99, 2501-2508, 2002. Schwarz, U., Kurths, J. Klien, B., Kruger, A., and Upro, S.: Multiresolution analysis of solar mm-wave bursts, Astron. Astrophys. Suppl. Ser., 127, 309-318, 1998 Shannon, C. E.: A mathematical theory of communication, The Bell System Tech. J., 27, 379-423, 623—656, 1948. Silva, R., Franca, G., Vilar, C., and Alcaniz, J.: Nonextensive models for earthquakes, Phys. Rev. E, 73, 026102-1/5, 2006. Sotolongo-Costa, O., and Posadas, A.: Fragment-asperity interaction model for EQ, Phys. Rev. Lett., 92, 048501 / 1-4, 2004. Sornette, D., and Andersen, J.V.: Scaling with respect to disorder in time-to-failure, European Physical Journal B, 1, 353-357, 1998. Sornette, D.: Critical Phenomena in Natural Sciences, Chaos, Fractals, Self-organization and Disorder: Concepts and Tools, Second edition, Springer Series in Synergetics, Heidelberg, 2004. Sornette, D.: Predictability of catastrophic events: Material ruptures, EQ, turbulence, financial crashes, and human birth, PNAS, 99, 2522-2529, 2002. Sornette D. and A. Helmstetter.: Occurrence of finite-time singularities in epidemic models of rupture, EQ, and starquakes, Phys. Rev. Lett., 89, 158501/1–4, 2002. Stanley, H.: Scaling, universality, and renormalization: Three pillars of modern critical phenomena, Rev. Mod. Phys., 71, S358-S366, 1999. Stanley, H., Amaral, L., Goldberger, A., Havlin, S., Ivanov, P., and Peng, C.: Statistical physics and physiology: Monofractal and multifractal approaches, Physica A, 106, 309-324, 1999. Stanley, H.: Exotic statistical physics: Applications to biology, medicine, and economics, Physica A, 285, 1-17, 2000. Steuer, R., Molgedey, L., Ebeling, W., and Jimenez-Montano, M.: Entropy and optimal partition gor data analysis, Eur. Phys. J. B, 19, 265–269, 2001. Telesca, L. and Lasaponara, R.: Vegetational patterns in burned and unburned areas investigated by using the detredted fluctuation analysis, Physica A, 368, 531–535, 20006. Titchener, M., Nicolescu, R., Staiger, L., Gulliver, A., and Speidel, U.: Deterministic Complexity and Entropy, Fundamenta Informaticae, 64, 443–461, 2005. Torrence, C. and Compo, G. P.: A Practical Guide toWavelet Analysis, B. Am. Meteorol. Soc., 79, 61-78, 1998. Tsallis, C.: Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys., 52, 479–487, 1988. Tsallis, C.: Introduction to Nonextensive Statistical Mechanics, Approaching a Complex Word, Springer, 2009. Turcotte, D.: Fractals and chaos in geology and geophysics, 2nd edn., Cambridge University Press, 398~pp., 1997. Uyeda, S: EOS Transactions, AGU, 81, 3–6, 2000. Vicsek, T.: A question of scale, Nature, 411, 421~pp., 2001. Vicsek, T.: The bigger picture, Nature, 418, 131~pp., 2002. Vilar, C., Franca, G., Silva, R., and Alcaniz, J.: Nonextensivity in geological faults?, Physica A, 377, 285–290, 2007. Voss, A., Kurths, J., Kleiner, H., Witt, A., Wessel, N., Saparin, N., Osterziel, K., Schurath, R., and Dietz, R.: The application of methods of non-linear dynamics for the improved and predictive recognition of patients threatened by sudden cardiac death, Cardiovascular Research 1996 31(3), 419–433, 1996. Zunino, L., Perez, D., Kowalski, A., Martin, M., Garavaglia, M., Plastino, A., and Rosso, O.: Fractional Brownian motion, fractional Gaussian noise and Tsallis permutation entropy, Physica A, 387, 6057–6068, 2008.