Unified approach to catastrophic events: from the normal state to geological or biological shock in terms of spectral fractal and nonlinear analysis

An important question in geophysics is whether earthquakes (EQs) can be anticipated prior to their occurrence. Pre-seismic electromagnetic (EM) emissions provide a promising window through which the dynamics of EQ preparation can be investigated. However, the existence of precursory features in pre-seismic EM emissions is still debatable: in principle, it is difficult to prove associations between events separated in time, such as EQs and their EM precursors. The scope of this paper is the investigation of the pre-seismic EM activity in terms of complexity. A basic reason for our interest in complexity is the striking similarity in behavior close to irreversible phase transitions among systems that are otherwise quite different in nature. Interestingly, theoretical studies (Hopfield, 1994; Herz and Hopfield 1995; Rundle et al., 1995; Corral et al., 1997) suggest that the EQ dynamics at the final stage and neural seizure dynamics should have many similar features and can be analyzed within similar mathematical frameworks. Motivated by this hypothesis, we evaluate the capability of linear and non-linear techniques to extract common features from brain electrical activities and pre-seismic EM emissions predictive of epileptic seizures and EQs respectively. The results suggest that a unified theory may exist for the ways in which firing neurons and opening cracks organize themselves to produce a large crisis, while the preparation of an epileptic shock or a large EQ can be studied in terms of ''Intermittent Criticality''.

[1]  Konstantinos Karamanos,et al.  Extracting preseismic electromagnetic signatures in terms of symbolic dynamics , 2005 .

[2]  J. Sackellares,et al.  EPILEPSY – WHEN CHAOS FAILS , 2000 .

[3]  Klaus Lehnertz,et al.  Automated detection of a preseizure state based on a decrease in synchronization in intracranial electroencephalogram recordings from epilepsy patients. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  K. Linkenkaer-Hansen,et al.  Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations , 2001, The Journal of Neuroscience.

[5]  Mousseau.  Synchronization by Disorder in Coupled Systems. , 1996, Physical review letters.

[6]  H. Stanley,et al.  Scaling, Universality, and Renormalization: Three Pillars of Modern Critical Phenomena , 1999 .

[7]  V. Hadjicontis,et al.  Signature of pending earthquake from electromagnetic anomalies , 2001 .

[8]  Jeffrey M. Hausdorff,et al.  Multiscaled randomness: A possible source of 1/f noise in biology. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  K. Nomicos,et al.  Distinguished seismological and electromagnetic features of the impending global failure: Did the 7/9/1999 M5.9 Athens earthquake come with a warning? , 2005 .

[10]  M. Titchener.  Deterministic computation of complexity, information and entropy , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[11]  M. Marchesi,et al.  Scaling and criticality in a stochastic multi-agent model of a financial market , 1999, Nature.

[12]  D. Turcotte,et al.  Forest fires: An example of self-organized critical behavior , 1998, Science.

[13]  T. Chelidze,et al.  Electromagnetic signature of prefracture criticality in heterogeneous media. , 2004, Physical review letters.

[14]  D. Sornette,et al.  Scaling with respect to disorder in time-to-failure , 1997, cond-mat/9707114.

[15]  H. Jensen,et al.  Anisotropy and universality: the Oslo model, the rice pile experiment, and the quenched Edwards-Wilkinson equation. , 2003, Physical review letters.

[16]  Konstantinos Eftaxias,et al.  Experience of short term earthquake precursors with VLF–VHF electromagnetic emissions , 2003 .

[17]  T. Vicsek,et al.  Synchronization of oscillators with long range interaction: Phase transition and anomalous finite size effects. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Abraham Lempel,et al.  On the Complexity of Finite Sequences , 1976, IEEE Trans. Inf. Theory.

[19]  Tamas Vicsek,et al.  A question of scale , 2001, Nature.

[20]  Mark R. Titchener.  A measure of information , 2000, Proceedings DCC 2000. Data Compression Conference.

[21]  D. Sornette,et al.  Tricritical Behavior in Rupture Induced by Disorder , 1997 .

[22]  J. Nicolis,et al.  Chaos and information processing , 1991 .

[23]  V. V. Ivanov,et al.  Burridge–Knopoff model and self-similarity , 1997 .

[24]  R. Mantegna,et al.  Scaling behaviour in the dynamics of an economic index , 1995, Nature.

[25]  Self-Organized Criticality in Stick-Slip Models with Periodic Boundaries , 1997, cond-mat/9704153.

[26]  Leonidas D. Iasemidis,et al.  Chaos Theory and Epilepsy , 1996 .

[27]  Jin Ma,et al.  Do earthquakes exhibit self-organized criticality? , 2004, Physical review letters.

[28]  K. Eftaxias,et al.  Monitoring of a preseismic phase from its electromagnetic precursors. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  C. Pantano,et al.  Fractoemission from fused silica and sodium silicate glasses , 1988 .

[30]  I. Main,et al.  Testing self-organized criticality in the crust using entropy: A regionalized study of the CMT global earthquake catalogue , 2003 .

[31]  XiaoWei Zhao,et al.  Type of self-organized criticality model based on neural networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  K. Mellanby.  How Nature works , 1978, Nature.

[33]  Didier Sornette,et al.  Universal Log-Periodic Correction to Renormalization Group Scaling for Rupture Stress Prediction From Acoustic Emissions , 1995 .

[34]  C. Pantano,et al.  Fractoemission during crack propagation in glass , 1990 .

[35]  Jay Fineberg,et al.  Confirming the continuum theory of dynamic brittle fracture for fast cracks , 1999, Nature.

[36]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[37]  Synchronization and intermittency in three-coupled chaotic oscillators. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  J. Dickinson,et al.  Simultaneous measurements of the electron and photon emission accompanying fracture of single‐crystal MgO , 1987 .

[39]  John J. Hopfield,et al.  Neurons, Dynamics and Computation , 1994 .

[40]  Influence of Nonlinear Processes in Seismic Foci on Released Energy , 1997 .

[41]  Tang,et al.  Self-Organized Criticality: An Explanation of 1/f Noise , 2011 .

[42]  H. Stanley,et al.  Exotic statistical physics: Applications to biology, medicine, and economics , 2000 .

[43]  G. McDarby,et al.  Establishing the relation between detrended fluctuation analysis and power spectral density analysis for stochastic processes , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[44]  Xiaoli Li,et al.  Similarities in precursory features in seismic shocks and epileptic seizures , 2005 .

[45]  Sornette,et al.  Dynamics and memory effects in rupture of thermal fuse networks. , 1992, Physical review letters.

[46]  Georgios Balasis,et al.  Scaling similarities of multiple fracturing of solid materials , 2004 .

[47]  D. Lockner,et al.  Physical modeling of the formation and evolution of seismically active fault zones , 1997 .

[48]  Tamaz Chelidze,et al.  Electromagnetic and mechanical control of slip: laboratory experiments with slider system , 2003 .

[49]  D. Sornette,et al.  Precursors, aftershocks, criticality and self-organized criticality , 1998 .

[50]  D. Sornette,et al.  Testing self‐organized criticality by induced seismicity , 1998, cond-mat/9810190.

[51]  Klein,et al.  Boltzmann Fluctuations in Numerical Simulations of Nonequilibrium Lattice Threshold Systems. , 1995, Physical review letters.

[52]  Paczuski,et al.  Avalanches and 1/f noise in evolution and growth models. , 1994, Physical review letters.

[53]  V. Hadjicontis,et al.  EM anomalies before the Kozani earthquake: A study of their behavior through laboratory experiments , 2002 .

[54]  Xinglin Lei,et al.  Detailed analysis of acoustic emission activity during catastrophic fracture of faults in rock , 2004 .

[55]  A Rabinovitch,et al.  Gutenberg-Richter-type relation for laboratory fracture-induced electromagnetic radiation. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[56]  D Sornette,et al.  Log-periodic route to fractal functions. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[57]  Sornette,et al.  Experimental Realization of Critical Thermal Fuse Rupture. , 1996, Physical review letters.

[58]  P. Varotsos,et al.  Detection of electromagnetic earthquake precursory signals in Greece , 2000 .

[59]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[60]  Ying-Cheng Lai,et al.  Correlation-dimension and autocorrelation fluctuations in epileptic seizure dynamics. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[61]  K. Eftaxias,et al.  A Unified approach of catastrophic events , 2004 .

[62]  Alvaro Corral,et al.  Self-Organized Criticality Induced by Diversity , 1997 .

[63]  Gil,et al.  Landau-Ginzburg theory of self-organized criticality. , 1996, Physical review letters.

[64]  Gerald Kaiser,et al.  A Friendly Guide to Wavelets , 1994 .

[65]  Dimitri D. Vvedensky,et al.  Differential renormalization-group generators for static and dynamic critical phenomena , 1992 .

[66]  P. Hohenberg,et al.  Theory of Dynamic Critical Phenomena , 1977 .

[67]  D. Sornette.  Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools , 2000 .

[68]  Keisuke Ito,et al.  Fractal structure of spatial distribution of microfracturing in rock , 1987 .

[69]  I. Main,et al.  Entropy, energy, and proximity to criticality in global earthquake populations , 2002 .

[70]  M. Sahimi,et al.  Scaling Laws for Fracture of Heterogeneous Materials and Rock. , 1996, Physical review letters.

[71]  B. Litt,et al.  For Personal Use. Only Reproduce with Permission from the Lancet Publishing Group. Review Prediction of Epileptic Seizures Are Seizures Predictable? Prediction of Epileptic Seizures , 2022 .

[72]  J. B. Rundle,et al.  Self-organization in leaky threshold systems: The influence of near-mean field dynamics and its implications for earthquakes, neurobiology, and forecasting , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[73]  Golomb,et al.  Dynamics of globally coupled inhibitory neurons with heterogeneity. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[74]  Didier Sornette,et al.  Predictability of catastrophic events: Material rupture, earthquakes, turbulence, financial crashes, and human birth , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[75]  D. Plenz.  When inhibition goes incognito: feedback interaction between spiny projection neurons in striatal function , 2003, Trends in Neurosciences.

[76]  L. Amaral,et al.  Multifractality in human heartbeat dynamics , 1998, Nature.

[77]  D. Sornette,et al.  Positive feedback, memory, and the predictability of earthquakes , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[78]  Drossel.  Self-organized criticality and synchronization in a forest-fire model. , 1996, Physical review letters.

[79]  DESYNCHRONIZATION AND SYNCHRONIZATION PROCESSES IN A RANDOMLY COUPLED ENSEMBLE OF NEURONS , 1998 .

[80]  Cinna Lomnitz,et al.  Fundamentals of Earthquake Prediction , 1994 .

[81]  Usher,et al.  Dynamic pattern formation leads to 1/f noise in neural populations. , 1995, Physical review letters.

[82]  From normal state to magnetic storms in terms of fractal dynamics , 2004, physics/0411157.

[83]  H. Stanley,et al.  Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. , 1995, Chaos.

[84]  Leon D. Iasemidis,et al.  Epileptic seizure prediction and control , 2003, IEEE Transactions on Biomedical Engineering.

[85]  H. Jaeger,et al.  Granular solids, liquids, and gases , 1996 .

[86]  Y. Fujinawa,et al.  Experiments to Locate Sources of Earthquake-related VLF Electromagnetic Signals , 1997 .

[87]  A. Johansen,et al.  Critical ruptures , 2000 .

[88]  C. Sparrow.  The Fractal Geometry of Nature , 1984 .

[89]  D. Sornette,et al.  Stock Market Crashes, Precursors and Replicas , 1995, cond-mat/9510036.

[90]  M. D. S. Vieira.  Chaos and Synchronized Chaos in an Earthquake Model , 1998, cond-mat/9811305.

[91]  Brian Litt,et al.  Evidence for self-organized criticality in human epileptic hippocampus , 2002, Neuroreport.

[92]  D. E. Aspnes,et al.  Static Phenomena Near Critical Points: Theory and Experiment , 1967 .

[93]  T. Reuschlé,et al.  A theoretical investigation of the fracture energy of heterogeneous brittle materials , 1994 .

[94]  C. Elger,et al.  Spatio-temporal dynamics of the primary epileptogenic area in temporal lobe epilepsy characterized by neuronal complexity loss. , 1995, Electroencephalography and clinical neurophysiology.

[95]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[96]  J. Hopfield,et al.  Earthquake cycles and neural reverberations: Collective oscillations in systems with pulse-coupled threshold elements. , 1995, Physical review letters.

[97]  Jürgen Kurths,et al.  Seismic quiescence as an indicator for large earthquakes in a system of self‐organized criticality , 2000 .

[98]  Xinglin Lei,et al.  Compressive failure of mudstone samples containing quartz veins using rapid AE monitoring: the role of asperities , 2000 .

[99]  Akihiro Takeuchi,et al.  Scaling laws between seismo‐electric/magnetic fields and earthquake magnitude , 2004 .

[100]  M. Heimpel.  Critical behaviour and the evolution of fault strength during earthquake cycles , 1997, Nature.

[101]  K. Nakayama,et al.  Spectral analysis of photons emitted during scratching of an insulator surface by a diamond in air , 2000 .

[102]  Arenas,et al.  Self-organized criticality and synchronization in a lattice model of integrate-and-fire oscillators. , 1994, Physical review letters.

[103]  A simple model for the earthquake cycle combining self-organized complexity with critical point behavior , 2002 .

[104]  T. Vicsek.  The bigger picture. , 2002, Nature.

[105]  P. Bak,et al.  Earthquakes as a self‐organized critical phenomenon , 1989 .

[106]  Werner Ebeling,et al.  PARTITION-BASED ENTROPIES OF DETERMINISTIC AND STOCHASTIC MAPS , 2001 .

[107]  G. Buzsáki,et al.  Neuronal Oscillations in Cortical Networks , 2004, Science.

[108]  D L Gilden,et al.  1/f noise in human cognition. , 1995, Science.

[109]  J. Fineberg,et al.  Microbranching instability and the dynamic fracture of brittle materials. , 1996, Physical review. B, Condensed matter.

[110]  M. Riley,et al.  IN FRACTAL PHYSIOLOGY , 2022 .

[111]  C. Elger,et al.  CAN EPILEPTIC SEIZURES BE PREDICTED? EVIDENCE FROM NONLINEAR TIME SERIES ANALYSIS OF BRAIN ELECTRICAL ACTIVITY , 1998 .

[112]  Yuhua Wu,et al.  Infrared radiation of rock impacted at low velocity , 2004 .

[113]  The anisotropic correlation in percolation theory , 1985 .

[114]  Yanqing Chen,et al.  Long Memory Processes ( 1 / f α Type) in Human Coordination , 1997 .

[115]  Konstantinos Eftaxias,et al.  Intermittent dynamics of critical pre-seismic electromagnetic fluctuations , 2004 .

[116]  Didier Sornette,et al.  Complex Critical Exponents from Renormalization Group Theory of Earthquakes: Implications for Earthquake Predictions , 1995 .

[117]  C. Leeuwen,et al.  Scale-invariant fluctuations of the dynamical synchronization in human brain electrical activity , 2003, Neuroscience Letters.

[118]  C. Mavromatou,et al.  Understanding the fracture phenomena in inhomogeneous rock samples and ionic crystals, by monitoring the electromagnetic emission during their deformation , 2004 .