Scaling similarities of multiple fracturing of solid materials

It has recently reported that electromagnetic flashes of low-energy <IMG WIDTH='12' HEIGHT='29' ALIGN='MIDDLE' BORDER='0' src='http://www.nonlin-processes-geophys.net/11/137/2004/npg-11-137-img1.gif' ALT='$gamma$'>-rays emitted during multi-fracturing on a neutron star, and electromagnetic pulses emitted in the laboratory by a disordered material subjected to an increasing external load, share distinctive statistical properties with earthquakes, such as power-law energy distributions (Cheng et al., 1996; Kossobokov et al., 2000; Rabinovitch et al., 2001; Sornette and Helmstetter, 2002). The neutron starquakes may release strain energies up to <IMG WIDTH='32' HEIGHT='16' ALIGN='BOTTOM' BORDER='0' src='http://www.nonlin-processes-geophys.net/11/137/2004/npg-11-137-img2.gif' ALT='$10^{46}$'>erg, while, the fractures in laboratory samples release strain energies approximately a fraction of an erg. An earthquake fault region can build up strain energy up to approximately <IMG WIDTH='32' HEIGHT='16' ALIGN='BOTTOM' BORDER='0' src='http://www.nonlin-processes-geophys.net/11/137/2004/npg-11-137-img3.gif' ALT='$10^{26}$'>erg for the strongest earthquakes. Clear sequences of kilohertz-megahertz electromagnetic avalanches have been detected from a few days up to a few hours prior to recent destructive earthquakes in Greece. A question that arises effortlessly is if the pre-seismic electromagnetic fluctuations also share the same statistical properties. Our study justifies a positive answer. Our analysis also reveals 'symptoms' of a transition to the main rupture common with earthquake sequences and acoustic emission pulses observed during laboratory experiments (Maes et al., 1998)

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''

Evolving towards a critical point: A possible electromagnetic way in which the critical regime is reached as the rupture approaches

International audienceIn analogy to the study of critical phase transitions in statistical physics, it has been argued recently that the fracture of heterogeneous materials could be viewed as a critical phenomenon, either at laboratory or at geophysical scales. If the picture of the development of the fracture is correct one may guess that the precursors may reveal the critical approach of the main-shock. When a heterogeneous material is stretched, its evolution towards breaking is characterized by the appearance of microcracks before the final break-up. Microcracks produce both acoustic and electromagnetic(EM) emission in the frequency range from VLF to VHF. The microcracks and the associated acoustic and EM activities constitute the so-called precursors of general fracture. These precursors are detectable not only at laboratory but also at geophysical scales. VLF and VHF acoustic and EM emissions have been reported resulting from volcanic and seismic activities in various geologically distinct regions of the world. In the present work we attempt to establish the hypothesis that the evolution of the Earth's crust towards the critical point takes place not only in a mechanical but also in an electromagnetic sense. In other words, we focus on the possible electromagnetic criticality, which is reached while the catastrophic rupture in the Earth's crust approaches. Our main tool is the monitoring of micro-fractures that occur before the final breakup, by recording their radio-electromagnetic emissions. We show that the spectral power law analysis of the electromagnetic precursors reveals distinguishing signatures of underlying critical dynamics, such as: (i) the emergence of memory effects; (ii) the decrease with time of the anti-persistence behaviour; (iii) the presence of persistence properties in the tail of the sequence of the precursors; and (iv) the acceleration of the precursory electro-magnetic energy release. Moreover, the statistical analysis of the amplitudes of the electromagnetic fluctuations reveals the breaking of the symmetry as the theory predicts. Finally, we try to answer the question: how universal the observed electromagnetic critical behaviour of the failing system is

Estimation of critical behavior from the density of states in classical statistical models

An approximation scheme which facilitates the application of Wang-Landau sampling in large systems for the estimation of critical behavior was discussed. The finite-size behavior of the specific heat was studied for both square and cubic Ising lattices. It was found that a relatively small part of spectral degeneracies in order to obtain good estimation of the specific-heat peaks. A scaling law for the finite-size behavior of the extensions of the critical part of the minimum energy subspace (CrMES) determined with the help of a predefined level of accuracy was proposed

Estimation of critical behavior from the density of states in classical statistical models

We present a simple and efficient approximation scheme which greatly facilitates the extension of Wang-Landau sampling (or similar techniques) in large systems for the estimation of critical behavior. The method, presented in an algorithmic approach, is based on a very simple idea, familiar in statistical mechanics from the notion of thermodynamic equivalence of ensembles and the central limit theorem. It is illustrated that we can predict with high accuracy the critical part of the energy space and by using this restricted part we can extend our simulations to larger systems and improve the accuracy of critical parameters. It is proposed that the extensions of the finite-size critical part of the energy space, determining the specific heat, satisfy a scaling law involving the thermal critical exponent. The method is applied successfully for the estimation of the scaling behavior of specific heat of both square and simple cubic Ising lattices. The proposed scaling law is verified by estimating the thermal critical exponent from the finite-size behavior of the critical part of the energy space. The density of states of the zero-field Ising model on these lattices is obtained via a multirange Wang-Landau sampling

Experience of short term earthquake precursors with VLF?VHF electromagnetic emissions

International audienceElectromagnetic anomalies (EMA) covering a wide range of frequencies from ULF, VLF up to VHF have been observed before recent destructive earthquakes in continental Greece. We show that the features of these signals are possibly correlated with the fault model characteristics of the associated earthquake and with the degree of geotectonic heterogeneity within the focal zone. The time evolution of these electromagnetic sequences reveals striking similarities to that observed in laboratory acoustic and electromagnetic emissions during different stages of failure preparation process in rocks. If we consider that the same dynamics governs the large-scale earthquakes and the microscopic scale sample rheological structure, the results of this analysis suggest that the recorded EMA might reflect the nucleation phase of the associated impending earthquake. We focus on the rise of the statistical view of earthquakes. We find electro-magnetic fingerprints of an underlying critical mechanism. Finally, we conclude that it is useful to combine ULF and VLF-VHF field measurements in an attempt to enhance the understanding of the physics behind these observations and thus to improve the quality of earthquake prediction. Further, the identification of an EMA as a seismogenic one supports the characterization of a sequence of shocks as foreshocks at the time they occur, further helping the earthquake prediction effort

On the wang-landau method using the N-fold way

We present a variation of the N-fold way algorithm, which improves efficiency when one combines the Wang-Landau method with the N-fold way. It is shown that the new version of the N-fold way algorithm has good performance when used for importance sampling and compared with the usual N-fold version or the Metropolis algorithm. The new N-fold algorithm combined with the Wang-Landau method is applied to the square Ising model using a multi-range approach. A comparative study is presented for all these algorithms, Wang-Landau and the two combined versions with the N-fold way. The role of boundary effects is discussed

VHF-electromagnetic evidence of the underlying pre-seismic critical stage

Based on the study of pre-seismic very high frequency (VHF) and very low frequency (VLF) electromagnetic signals, we attempt to establish a set of necessary conditions referring to the underlying critical stage of the earthquake preparation process. This study combines concepts from spectral analysis associated with critical point hypothesis, results from laboratory experiments of rupture and seismological arguments. These conditions are fully satisfied in the case of the VLF-VHF pre-seismic signals associated with the Kozani-Grevena earthquake in Greece. Copyright © The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences