Natural time analysis of critical phenomena

Analysis of critical states based on acoustic emission signals during progressive failure of wood

The analysis of critical states during fracture of wood materials is crucial for wood building safety monitoring, wood processing, etc. In this paper, beech and camphor pine are selected as the research objects, and the acoustic emission signals during the fracture process of the specimens are analyzed by three-point bending load experiments. On the one hand, the critical state interval of a complex acoustic emission signal system is determined by selecting characteristic parameters in the natural time domain. On the other hand, an improved method of b_value analysis in the natural time domain is proposed based on the characteristics of the acoustic emission signal. The K-value, which represents the beginning of the critical state of a complex acoustic emission signal system, is further defined by the improved method of b_value in the natural time domain. For beech, the analysis of critical state time based on characteristic parameters can predict the "collapse" time 8.01 s in advance, while for camphor pines, 3.74 s in advance. K-value can be analyzed at least 3 s in advance of the system "crash" time for beech and 4 s in advance of the system "crash" time for camphor pine. The results show that compared with traditional time-domain acoustic emission signal analysis, natural time-domain acoustic emission signal analysis can discover more available feature information to characterize the state of the signal. Both the characteristic parameters and Natural_Time_b_value analysis in the natural time domain can effectively characterize the time when the complex acoustic emission signal system enters the critical state. Critical state analysis can provide new ideas for wood health monitoring and complex signal processing, etc.

Tsallis Entropy and Mutability to Characterize Seismic Sequences: The Case of 2007-2014 Northern Chile Earthquakes

Seismic data have improved in quality and quantity over the past few decades, enabling better statistical analysis. Statistical physics has proposed new ways to deal with these data to focus the attention on specific matters. The present paper combines these two progressions to find indicators that can help in the definition of areas where seismic risk is developing. Our data comes from the IPOC catalog for 2007 to 2014. It covers the intense seismic activity near Iquique in Northern Chile during March/April 2014. Centered in these hypocenters we concentrate on the rectangle Lat-22-18 and Lon-68-72 and deepness between 5 and 70 km, where the major earthquakes originate. The analysis was performed using two complementary techniques: Tsallis entropy and mutability (dynamical entropy). Two possible forecasting indicators emerge: (1) Tsallis entropy (mutability) increases (decreases) broadly about two years before the main MW8.1 earthquake. (2) Tsallis entropy (mutability) sharply decreases (increases) a few weeks before the MW8.1 earthquake. The first one is about energy accumulation, and the second one is because of energy relaxation in the parallelepiped of interest. We discuss the implications of these behaviors and project them for possible future studies.

Earthquake Nowcasting: Retrospective Testing in Greece

Earthquake nowcasting (EN) is a modern method of estimating seismic risk by evaluating the progress of the earthquake (EQ) cycle in fault systems. EN evaluation is based on a new concept of time, termed 'natural time'. EN employs natural time, and uniquely estimates seismic risk by means of the earthquake potential score (EPS), which has been found to have useful applications both regionally and globally. Amongst these applications, here we focused on Greece since 2019, for the estimation of the EPS for the largest-magnitude events, MW(USGS) ≥ 6, that occurred during our study period: for example, the MW= 6.0 WNW-of-Kissamos EQ on 27 November 2019, the MW= 6.5 off-shore Southern Crete EQ on 2 May 2020, the MW= 7.0 Samos EQ on 30 October 2020, the MW= 6.3 Tyrnavos EQ on 3 March 2021, the MW= 6.0 Arkalohorion Crete EQ on 27 September 2021, and the MW= 6.4 Sitia Crete EQ on 12 October 2021. The results are promising, and reveal that the EPS provides useful information on impending seismicity.

Natural Time Analysis of Global Seismicity

Natural time analysis enables the introduction of an order parameter for seismicity, which is just the variance of natural time χ, κ1=⟨χ2⟩−⟨χ⟩2. During the last years, there has been significant progress in the natural time analysis of seismicity. Milestones in this progress are the identification of clearly distiguishable minima of the fluctuations of the order parameter κ1 of seismicity both in the regional and global scale, the emergence of an interrelation between the time correlations of the earthquake (EQ) magnitude time series and these minima, and the introduction by Turcotte, Rundle and coworkers of EQ nowcasting. Here, we apply all these recent advances in the global seismicity by employing the Global Centroid Moment Tensor (GCMT) catalog. We show that the combination of the above three milestones may provide useful precursory information for the time of occurrence and epicenter location of strong EQs with M≥8.5 in GCMT. This can be achieved with high statistical significance (p-values of the order of 10−5), while the epicentral areas lie within a region covering only 4% of that investigated.

The Evolution of Preseismic Patterns Related to the Central Crete (Mw6.0) Strong Earthquake on 27 September 2021 Revealed by Multiresolution Wavelets and Natural Time Analysis

On 27 September 2021, a shallow earthquake with focal depth of 10 km and moment magnitude Mw6.0 occurred onshore in central Crete (Greece). The evolution of possible preseismic patterns in the area of central Crete before the Mw6.0 event was investigated by applying the method of multiresolution wavelet analysis (MRWA), along with that of natural time (NT). The monitoring of preseismic patterns by critical parameters defined by NT analysis, integrated with the results of MRWA as the initiation point for the NT analysis, forms a promising framework that may lead to new universal principles that describe the evolution patterns before strong earthquakes. Initially, we apply MRWA to the interevent time series of the successive regional earthquakes in order to investigate the approach of the regional seismicity towards critical stages and to define the starting point of the natural time domain. Then, using the results of MRWA, we apply the NT analysis, showing that the regional seismicity approached criticality for a prolonged period of ~40 days before the occurrence of the Mw6.0 earthquake, when the κ1 natural time parameter reached the critical value of κ1 = 0.070, as suggested by the NT method.

Detecting Criticality by Exploring the Acoustic Activity in Terms of the “Natural-Time” Concept

The acoustic activity developed in marble specimens under various loading schemes is explored in terms of the recently introduced F-function. The novelty of the study is that instead of describing the temporal evolution of the F-function in terms of conventional time, the Natural Time concept is employed. Although completely different geometries and loading schemes were considered, the evolution of the F-function in the Natural Time domain exhibits a self-consistent motive: its values increase progressively with fluctuations of varying intensity, however, while the fracture is approaching, a power law appears to systematically govern the response of the specimen/structure loaded. The exponent of this law, somehow corresponding to the intensity of the acoustic activity within the loaded complex, varies within broad limits. The onset of validity of the power law designates that the system has entered into its critical stage, namely that of impending fracture, providing a useful pre-failure signal.

Estimating the Epicenter of a Future Strong Earthquake in Southern California, Mexico, and Central America by Means of Natural Time Analysis and Earthquake Nowcasting

It has recently been shown in the Eastern Mediterranean that by combining natural time analysis of seismicity with earthquake networks based on similar activity patterns and earthquake nowcasting, an estimate of the epicenter location of a future strong earthquake can be obtained. This is based on the construction of average earthquake potential score maps. Here, we propose a method of obtaining such estimates for a highly seismically active area that includes Southern California, Mexico and part of Central America, i.e., the area N1035W80120. The study includes 28 strong earthquakes of magnitude M ≥7.0 that occurred during the time period from 1989 to 2020. The results indicate that there is a strong correlation between the epicenter of a future strong earthquake and the average earthquake potential score maps. Moreover, the method is also applied to the very recent 7 September 2021 Guerrero, Mexico, M7 earthquake as well as to the 22 September 2021 Jiquilillo, Nicaragua, M6.5 earthquake with successful results. We also show that in 28 out of the 29 strong M ≥7.0 EQs studied, their epicenters lie close to an estimated zone covering only 8.5% of the total area.

Estimating the Epicenter of an Impending Strong Earthquake by Combining the Seismicity Order Parameter Variability Analysis with Earthquake Networks and Nowcasting: Application in the Eastern Mediterranean

The variance κ1 of the natural time analysis of earthquake catalogs was proposed in 2005 as an order parameter for seismicity, whose fluctuations proved, in 2011, to be minimized a few months before the strongest mainshock when studying the earthquakes in a given area. After the introduction of earthquake networks based on similar activity patterns, in 2012, the study of their higher order cores revealed, in 2019, the selection of appropriate areas in which the precursory minima βmin of the fluctuations β of the seismicity order parameter κ1 could be observed up to six months before all strong earthquakes above a certain threshold. The eastern Mediterranean region was studied in 2019, where all earthquakes of magnitude M≥7.1 were found to be preceded by βmin without any false alarm. Combining these results with the method of nowcasting earthquakes, introduced in 2016, for seismic risk estimation, here, we show that the epicenter of an impending strong earthquake can be estimated. This is achieved by employing—at the time of observing the βmin—nowcasting earthquakes in a square lattice grid in the study area and by averaging, self-consistently, the results obtained for the earthquake potential score. This is understood in the following context: The minimum βmin is ascertained to almost coincide with the onset of Seismic Electric Signals activity, which is accompanied by the development of long range correlations between earthquake magnitudes in the area that is a candidate for a mainshock.

Seismicity Patterns Prior to the Thessaly (Mw6.3) Strong Earthquake on 3 March 2021 in Terms of Multiresolution Wavelets and Natural Time Analysis

On 3 March 2021, a strong, shallow earthquake of moment magnitude, Mw6.3, occurred in northern Thessaly (Central Greece). To investigate possible complex correlations in the evolution of seismicity in the broader area of Central Greece before the Mw6.3 event, we apply the methods of multiresolution wavelet analysis (MRWA) and natural time (NT) analysis. The description of seismicity evolution by critical parameters defined by NT analysis, integrated with the results of MRWA as the initiation point for the NT analysis, forms a new framework that may possibly lead to new universal principles that describe the generation processes of strong earthquakes. In the present work, we investigate this new framework in the seismicity prior to the Mw6.3 Thessaly earthquake. Initially, we apply MRWA to the interevent time series of the successive regional earthquakes in order to investigate the approach of the regional seismicity at critical stages and to define the starting point of the natural time domain. Then, we apply the NT analysis, showing that the regional seismicity approached criticality a few days before the occurrence of the Mw6.3 earthquake, when the κ1 natural time parameter reached the critical value of κ1 = 0.070.

Criticality Hidden in Acoustic Emissions and in Changing Electrical Resistance during Fracture of Rocks and Cement-Based Materials

Acoustic emissions (AE) due to microcracking in solid materials permit the monitoring of fracture processes and the study of failure dynamics. As an alternative method of integrity assessment, measurements of electrical resistance can be used as well. In the literature, however, many studies connect the notion of criticality with AE originating from the fracture, but not with the changes in the electrical properties of materials. In order to further investigate the possible critical behavior of fracture processes in rocks and cement-based materials, we apply natural time (NT) analysis to the time series of AE and resistance measurements, recorded during fracture experiments on cement mortar (CM) and Luserna stone (LS) specimens. The NT analysis indicates that criticality in terms of electrical resistance changes systematically precedes AE criticality for all investigated specimens. The observed greater unpredictability of the CM fracture behavior with respect to LS could be ascribed to the different degree of material homogeneity, since LS (heterogeneous material) expectedly offers more abundant and more easily identifiable fracture precursors than CM (homogenous material). Non-uniqueness of the critical point by varying the detection threshold of cracking events is apparently due to finite size effects which introduce deviations from the self-similarity.

Nowcasting Avalanches as Earthquakes and the Predictability of Strong Avalanches in the Olami-Feder-Christensen Model

Nowcasting earthquakes, suggested recently as a method to estimate the state of a fault and hence the seismic risk, is based on the concept of natural time. Here, we generalize nowcasting to a prediction method the merits of which are evaluated by means of the receiver operating characteristics. This new prediction method is applied to a simple (toy) model for the waiting (natural) time of the stronger earthquakes, real seismicity, and the Olami-Feder-Christensen earthquake model with interesting results revealing acceptable to excellent or even outstanding performance.

On the Statistical Significance of the Variability Minima of the Order Parameter of Seismicity by Means of Event Coincidence Analysis

Natural time analysis has led to the introduction of an order parameter for seismicity when considering earthquakes as critical phenomena. The study of the fluctuations of this order parameter has shown that its variability exhibits minima before strong earthquakes. In this paper, we evaluate the statistical significance of such minima by using the recent method of event coincidence analysis. Our study includes the variability minima identified before major earthquakes in Japan and Eastern Mediterranean as well as in global seismicity.

Identifying the Occurrence Time of the Deadly Mexico M8.2 Earthquake on 7 September 2017

It has been shown that some dynamic features hidden in the time series of complex systems can be unveiled if we analyze them in a time domain termed natural time. In this analysis, we can identify when a system approaches a critical point (dynamic phase transition). Here, based on natural time analysis, which enables the introduction of an order parameter for seismicity, we discuss a procedure through which we could achieve the identification of the occurrence time of the M8.2 earthquake that occurred on 7 September 2017 in Mexico in Chiapas region, which is the largest magnitude event recorded in Mexico in more than a century. In particular, we first investigated the order parameter fluctuations of seismicity in the entire Mexico and found that, during an almost 30-year period, i.e., from 1 January 1988 until the M8.2 earthquake occurrence, they were minimized around 27 July 2017. From this date, we started computing the variance of seismicity in Chiapas region and found that it approached the critical value 0.070 on 6 September 2017, almost one day before this M8.2 earthquake occurrence.

Statistical physics models for aftershocks and induced seismicity

A standard approach to quantifying the seismic hazard is the relative intensity (RI) method. It is assumed that the rate of seismicity is constant in time and the rate of occurrence of small earthquakes is extrapolated to large earthquakes using Gutenberg-Richter scaling. We introduce nowcasting to extend RI forecasting to time-dependent seismicity, for example, during an aftershock sequence. Nowcasting uses 'natural time'; in seismicity natural time is the event count of small earthquakes. The event count for small earthquakes is extrapolated to larger earthquakes using Gutenberg-Richter scaling. We first review the concepts of natural time and nowcasting and then illustrate seismic nowcasting with three examples. We first consider the aftershock sequence of the 2004 Parkfield earthquake on the San Andreas fault in California. Some earthquakes have higher rates of aftershock activity than other earthquakes of the same magnitude. Our approach allows the determination of the rate in real time during the aftershock sequence. We also consider two examples of induced earthquakes. Large injections of waste water from petroleum extraction have generated high rates of induced seismicity in Oklahoma. The extraction of natural gas from the Groningen gas field in The Netherlands has also generated very damaging earthquakes. In order to reduce the seismic activity, rates of injection and withdrawal have been reduced in these two cases. We show how nowcasting can be used to assess the success of these efforts.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.

Study in Natural Time of Geoelectric Field and Seismicity Changes Preceding the Mw6.8 Earthquake on 25 October 2018 in Greece

A strong earthquake of magnitude M w 6.8 struck Western Greece on 25 October 2018 with an epicenter at 37.515 ∘ N 20.564 ∘ E. It was preceded by an anomalous geolectric signal that was recorded on 2 October 2018 at a measuring station 70 km away from the epicenter. Upon analyzing this signal in natural time, we find that it conforms to the conditions suggested for its identification as precursory Seismic Electric Signal (SES) activity. Notably, the observed lead time of 23 days lies within the range of values that has been very recently identified as being statistically significant for the precursory variations of the electric field of the Earth. Moreover, the analysis in natural time of the seismicity subsequent to the SES activity in the area candidate to suffer this strong earthquake reveals that the criticality conditions were obeyed early in the morning of 18 October 2018, i.e., almost a week before the strong earthquake occurrence, in agreement with earlier findings. Finally, when employing the recent method of nowcasting earthquakes, which is based on natural time, we find an earthquake potential score around 80%.

Tsallis Entropy Index q and the Complexity Measure of Seismicity in Natural Time under Time Reversal before the M9 Tohoku Earthquake in 2011

The observed earthquake scaling laws indicate the existence of phenomena closely associated with the proximity of the system to a critical point. Taking this view that earthquakes are critical phenomena (dynamic phase transitions), here we investigate whether in this case the Lifshitz–Slyozov–Wagner (LSW) theory for phase transitions showing that the characteristic size of the minority phase droplets grows with time as t1/3 is applicable. To achieve this goal, we analyzed the Japanese seismic data in a new time domain termed natural time and find that an LSW behavior is actually obeyed by a precursory change of seismicity and in particular by the fluctuations of the entropy change of seismicity under time reversal before the Tohoku earthquake of magnitude 9.0 that occurred on 11 March 2011 in Japan. Furthermore, the Tsallis entropic index q is found to exhibit a precursory increase.

A Complexity View into the Physics of the Accelerating Seismic Release Hypothesis: Theoretical Principles

Observational indications support the hypothesis that many large earthquakes are preceded by accelerating-decelerating seismic release rates which are described by a power law time to failure relation. In the present work, a unified theoretical framework is discussed based on the ideas of non-extensive statistical physics along with fundamental principles of physics such as the energy conservation in a faulted crustal volume undergoing stress loading. We define a generalized Benioff strain function Ω ξ ( t ) = ∑ i = 1 n ( t ) E i ξ ( t ) , where E_i is the earthquake energy, 0 ≤ ξ ≤ 1 . and a time-to-failure power-law of Ω ξ ( t ) derived for a fault system that obeys a hierarchical distribution law extracted from Tsallis entropy. In the time-to-failure power-law followed by Ω ξ ( t ) the existence of a common exponent m_ξ which is a function of the non-extensive entropic parameter q is demonstrated. An analytic expression that connects m_ξ with the Tsallis entropic parameter q and the b value of Gutenberg-Richter law is derived. In addition the range of q and b values that could drive the system into an accelerating stage and to failure is discussed, along with precursory variations of m_ξ resulting from the precursory b-value anomaly. Finally our calculations based on Tsallis entropy and the energy conservation give a new view on the empirical laws derived in the literature, the associated average generalized Benioff strain rate during accelerating period with the background rate and connecting model parameters with the expected magnitude of the main shock.

Statistical Significance of Earth's Electric and Magnetic Field Variations Preceding Earthquakes in Greece and Japan Revisited

By analyzing the seismicity in a new time domain, termed natural time, we recently found that the change of the entropy under time reversal (Physica A2018, 506, 625–634) and the relevant complexity measures (Entropy2018, 20, 477) exhibit pronounced variations before the occurrence of the M8.2 earthquake in Mexico on 7 September 2017. Here, the statistical significance of precursory phenomena associated with other physical properties and in particular the anomalous variations observed in the Earth’s electric and magnetic fields before earthquakes in different regions of the world and in particular in Greece since 1980s and Japan during 2001–2010 are revisited (the latter, i.e., the magnetic field variations are alternatively termed ultra low frequency (ULF) seismo-magnetic phenomena). Along these lines we employ modern statistical tools like the event coincidence analysis and the receiver operating characteristics technique. We find that these precursory variations are far beyond chance and in addition their lead times fully agree with the experimental findings in Greece since the 1980s.

The Complexity Measures Associated with the Fluctuations of the Entropy in Natural Time before the Deadly México M8.2 Earthquake on 7 September 2017

We analyse seismicity during the 6-year period 2012-2017 in the new time domain termed natural time in the Chiapas region where the M8.2 earthquake occurred, Mexico's largest earthquake in more than a century, in order to study the complexity measures associated with fluctuations of entropy as well as with entropy change under time reversal. We find that almost three months before the M8.2 earthquake, i.e., on 14 June 2017, the complexity measure associated with the fluctuations of entropy change under time reversal shows an abrupt increase, which, however, does not hold for the complexity measure associated with the fluctuations of entropy in forward time. On the same date, the entropy change under time reversal has been previously found to exhibit a minimum [Physica A 506, 625-634 (2018)]; we thus find here that this minimum is also accompanied by increased fluctuations of the entropy change under time reversal. In addition, we find a simultaneous increase of the Tsallis entropic index q.

Micro-scale, mid-scale, and macro-scale in global seismicity identified by empirical mode decomposition and their multifractal characteristics

The magnitude time-series of the global seismicity is analyzed by the empirical mode decomposition giving rise to 14 intrinsic mode functions (IMF) and a trend. Using Hurst analysis one can identify three different sums of these IMFs and the trend which exhibit distinct multifractal behaviour and correspond to micro-, mid- and macro-scales. Their multifractal detrended fluctuation analysis reveals that the micro-scale time-series exhibits anticorrelated behaviour in contrast to the mid-scale one which is long-range correlated. Concerning the mid-scale one, in the range of 30 to 300 consecutive events the maximum entropy method power spectra indicates that it exhibits an 1/f^α behaviour with α close to 1/3 which is compatible with the long-range correlations identified by detrended fluctuation analysis during periods of stationary seismicity. The results have been also verified to hold regionally for the earthquakes in Japan and shed light on the significance of the mid-scale of 30 to 300 events in the natural time analysis of global (and regional) seismicity. It is shown that when using the mid-scale time-series only, we can obtain results similar to those obtained by the natural time analysis of global seismicity when focusing on the prediction of earthquakes with M ≥ 8.4.

Criticality Analysis of the Lower Ionosphere Perturbations Prior to the 2016 Kumamoto (Japan) Earthquakes as Based on VLF Electromagnetic Wave Propagation Data Observed at Multiple Stations

The perturbations of the ionosphere which are observed prior to significant earthquakes (EQs) have long been investigated and could be considered promising for short-term EQ prediction. One way to monitor ionospheric perturbations is by studying VLF/LF electromagnetic wave propagation through the lower ionosphere between specific transmitters and receivers. For this purpose, a network of eight receivers has been deployed throughout Japan which receive subionospheric signals from different transmitters located both in the same and other countries. In this study we analyze, in terms of the recently proposed natural time analysis, the data recorded by the above-mentioned network prior to the catastrophic 2016 Kumamoto fault-type EQs, which were as huge as the former 1995 Kobe EQ. These EQs occurred within a two-day period (14 April: MW=6.2 and MW=6.0, 15 April: MW=7.0) at shallow depths (~10 km), while their epicenters were adjacent. Our results show that lower ionospheric perturbations present critical dynamics from two weeks up to two days before the main shock occurrence. The results are compared to those by the conventional nighttime fluctuation method obtained for the same dataset and exhibit consistency. Finally, the temporal evolutions of criticality in ionospheric parameters and those in the lithosphere as seen from the ULF electromagnetic emissions are discussed in the context of the lithosphere-atmosphere-ionosphere coupling.

Temporal analysis of acoustic emission from a plunged granular bed

The statistical property of acoustic emission (AE) events from a plunged granular bed is analyzed by means of actual-time and natural-time analyses. These temporal analysis methods allow us to investigate the details of AE events that follow a power-law distribution. In the actual-time analysis, the calm-time distribution, and the decay of the event-occurrence density after the largest event (i.e., the Omori-Utsu law) are measured. Although the former always shows a power-law form, the latter does not always obey a power law. Markovianity of the event-occurrence process is also verified using a scaling law by assuming that both of them exhibit power laws. We find that the effective shear strain rate is a key parameter to classify the emergence rate of power-law nature and Markovianity in granular AE events. For the natural-time analysis, the existence of self-organized critical states is revealed by calculating the variance of natural time χ(k), where kth natural time of N events is defined as χ(k)=k/N. In addition, the energy difference distribution can be fitted by a q-Gaussian form, which is also consistent with the criticality of the system.

Minima of the fluctuations of the order parameter of global seismicity

It has been recently shown [N. V. Sarlis, Phys. Rev. E 84, 022101 (2011) and N. V. Sarlis and S.-R. G. Christopoulos, Chaos 22, 023123 (2012)] that earthquakes of magnitude M greater or equal to 7 are globally correlated. Such correlations were identified by studying the variance κ1 of natural time which has been proposed as an order parameter for seismicity. Here, we study the fluctuations of this order parameter using the Global Centroid Moment Tensor catalog for a magnitude threshold Mthres = 5.0 and focus on its behavior before major earthquakes. Natural time analysis reveals that distinct minima of the fluctuations of the order parameter of seismicity appear within almost five and a half months on average before all major earthquakes of magnitude larger than 8.4. This phenomenon corroborates the recent finding [N. V. Sarlis et al., Proc. Natl. Acad. Sci. U.S.A. 110, 13734 (2013)] that similar minima of the seismicity order parameter fluctuations had preceded all major shallow earthquakes in Japan. Moreover, on the basis of these minima a statistically significant binary prediction method for earthquakes of magnitude larger than 8.4 with hit rate 100% and false alarm rate 6.67% is suggested.

Criticality features in ULF magnetic fields prior to the 2011 Tohoku earthquake

The criticality of ULF (Ultra-low-frequency) magnetic variations is investigated for the 2011 March 11 Tohoku earthquake (EQ) by natural time analysis. For this attempt, some ULF parameters were considered: (1) Fh (horizontal magnetic field), (2) Fz (vertical magnetic field), and (3) Dh (inverse of horizontal magnetic field). The first two parameters refer to the ULF radiation, while the last parameter refers to another ULF effect of ionospheric signature. Nighttime (L.T. = 3 am ± 2 hours) data at Kakioka (KAK) were used, and the power of each quantity at a particular frequency band of 0.03-0.05 Hz was averaged for nighttime hours. The analysis results indicate that Fh fulfilled all criticality conditions on March 3-5, 2011, and that the additional parameter, Dh reached also a criticality on March 6 or 7. In conclusion, criticality has reached in the pre-EQ fracture region a few days to one week before the main shock of the Tohoku EQ.

Spatiotemporal variations of seismicity before major earthquakes in the Japanese area and their relation with the epicentral locations

Using the Japan Meteorological Agency earthquake catalog, we investigate the seismicity variations before major earthquakes in the Japanese region. We apply natural time, the new time frame, for calculating the fluctuations, termed β, of a certain parameter of seismicity, termed κ1. In an earlier study, we found that β calculated for the entire Japanese region showed a minimum a few months before the shallow major earthquakes (magnitude larger than 7.6) that occurred in the region during the period from 1 January 1984 to 11 March 2011. In this study, by dividing the Japanese region into small areas, we carry out the β calculation on them. It was found that some small areas show β minimum almost simultaneously with the large area and such small areas clustered within a few hundred kilometers from the actual epicenter of the related main shocks. These results suggest that the present approach may help estimation of the epicentral location of forthcoming major earthquakes.

Minimum of the order parameter fluctuations of seismicity before major earthquakes in Japan

It has been shown that some dynamic features hidden in the time series of complex systems can be uncovered if we analyze them in a time domain called natural time χ. The order parameter of seismicity introduced in this time domain is the variance of χ weighted for normalized energy of each earthquake. Here, we analyze the Japan seismic catalog in natural time from January 1, 1984 to March 11, 2011, the day of the M9 Tohoku earthquake, by considering a sliding natural time window of fixed length comprised of the number of events that would occur in a few months. We find that the fluctuations of the order parameter of seismicity exhibit distinct minima a few months before all of the shallow earthquakes of magnitude 7.6 or larger that occurred during this 27-y period in the Japanese area. Among the minima, the minimum before the M9 Tohoku earthquake was the deepest. It appears that there are two kinds of minima, namely precursory and nonprecursory, to large earthquakes.

Natural time analysis of critical phenomena: the case of pre-fracture electromagnetic emissions

Criticality of complex systems reveals itself in various ways. One way to monitor a system at critical state is to analyze its observable manifestations using the recently introduced method of natural time. Pre-fracture electromagnetic (EM) emissions, in agreement to laboratory experiments, have been consistently detected in the MHz band prior to significant earthquakes. It has been proposed that these emissions stem from the fracture of the heterogeneous materials surrounding the strong entities (asperities) distributed along the fault, preventing the relative slipping. It has also been proposed that the fracture of heterogeneous material could be described in analogy to the critical phase transitions in statistical physics. In this work, the natural time analysis is for the first time applied to the pre-fracture MHz EM signals revealing their critical nature. Seismicity and pre-fracture EM emissions should be two sides of the same coin concerning the earthquake generation process. Therefore, we also examine the corresponding foreshock seismic activity, as another manifestation of the same complex system at critical state. We conclude that the foreshock seismicity data present criticality features as well.

Dynamic systems approaches and levels of analysis in the nervous system

Various analyses are applied to physiological signals. While epistemological diversity is necessary to address effects at different levels, there is often a sense of competition between analyses rather than integration. This is evidenced by the differences in the criteria needed to claim understanding in different approaches. In the nervous system, neuronal analyses that attempt to explain network outputs in cellular and synaptic terms are rightly criticized as being insufficient to explain global effects, emergent or otherwise, while higher-level statistical and mathematical analyses can provide quantitative descriptions of outputs but can only hypothesize on their underlying mechanisms. The major gap in neuroscience is arguably our inability to translate what should be seen as complementary effects between levels. We thus ultimately need approaches that allow us to bridge between different spatial and temporal levels. Analytical approaches derived from critical phenomena in the physical sciences are increasingly being applied to physiological systems, including the nervous system, and claim to provide novel insight into physiological mechanisms and opportunities for their control. Analyses of criticality have suggested several important insights that should be considered in cellular analyses. However, there is a mismatch between lower-level neurophysiological approaches and statistical phenomenological analyses that assume that lower-level effects can be abstracted away, which means that these effects are unknown or inaccessible to experimentalists. As a result experimental designs often generate data that is insufficient for analyses of criticality. This review considers the relevance of insights from analyses of criticality to neuronal network analyses, and highlights that to move the analyses forward and close the gap between the theoretical and neurobiological levels, it is necessary to consider that effects at each level are complementary rather than in competition.

On the recent seismic activity in North-Eastern Aegean Sea including the M(w)5.8 earthquake on 8 January 2013

In the last week of November 2012, we announced that a strong electrotelluric disturbance, which we judged to be a Seismic Electric Signal (SES) activity, was recorded at station Assiros located in Northern Greece. This disturbance was actually followed by an Mw5.8 earthquake on 8 January 2013 in North-Eastern Aegean Sea. Here we show that, by analyzing this SES activity and employing the natural time analysis of subsequent seismicity, we estimated the epicentral location, magnitude and occurrence time which are reasonably compatible with those of the Mw5.8 event.

Natural time analysis of the Centennial Earthquake Catalog

By using the most recent version (1900-2007) of the Centennial Earthquake Catalog, we examine the properties of the global seismicity. Natural time analysis reveals that the fluctuations of the order parameter κ(1) of seismicity exhibit for at least three orders of magnitude a characteristic feature similar to that of the order parameter for other equilibrium or non-equilibrium critical systems-including self-organized critical systems. Moreover, we find non-trivial magnitude correlations for earthquakes of magnitude greater than or equal to 7.

Predictability of the coherent-noise model and its applications

We study the threshold distribution function of the coherent-noise model for the case of infinite number of agents. This function is piecewise constant with a finite number of steps n. The latter exhibits a 1/f behavior as a function of the order of occurrence of an avalanche and hence versus natural time. An analytic expression of the expectation value E(S) for the size S of the next avalanche is obtained and used for the prediction of the next avalanche. Apart from E(S), the number of steps n can also serve for this purpose. This enables the construction of a similar prediction scheme which can be applied to real earthquake aftershock data.

From self-organized to extended criticality

We address the issue of criticality that is attracting the attention of an increasing number of neurophysiologists. Our main purpose is to establish the specific nature of some dynamical processes that although physically different, are usually termed as “critical,” and we focus on those characterized by the cooperative interaction of many units. We notice that the term “criticality” has been adopted to denote both noise-induced phase transitions and Self-Organized Criticality (SOC) with no clear connection with the traditional phase transitions, namely the transformation of a thermodynamic system from one state of matter to another. We notice the recent attractive proposal of extended criticality advocated by Bailly and Longo, which is realized through a wide set of critical points rather than emerging as a singularity from a unique value of the control parameter. We study a set of cooperatively firing neurons and we show that for an extended set of interaction couplings the system exhibits a form of temporal complexity similar to that emerging at criticality from ordinary phase transitions. This extended criticality regime is characterized by three main properties: (i) In the ideal limiting case of infinitely large time period, temporal complexity corresponds to Mittag-Leffler complexity; (ii) For large values of the interaction coupling the periodic nature of the process becomes predominant while maintaining to some extent, in the intermediate time asymptotic region, the signature of complexity; (iii) Focusing our attention on firing neuron avalanches, we find two of the popular SOC properties, namely the power indexes 2 and 1.5 respectively for time length and for the intensity of the avalanches. We derive the main conclusion that SOC emerges from extended criticality, thereby explaining the experimental observation of Plenz and Beggs: avalanches occur in time with surprisingly regularity, in apparent conflict with the temporal complexity of physical critical points.