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It has recently been found that the evolution of the preparation of a strong earthquake (EQ), as it is monitored through fracture-induced electromagnetic emissions (EME) in the MHz band, presents striking similarity with the evolution of a thermal system as temperature drops, since distinct steps of the evolution of the phenomenon of spontaneous symmetry breaking (SSB) can be identified. Here, the study of fracture-induced EME in the MHz band in analogy to thermal systems is extended to the phase of local fracture structures that follow after the SSB (and the occurrence of the main EQ). By comparing fracture-induced MHz EME associated with the strongest EQs (MW=6.9) that occurred in Greece during the last twenty years with the 3D Ising model, a way to distinguish whether a possible identification of post-SSB power-laws immediately after a very strong EQ is a sign for the preparation of a new strong EQ or not is provided. In the suggested approach, the time series analysis method known as the method of critical fluctuations is used, enhanced by the autocorrelation function. © 2021 Elsevier B.V.

In the frame of complex systems research, methods used to quantitatively analyze specific dynamic phenomena are often used to analyze phenomena from other disciplines on the grounds that are governed by similar dynamics. Technical analysis is considered the oldest, currently omnipresent, method for financial markets analysis, which uses past prices aiming at the possible short-term forecast of future prices. This work is the first attempt to explore the applicability of technical analysis tools on disturbance storm time (Dst) index time series, aiming at the identification of similar features between the Dst time series during magnetic storms (MSs) and asset price time series. We employ the following financial analysis tools: simple moving average (SMA), Bollinger bands, and relative strength index (RSI), formulating an analysis approach based on various features, appearing in financial time series during high volatility periods, that could be found during the different phases of the evolution of an MS (onset, main development, and recovery phase), focusing on the temporal sequence they occur. The applicability of the proposed analysis approach is examined on several MS events and the results reveal similar behavior with the financial time series in high volatility periods. We postulate that these specialized data analysis methods could be combined in the future with other statistical and complex systems time series analysis methods in order to form a useful toolbox for the study of geospace perturbations related to natural hazards. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.

A wide variety of electromagnetic phenomena possibly related with earthquake (EQ) preparation processes have been reported in the literature during the last few decades. An interesting aspect in their study is the time series analysis of the related observables aiming at the investigation of any embedded dynamics. In this review article we focus on the study of fracto-electromagnetic emissions (fracto-EME) at the MHz band, the ultra-low frequency (ULF) magnetic field variations (

In course of the preparation of a strong earthquake (EQ), the fracture of the highly heterogeneous system surrounding the fault has been suggested to follow the theory of critical phenomena and continuous phase transitions. Among the variety of electromagnetic phenomena which have been reported to be observed prior to a strong EQ, the ground-observed fracture-induced electromagnetic emissions (EME) in the MHz band have repeatedly been reported to present intermittency-induced criticality, while it has been suggested that reflect the specific stage of EQ preparation. Moreover, based on the analysis of pre-EQ MHz EME time series, it has been suggested that the underlying cracking procedure is organized to criticality by means of the Lévy flight mechanism. In an attempt to gain a deeper understanding to the involved EQ preparation processes and the organization to critical state, we study here the pre-EQ MHz EME presenting critical characteristics in terms of the mechanism of Lévy flight and its possible engagement with Gaussian stochastic processes. We suggest that if the analysis of the MHz EME time series according to the method of critical fluctuations indicates critical characteristics with a power law exponent, p2, value in the range 1.5,2, then a strong EQ should not be expected to follow. This is because such a result indicates a slow transition from the Lévy to the Gaussian process, cutting-off the long scales due to the Gaussian mechanism. This prevents the organization of the critical state to be completed according to the Lévy flight scenario and the spreading of the correlations all over the focal area. The above hypothesis is corroborated by a number of MHz EME time series analyses. © 2019 Elsevier B.V.

Ultra low frequency-ULF (1 Hz or lower), kHz and MHz electromagnetic (EM) anomalies were recorded prior to the L'Aquila catastrophic earthquake (EQ) that occurred on 6 April 2009. The detected anomalies followed this temporal scheme. (i) The MHz EM anomalies were detected on 26 March 2009 and 2 April 2009. The kHz EM anomalies were emerged on 4 April 2009. The ULF EM anomaly was appeared from 29 March 2009 up to 3 April 2009. The question effortlessly arises as to whether the observed anomalies before the L'Aquila EQ were seismogenic or not. The main goal of this work is to provide some insight into this issue. More precisely, the main aims of this contribution are threefold: How can we recognize an EM observation as pre-seismic one? We aim, through a multidisciplinary analysis to provide some elements of a definition. How can we link an individual EM anomaly with a distinctive stage of the EQ preparation process? The present analysis is consistent with the hypothesis that the kHz EM anomalies were associated with the fracture of asperities that were distributed along the L'Aquila fault sustaining the system, while the MHz EM anomalies could be triggered by fractures in the highly disordered system that surrounded the backbone of asperities of the activated fault. How can we identify precursory symptoms in an individual EM precursor that indicate that the occurrence of the EQ is unavoidable? We clearly state that the detection of a MHz EM precursor does not mean that the occurrence of EQ is unavoidable; the abrupt emergence of kHz EM emissions indicate the fracture of asperities. The observed ULF EM anomaly supports the hypothesis of a relationship between processes produced by increasing tectonic stresses in the Earth's crust and attendant EM interactions between the crust and ionosphere. We emphasize that we attempt to specify not only whether or not a single EM anomaly is pre-seismic in itself, but mainly whether a combination of emergent ULF, MHz and kHz EM anomalies could be characterized as pre-earthquake.

The nonlinear criticality of ultra-low frequency (ULF) magnetic variations is investigated before a particular earthquake (EQ) occurred in Kobe on April 12, 2013, by applying the "natural time" analysis on a few ULF parameters: Fh, Fz and Dh. The first two refer to radiation from the lithosphere, and the last parameter corresponds to depression of horizontal component as a signature of ionospheric perturbation. A recent paper of our team has indicated, using the same data as in this paper but by means of conventional statistical analysis, a clear effect of depression in the horizontal component as an ionospheric signature. But there seems to be no convincing signature of lithospheric ULF radiation according to the specific analysis, so this paper aims at extending our study on the electromagnetic data recorded prior to the specific EQ by trying to find any significant phenomenon in ULF effects (both lithospheric radiation and the depression of horizontal component) using the critical, natural time analysis. The natural time analysis has yielded that criticality at Shigaraki (SGA), as the station closest to the EQ epicenter, is reached on March 27-29 for Fh and March 27 to April 1 for Fz (about two weeks before the EQ). But, the criticality for Dh was not observed at SGA probably due to high noise, on the other hand such criticality was observed at Kanoya (KNY) because of its known property of a wider range of detection of ULF depression. © 2016 by the Istituto Nazionale di Geofisica e Vulcanologia. All rights reserved.

The ultra-low-frequency (ULF) magnetic variations recorded prior to the 11 March 2011 Tohoku earthquake (EQ) are analyzed using the method of critical fluctuations (MCF). The first application of this specific method to ULF magnetic variations is performed on the unprocessed H-(horizontal) and Z-(vertical) components, as well as on the unprocessed total intensity, F, of the recorded magnetic field. The motivation for the present study was given by recent research results reporting criticality features in the ULF magnetic fields prior to the 2011 Tohoku EQ. These results call for a further analysis in order to verify the existence of criticality embedded in the specific ULF recordings using an independent method, as well as to investigate the type of the embedded criticality. The application of MCF indeed verifies the existence of criticality in the ULF magnetic fields a few days to one week before the occurrence of the main shock. Specifically, clear signatures of intermittent criticality are found in the recordings of 4 March 2011, while indications of critical behavior are also found in 3 and 6 March recordings, although not of the "stability" of those of 4 March. Moreover, it is found that only the ULF data of the nearest, to the epicenter of the EQ, geomagnetic observatory presented criticality. This finding further corroborates the view that the presented signal is indeed a precursor to the specific EQ. © 2016 Elsevier B.V. All rights reserved.

In this letter, we show, in terms of the fracture-induced electromagnetic emissions (EME) recorded prior to the earthquake of Chania, Greece [(35.50° N, 23.28° E); October 12, 2013; Mw = 6.4] and the seismicity of the area, that there were different evidence indicating the advent of the main shock a few days before its occurrence. Specifically, both the megahertz (MHz) EME and the foreshock seismicity activity came to critical condition a few days before the main shock occurrence. The analysis was performed by means of two independent methods, namely, the method of critical fluctuations and the natural time method, both revealing critical features. © 2014 IEEE.

Fracture-induced electromagnetic emissions (EME) have been observed from the laboratory to the geophysical scale permitting the monitoring of damage evolution. It has been shown that the first appearing MHz EME presents second-order phase transition characteristics and has been attributed to the fracture process of the heterogeneous medium surrounding the family of strong entities (asperities) distributed along the fault sustaining the system. The finally, abruptly, emerged strong avalanche-like kHz EME do not present any footprint of a second-order transition in equilibrium, while they have been attributed to the fracture of the family of the, relatively homogeneous, asperities themselves. In the present work we show that between these two stages of the fracture process, an intermediate stage exists. This is reflected to the tricritical behavior which is revealed for the kHz EME just before the emergence of the strong avalanche-like kHz emission. The identification of this tricritical behavior is performed using the method of critical fluctuations (MCF). The results obtained for the kHz time-series are compatible with the results obtained for an introduced model map which describes the tricritical crossover. A Hurst exponent analysis shows that this crossover indicates the limit of an antipersistence dynamics. It is finally shown, by the MCF, that first-order phase transition characterizes the final rupture of the asperities. © 2014 Elsevier Ltd.

•We present new measures of dynamical complexity based on linear correlations.•We study pre-seismic kHz electro-magnetic emissions prior to 3 major earthquakes.•Complexity variations reveal 3 sub-stages of earthquake preparation processes.•A refined model of earthquake preparation processes is presented. In the last years, continuous recordings of electromagnetic emissions from geophysical observatories have been recognized to exhibit characteristic fluctuation patterns prior to some major earthquakes. To further evaluate and quantify these findings, this work presents a detailed assessment of the time-varying correlation properties of such emissions during the preparatory phases preceding some recent earthquakes in Greece and Italy. During certain stages before the earthquakes' occurrences, the electromagnetic variability profiles are characterized by a marked increase in the degree of organization of fluctuations, which allow developing hypotheses about the underlying physical mechanisms. Based on the preparatory phases of selected seismic events, the information provided by different statistical properties characterizing complementary aspects of the time-varying complexity based on temporal correlations is systematically assessed. The obtained results allow further insights into different pre-seismic stages based on the variability of electromagnetic emissions, which are probably associated with distinct geophysical processes. © 2015 Elsevier Ltd.

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. = 3am ± 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. © 2015 The Japan Academy.

Purpose: Sleep is a complex physiological state and an indicator of the changes in the brain function similar to those occurring in many psychiatric and neurological conditions. Since visual sleep scoring consuming process, automatic sleep staging methods, also called scoring, hold promise in diagnosing alterations in the sleep process and the sleep EEG more effectively.\ud Method: In this paper, a supervised approach for sleep scoring from single channel EEG signals is proposed. First, a supervised singular spectrum analysis (SSA) which is a subspace based method is used to extract the desired signal for each stage of sleep. Then, two recursive least squares (RLS) adaptive filters are trained and used to identify first and deep sleep stages.\ud Result: The proposed system which can be considered as a filter bank for separating multiple signal subbands is tested using real EEG where the results verify the accuracy of the proposed method.\ud Conclusion: The overall result show the effectiveness of algorithm for detection of sleep stages from EEG signals often characterised by a sharp increase in delta and a rapid decrease in alpha as sleep deepens.

The field of study of complex systems considers that the dynamics of complex systems are founded on universal principles that may be used to describe a great variety of scientific and technological approaches of different types of natural, artificial, and social systems. Several authors have suggested that earthquake dynamics and the dynamics of economic (financial) systems can be analyzed within similar mathematical frameworks. We apply concepts of the nonextensive statistical physics, on time-series data of observable manifestations of the underlying complex processes ending up with these different extreme events, in order to support the suggestion that a dynamical analogy exists between a financial crisis (in the form of share or index price collapse) and a single earthquake. We also investigate the existence of such an analogy by means of scale-free statistics (the Gutenberg-Richter distribution of event sizes). We show that the populations of: (i) fracto-electromagnetic events rooted in the activation of a single fault, emerging prior to a significant earthquake, (ii) the trade volume events of different shares/economic indices, prior to a collapse, and (iii) the price fluctuation (considered as the difference of maximum minus minimum price within a day) events of different shares/economic indices, prior to a collapse, follow both the traditional Gutenberg-Richter law as well as a nonextensive model for earthquake dynamics, with similar parameter values. The obtained results imply the existence of a dynamic analogy between earthquakes and economic crises, which moreover follow the dynamics of seizures, magnetic storms and solar flares. © 2013 Elsevier B.V. All rights reserved.

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. © 2013 AIP Publishing LLC.

Are there credible electromagnetic (EM) potential earthquake (EQ) precursors? This a question debated in the scientific community and there may be legitimate reasons for the critical views. The negative view concerning the existence of EM potential precursors is enhanced by features that accompany their observation which are considered as paradox ones, namely, these signals: (i) are not observed at the time of EQs occurrence and during the aftershock period, (ii) are not accompanied by large precursory strain changes, (iii) are not accompanied by simultaneous geodetic or seismological precursors and (iv) their traceability is considered problematic. In this work, the detected candidate EM potential precursors are studied through a shift in thinking towards the basic science findings relative to granular packings, micron-scale plastic flow, interface depinning, fracture size effects, concepts drawn from phase transitions, self-affine notion of fracture and faulting process, universal features of fracture surfaces, recent high quality laboratory studies, theoretical models and numerical simulations. We try to contribute to the establishment of strict criteria for the definition of an emerged EM anomaly as a possibly EQ-related one, and to the explanation of potential precursory EM features which have been considered as paradoxes. A three-stage model for EQ generation by means of pre-EQ fracture-induced EM emissions is proposed. The claim that the observed EM potential precursors may permit a real-time and step-by-step monitoring of the EQ generation is tested. © Author(s) 2013.

The field of study of complex systems considers that the dynamics of complex systems are founded on universal principles that may be used to describe a great variety of scientific and technological approaches of different types of natural, artificial, and social systems. Several authors have suggested that earthquake dynamics and neurodynamics can be analyzed within similar mathematical frameworks. Recently, authors have shown that a dynamical analogy supported by scale-free statistics exists between seizures and earthquakes, analyzing populations of different seizures and earthquakes, respectively. The purpose of this paper is to suggest a shift in emphasis from the large to the small scale: our analyses focus on a single epileptic seizure generation and the activation of a single fault (earthquake) and not on the statistics of sequences of different seizures and earthquakes. We apply the concepts of the nonextensive statistical physics to support the suggestion that a dynamical analogy exists between the two different extreme events, seizures and earthquakes. We also investigate the existence of such an analogy by means of scale-free statistics (the Gutenberg-Richter distribution of event sizes and the distribution of the waiting time until the next event). The performed analysis confirms the existence of a dynamic analogy between earthquakes and seizures, which moreover follow the dynamics of magnetic storms and solar flares. © 2012 Elsevier B.V. All rights reserved.