Method Of Critical Fluctuations Research Articles

Indications for an alternative breaking of symmetry in fracture-induced electromagnetic emissions recorded prior to the 2023 Mw7.8 and Mw7.5 Turkey Earthquakes

Several evidence has been reported corroborating the view that the MHz band fracture-induced electromagnetic emissions (FEME), also known as fracture-induced electromagnetic radiation (FEMR), which are detected prior to shallow main earthquakes (EQs) of moment magnitude Mw>5.5 with epicenters on land or near coastline, can be studied in analogy to a Z(2) spin system undergoing a second-order phase transition. Specifically, by analyzing MHz FEME/FEMR time series recorded prior to several earthquakes in the past >20 years, information has been extracted about the organization to critical state, the critical state itself, as well as for the step-by-step development of the spontaneous symmetry breaking (SSB) phenomenon. Using the “method of critical fluctuations” (MCF) and a recently proposed method for the wavelet-based detection of scaling behavior in noisy experimental data, we identified for the first time a different way of breaking the symmetry embedded in the MHz FEME/FEMR time series recorded by the hELlenic Seismo-ElectroMagnetics Network (ELSEM-Net) prior to the devastating (Mw=7.8 and Mw=7.5) EQs that occurred in south-east Turkey on 06/02/2023. Particularly, after the achievement of the critical state, indications were found that, although the underlying system started to break the symmetry according to the second-order phase transition mechanism (through SSB), SSB was not completed. Instead, the system seems to have changed symmetry and presented indications that the break of symmetry was finally achieved according to the first-order phase transition mechanism. Specifically, after the incomplete SSB, it was found to present tricritical behavior, followed by indications of triple degeneration of the order parameter fixed-point. This change of behavior observed in the MHz FEME/FEMR is a puzzling phenomenon for several reasons, which are discussed in detail, whereas suggestions are expressed as a first attempt for the possible explanation of the new findings.

Lower-ionosphere anomalies prior to strong earthquakes that occurred in north-central mainland Greece on March 2021 as revealed by multi-method analysis of VLF sub-ionospheric propagation data

In this work we present the multi-method analysis of very low frequency (VLF) data, acquired by the radio receiver with call name UWA, located in Athens (Greece), in the University of West Attica, focusing on two strong ( ) earthquakes (EQs) that occurred in north-central mainland Greece sequentially, on 3 and 4 March 2021, with very close epicenters. Specifically, we used the data acquired from seven VLF transmitters located in Europe, North/North-West to UWA, and their propagation paths include the specific EQs epicenters. We analyzed these data using multiple analysis methods in order to investigate for possible EQ-related anomalies, taking also into account all the other possibly ionosphere-influencing extreme events that occurred during the studied period. Especially, we applied the “nighttime fluctuation method” (NFM), as well as, the “terminator time method” (TTM) in order to reveal any statistical anomaly in the nighttime amplitude recordings of VLF sub-ionospheric propagation data within 15 days before each one examined EQs. Also, we calculated the scalogram (wavelet power spectrum over time) using Morlet mother wavelet of the same nighttime data searching for possible imprints of wave-like structures during the same time period. In terms of criticality analysis, first we applied the “natural time” (NT) analysis method to the daily-valued NFM VLF propagation quantities, and subsequently applied the “method of critical fluctuations” (MCF) to the raw nighttime amplitude VLF recordings, to check for any criticality signatures up to two weeks before the examined EQs. Taking into account all the above-mentioned analysis results, we conclude that there are multiple indications that the lower ionosphere was indeed disturbed due to the preparation processes of the above-mentioned EQs, offering different types of seismogenic indications.

Post-spontaneous-symmetry-breaking power-laws after a very strong earthquake: Indication for the preparation of a new strong earthquake or not?

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.

Can high-frequency ECG fluctuations differentiate between healthy and myocardial infarction cases?

The Electrocardiogram (ECG) is a standard diagnostic tool for heart's health condition, while the “gold standard” in ECG interpretation is still by observation by the cardiologist. In this article we show that the analysis of the high frequency ECG amplitude fluctuations, which are ignored during the conventional interpretation of the ECG by the cardiologist, regarded as measurement noise, can reveal any deviations from the ideal critical behavior as well as the degree of stability of the heart in stochastic stimulus. By applying the time series analysis method termed “method of critical fluctuations” (MCF) to cardiologist-annotated human ECGs – Physikalisch-Technische Bundesanstalt (PTB) Diagnostic ECG database – we show that it is possible to discriminated between ECGs from healthy and myocardial infarction subjects, as well as to quantify the degree to which they approach the “ideal” critical state or how far from criticality they are, respectively. MCF analysis 100% verifies the characterization of the ECGs belonging to the “Myocardial infarction” class by absence of critical fluctuations. Interestingly, a disagreement with the medical classification of the order of ∼10% was found for the ECGs belonging to the “Healthy controls” set. For the specific ECGs we also find no critical fluctuations, which is a strong deviation from the rest ∼90% of the ECGs belonging to the same class and present critical fluctuations. Moreover, based on a proposed reference ECG, the autocorrelation function can also be used to reveal any differentiation of the studied ECGs from the ideal critical state.

Statistical and Criticality Analysis of the Lower Ionosphere Prior to the 30 October 2020 Samos (Greece) Earthquake (M6.9), Based on VLF Electromagnetic Propagation Data as Recorded by a New VLF/LF Receiver Installed in Athens (Greece).

In this work we present the statistical and criticality analysis of the very low frequency (VLF) sub-ionospheric propagation data recorded by a VLF/LF radio receiver which has recently been established at the University of West Attica in Athens (Greece). We investigate a very recent, strong (M6.9), and shallow earthquake (EQ) that occurred on 30 October 2020, very close to the northern coast of the island of Samos (Greece). We focus on the reception data from two VLF transmitters, located in Turkey and Israel, on the basis that the EQ’s epicenter was located within or very close to the 5th Fresnel zone, respectively, of the corresponding sub-ionospheric propagation path. Firstly, we employed in our study the conventional analyses known as the nighttime fluctuation method (NFM) and the terminator time method (TTM), aiming to reveal any statistical anomalies prior to the EQ’s occurrence. These analyses revealed statistical anomalies in the studied sub-ionospheric propagation paths within ~2 weeks and a few days before the EQ’s occurrence. Secondly, we performed criticality analysis using two well-established complex systems’ time series analysis methods—the natural time (NT) analysis method, and the method of critical fluctuations (MCF). The NT analysis method was applied to the VLF propagation quantities of the NFM, revealing criticality indications over a period of ~2 weeks prior to the Samos EQ, whereas MCF was applied to the raw receiver amplitude data, uncovering the time excerpts of the analyzed time series that present criticality which were closest before the Samos EQ. Interestingly, power-law indications were also found shortly after the EQ’s occurrence. However, it is shown that these do not correspond to criticality related to EQ preparation processes. Finally, it is noted that no other complex space-sourced or geophysical phenomenon that could disturb the lower ionosphere did occur during the studied time period or close after, corroborating the view that our results prior to the Samos EQ are likely related to this mainshock.

Evidence of critical dynamics in various electromagnetic precursors

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 (<3 Hz) and the subionospheric very low frequency (VLF) propagation anomalies. We present recent analysis results for these electromagnetic signals using two independent methods which are known for their ability to uncover critical dynamics, the recently proposed method of critical fluctuations (MCF) and the natural time (NT) analysis method. Our results show that all three considered electromagnetic signals present critical characteristics from a few weeks up to a few days before the main shock occurrence. On the other hand, signatures for the departure from the critical (highly symmetrical) state towards a low symmetry state, a state during which there is high localization of the EQ preparatory process, have been identified in specific cases for the MHz fracto-EME as well as for the ULF magnetic field variations. Based on a multidisciplinary analysis, a four-stage model of EQ dynamics by means of fracto-EME in the MHz and kHz bands has recently been proposed. The hypothesis that the precursors considered in this article emerge during the spatially extensive phase of EQ preparation, which corresponds to the first stage of the abovementioned four-stage model, as well as their relation with the foreshock seismic activity are discussed.

On Possible Electromagnetic Precursors to a Significant Earthquake (Mw = 6.3) Occurred in Lesvos (Greece) on 12 June 2017.

This paper reports an attempt to use ultra-low-frequency (ULF) magnetic field data from a space weather monitoring magnetometer array in the study of earthquake (EQ) precursors in Greece. The data from four magnetometer stations of the HellENIc GeoMagnetic Array (ENIGMA) have been analyzed in the search for possible precursors to a strong EQ that occurred south of Lesvos Island on 12 June 2017, with magnitude Mw = 6.3 and focal depth = 12 km. The analysis includes conventional statistical methods, as well as criticality analysis, using two independent methods, the natural time (NT) method and the method of critical fluctuations (MCF). In terms of conventional statistical methods, it is found that the most convincing ULF precursor was observed in the data of ULF (20–30 mHz) depression (depression of the horizontal component of the magnetic field), which is indicative of lower ionospheric perturbation just 1 day before the EQ. Additionally, there are indications of a precursor in the direct ULF emission from the lithosphere 4 days to 1 day before the EQ. Further study in terms of NT analysis identifies criticality characteristics from 8 to 2 days before the EQ both for lithospheric ULF emission and ULF depression, while MCF reveals indications of criticality in all recorded magnetic field components, extending from 10 to 3 days before the EQ. Beyond the recordings of the geomagnetic stations of ENIGMA, the recordings of the fracto-electromagnetic emission stations of the HELlenic Seismo-ElectroMagnetics Network (ELSEM-Net) in Greece have been analyzed. The MHz recordings at the station that is located on Lesvos Island presented criticality characteristics (by means of both NT analysis and MCF) 11 days before the EQ, while a few days later (7–6 days before the EQ), the kHz recordings of the same station presented tricritical behavior. It is noted that the magnetosphere was quiet for a period of two weeks before the EQ and including its occurrence.

Analysis of the ultra-low frequency magnetic field fluctuations prior to the 2016 Kumamoto (Japan) earthquakes in terms of the method of critical fluctuations

The method of critical fluctuations (MCF) is a time series analysis method which provides a way of both identifying the critical state and the departure from it. Its application to the ground-based ultra-low frequency (ULF) magnetic field fluctuations observed prior to the very strong earthquakes (EQs) of magnitudes MW=6.2, MW=6.0 and MW=7.0 which sequentially took place within a two days period (April 14–15, 2016) in Southwest Japan under the city of Kumamoto reveals when the underlying process reached critical state, as well as when it departed from critical state. Specifically, critical dynamics was identified in the raw total geomagnetic field intensity (F) ULF recordings of the Kanoya (Japan) station ∼4 d before the MW=6.2 and ∼5 d before the MW=7.0 event. Moreover, the progressive development of the symmetry breaking phenomenon, which signifies departure from critical state, was identified in later recordings. Specifically the phenomenon evolved from a few hours before the MW=6.0 event until a few hours after the occurrence of the specific EQ, which was a few hours before the MW=7.0 event. The detected combination of phenomena, i.e., the detection of critical state followed by the detection of the departure from the critical state by means of symmetry breaking, indicates that the main event was the third and strongest EQ, while the two preceding EQs were strong foreshocks.

Intermittency-induced criticality in the lower ionosphere prior to the 2016 Kumamoto earthquakes as embedded in the VLF propagation data observed at multiple stations

A network of 8 VLF/LF receivers has recently been established across Japan, receiving subionospheric signals from different transmitters located both in the same and other countries. The primary purpose of this network is to study disturbances in the VLF/LF propagation through the lower ionosphere in possible relation to earthquake (EQ) preparation processes. Ionospheric perturbations of possible seismic origin have long been investigated and considered very promising for short-term EQ prediction. The raw amplitude data on reception of the above-mentioned network, after being appropriately filtered, were analyzed by means of the method of critical fluctuations (MCF) in analogy to thermal critical systems. The MCF analysis of the VLF/LF propagation revealed that intermittency-induced criticality was reached in the lower ionosphere from ~1week to 3days prior to the catastrophic 2016 Kumamoto EQs. These fault-type EQs occurred within a two-day period (14 April: MW=6.2 and MW=6.0, 15 April: MW=7.0) at shallow depths (~10km) and very close epicenters, while the main event was as huge as the former 1995 Kobe EQ. MCF analysis results are compared to those by the conventional nighttime fluctuation method as well as to those by natural time analysis method obtained for the same dataset, and are found to exhibit remarkable consistency.

Recent seismic activity at Cephalonia (Greece): a study through candidate electromagnetic precursors in terms of non-linear dynamics

Abstract. The preparation process of two recent earthquakes (EQs) that occurred in Cephalonia (Kefalonia), Greece, ((38.22° N, 20.53° E), 26 January 2014, Mw = 6.0, depth ∼ 20 km) and ((38.25° N, 20.39° E), 3 February 2014, Mw = 5.9, depth ∼ 10 km), respectively, is studied in terms of the critical dynamics revealed in observables of the involved non-linear processes. Specifically, we show, by means of the method of critical fluctuations (MCF), that signatures of critical, as well as tricritical, dynamics were embedded in the fracture-induced electromagnetic emissions (EMEs) recorded by two stations in locations near the epicentres of these two EQs. It is worth noting that both the MHz EMEs recorded by the telemetric stations on the island of Cephalonia and the neighbouring island of Zante (Zakynthos) reached a simultaneously critical condition a few days before the occurrence of each earthquake. The critical characteristics embedded in the EME signals were further verified using the natural time (NT) method. Moreover, we show, in terms of the NT method, that the foreshock seismic activity also presented critical characteristics before each event. Importantly, the revealed critical process seems to be focused on the area corresponding to the western Cephalonia zone, following the seismotectonic and hazard zoning of the Ionian Islands area near Cephalonia.

Intermittent criticality revealed in ULF magnetic fields prior to the 11 March 2011 Tohoku earthquake ([formula omitted

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.

Recent Field Observations Indicating an Earth System in Critical Condition Before the Occurrence of a Significant Earthquake

In this letter, we show, in terms of the fractureinduced electromagnetic emissions (EME) recorded prior to the earthquake of Chania, Greece [(35.50° N, 23.28° E); October 12, 2013; M w = 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.

Tricritical crossover in earthquake preparation by analyzing preseismic electromagnetic emissions

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.