Entropy of seismic electric signals: analysis in natural time under time reversal

Critical Dynamics in Stratospheric Potential Energy Variations Prior to Significant (M > 6.7) Earthquakes

Lithosphere–atmosphere–ionosphere coupling (LAIC) is studied through various physical or chemical quantities, obtained from different sources, which are observables of the involved complex processes. LAIC has been proposed to be achieved through three major channels: the chemical, the acoustic, and the electromagnetic. Accumulated evidence supporting the acoustic channel hypothesis has been published, while atmospheric gravity waves (AGWs) play a key role in LAIC as the leading mechanism for the transmission of energy from the lower atmosphere to the stratosphere and mesosphere, associated with atmospheric disturbances observed prior to strong earthquakes (EQs). The seismogenic AGW is the result of temperature disturbances, usually studied through stratospheric potential energy (EP). In this work, we examined 11 cases of significant EQs (M > 6.7) that occurred during the last 10 years at different geographic areas by analyzing the temperature profile at the wider location of each one of the examined EQs. The “Sounding of the Atmosphere using Broadband Emission Radiometry” (SABER) instrument, part of the “Thermosphere Ionosphere Mesosphere Energetics Dynamics” (TIMED) satellite, data were employed to compute the potential energy (EP) of the AGW. Using the temperature profile, we first calculated EP and determined the altitudes’ range for which prominent pre-seismic disturbances were observed. Subsequently, the EP time series at specific altitudes, within the determined “disturbed” range, were for the first time analyzed using the criticality analysis method termed the “natural time” (NT) method in order to find any evidence of an approach to a critical state (during a phase transition from a symmetric phase to a low symmetry phase) prior to the EQ occurrence. Our results show criticality indications in the fluctuation of EP a few days (1 to 15 days) prior to the examined EQs, except from one case. In our study, we also examined all of the temperature-related extreme phenomena that have occurred near the examined geographic areas, in order to take into account any possible non-seismic influence on the obtained results.

Order Parameter and Entropy of Seismicity in Natural Time before Major Earthquakes: Recent Results

A lot of work in geosciences has been completed during the last decade on the analysis in the new concept of time, termed natural time, introduced in 2001. The main advances are presented, including, among others, the following: First, the direct experimental verification of the interconnection between a Seismic Electric Signals (SES) activity and seismicity, i.e., the order parameter fluctuations of seismicity exhibit a clearly detectable minimum when an SES activity starts. These two phenomena are also linked closely in space. Second, the identification of the epicentral area and the occurrence time of an impending major earthquake (EQ) by means of the order parameter of seismicity and the entropy change of seismicity under time reversal as well as the extrema of their fluctuations. An indicative example is the M9 Tohoku EQ in Japan on 11 March 2011. Third, to answer the crucial question—when a magnitude 7 class EQ occurs—whether it is a foreshock or a mainshock. This can be answered by means of the key quantities already mentioned, i.e., the order parameter of seismicity and the entropy change of seismicity under time reversal along with their fluctuations. The explanation of the experimental findings identified before major EQs is given in a unified way on the basis of a physical model already proposed in the 1980s.

Comparative Assessment of Criticality Indices Extracted from Acoustic and Electrical Signals Detected in Marble Specimens

The quantitative determination of the current load carrying capability of already loaded structural elements and the possibility to detect proper indices that could be considered as signals for timely warning that the load carrying capacity is exhausted is the subject of this study. More specifically, it aims to explore the possibility of detecting signals that can be considered as indices warning about upcoming fracture and then to compare quantitatively such signals provided by different techniques. The novelty of the present study lies exactly in this quantitative comparison of the pre-failure signals provided by various sensing techniques and various methods of analysis of the experimental data. To achieve this target, advantage is taken of data concerning the acoustic and electrical activities produced while marble specimens are subjected to mechanical loading. The respective signals are detected and recorded by means of the acoustic emissions technique and that of the pressure stimulated currents. The signals detected by the acoustic emissions technique are analyzed in terms of three formulations, i.e., the b-value, the F-function and the parameters variance κ1, entropy S and entropy under time reversal S_ according to the natural time analysis. The signals detected by the pressure stimulated currents technique are analyzed by means of the intensity of the electric current recorded. The study indicates that all quantities considered provide promising pre-failure indicators. Furthermore, when the specimen is subjected to near-to-failure load levels, the temporal evolution of three of the quantities studied (b-value, F-function, pressure stimulated currents) is governed by a specific power law. The onset of validity of this law designates some differentiation of the damage mechanisms activated. Quantitative differences are observed between the time instants at which this power law starts dictating the evolution of the above parameters, indicating the imperative need for further investigation, despite the quite encouraging results of the present study.

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.

Unusual Surface Latent Heat Flux Variations and Their Critical Dynamics Revealed before Strong Earthquakes

We focus on the possible thermal channel of the well-known Lithosphere–Atmosphere–Ionosphere Coupling (LAIC) mechanism to identify the behavior of thermal anomalies during and prior to strong seismic events. For this, we investigate the variation of Surface Latent Heat Flux (SLHF) as resulting from satellite observables. We demonstrate a spatio-temporal variation in the SLHF before and after a set of strong seismic events occurred in Kathmandu, Nepal, and Kumamoto, Japan, having magnitudes of 7.8, 7.3, and 7.0, respectively. Before the studied earthquake cases, significant enhancements in the SLHF were identified near the epicenters. Additionally, in order to check whether critical dynamics, as the signature of a complex phenomenon such as earthquake preparation, are reflected in the SLHF data, we performed a criticality analysis using the natural time analysis method. The approach to criticality was detected within one week before each mainshock.

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.

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.

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.

Natural Time Analysis of Seismicity within the Mexican Flat Slab before the M7.1 Earthquake on 19 September 2017

One of the most important subduction zones in the world is located in the Mexican Pacific Coast, where the Cocos plate inserts beneath the North American plate. One part of it is located in the Mexican Pacific Coast, where the Cocos plate inserts beneath the North American plate with different dip angles, showing important seismicity. Under the central Mexican area, such a dip angle becomes practically horizontal and such an area is known as flat slab. An earthquake of magnitude M7.1 occurred on 19 September 2017, the epicenter of which was located in this flat slab. It caused important human and material losses of urban communities including a large area of Mexico City. The seismicity recorded in the flat slab region is analyzed here in natural time from 1995 until the occurrence of this M7.1 earthquake in 2017 by studying the entropy change under time reversal and the variability β of the order parameter of seismicity as well as characterize the risk of an impending earthquake by applying the nowcasting method. The entropy change ΔS under time reversal minimizes on 21 June 2017 that is almost one week after the observation of such a minimum in the Chiapas region where a magnitude M8.2 earthquake took place on 7 September 2017 being Mexico’s largest quake in more than a century. A minimum of β was also observed during the period February–March 2017. Moreover, we show that, after the minimum of ΔS, the order parameter of seismicity starts diminishing, thus approaching gradually the critical value 0.070 around the end of August and the beginning of September 2017, which signals that a strong earthquake is anticipated shortly in the flat slab.

Natural Time Analysis of Global Navigation Satellite System Surface Deformation: The Case of the 2016 Kumamoto Earthquakes

In order to have further evidence of the atmospheric oscillation channel of the lithosphere-atmosphere-ionosphere coupling (LAIC), we have studied criticality in global navigation satellite system (GNSS) surface deformation as a possible agent for exciting atmospheric gravity waves (AGWs) in the atmosphere and GNSS fluctuations in the frequency range of AGWs with the use of the natural time (NT) method. The target earthquake (EQ) is the 2016 Kumamoto EQ with its main shock on 15 April 2016 (M = 7.3, universal time). As the result of the application of the NT method to GNSS data, we found that for the one-day sampled GNSS deformation data and its fluctuations in two AGW bands of 20-100 and 100-300 min, we could detect a criticality in the period of 1-14 April, which was one day to two weeks before the EQ. These dates of criticalities are likely to overlap with the time periods of previous results on clear AGW activity in the stratosphere and on the lower ionospheric perturbation. Hence, we suggest that the surface deformation could be a possible candidate for exciting those AGWs in the stratosphere, leading to the lower ionospheric perturbation, which lends further support to the AGW hypothesis of the LAIC process.

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.

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.

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%.

Time series analysis in earthquake complex networks

We introduce a new method of characterizing the seismic complex systems using a procedure of transformation from complex networks into time series. The undirected complex network is constructed from seismic hypocenters data. Network nodes are marked by their connectivity. The walk on the graph following the time of succeeding seismic events generates the connectivity time series which contains, both the space and time, features of seismic processes. This procedure was applied to four seismic data sets registered in Chile. It was shown that multifractality of constructed connectivity time series changes due to the particular geophysics characteristics of the seismic zones-it decreases with the occurrence of large earthquakes-and shows the spatiotemporal organization of these seismic systems.

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.

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.

Entropy measures, entropy estimators, and their performance in quantifying complex dynamics: Effects of artifacts, nonstationarity, and long-range correlations

Entropy measures are widely applied to quantify the complexity of dynamical systems in diverse fields. However, the practical application of entropy methods is challenging, due to the variety of entropy measures and estimators and the complexity of real-world time series, including nonstationarities and long-range correlations (LRC). We conduct a systematic study on the performance, bias, and limitations of three basic measures (entropy, conditional entropy, information storage) and three traditionally used estimators (linear, kernel, nearest neighbor). We investigate the dependence of entropy measures on estimator- and process-specific parameters, and we show the effects of three types of nonstationarities due to artifacts (trends, spikes, local variance change) in simulations of stochastic autoregressive processes. We also analyze the impact of LRC on the theoretical and estimated values of entropy measures. Finally, we apply entropy methods on heart rate variability data from subjects in different physiological states and clinical conditions. We find that entropy measures can only differentiate changes of specific types in cardiac dynamics and that appropriate preprocessing is vital for correct estimation and interpretation. Demonstrating the limitations of entropy methods and shedding light on how to mitigate bias and provide correct interpretations of results, this work can serve as a comprehensive reference for the application of entropy methods and the evaluation of existing studies.

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.

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.

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.

On the limits of the air pollution predictability: the case of the surface ozone at Athens, Greece

PURPOSE

The aim of this study is to investigate the potential effects of increased urbanization in the Athens city, Greece on the intrinsic features of the temporal fluctuations of the surface ozone concentration (SOC).

METHODS

The detrended fluctuation analysis was applied to the mean monthly values of SOC derived from ground-based observations collected at the centre of Athens basin during 1901-1940 and 1987-2007.

RESULTS

Despite the present-day SOC doubling in respect to SOC historic levels, its fluctuations exhibit long-range power-law persistence, with similar features in both time periods. This contributes to an improved understanding of our predictive powers and enables better environmental management and more efficient decision-making processes.

CONCLUSIONS

The extensive photochemistry enhancement observed in the Athens basin from the beginning of the twentieth century until the beginning of the twenty-first century seems not to have affected the long memory of SOC correlations. The strength of this memory stems from its temporal evolution and provides the limits of the air pollution predictability at various time scales.

The role of the isothermal bulk modulus in the molecular dynamics of super-cooled liquids

Elastic models imply that the energy expended for a flow event in ultra-viscous matter coincides with the elastic work required for deforming and re-arranging the environment of the moving entity. This is quite promising for explaining the strong non-Arrhenius behavior of dynamic quantities of fragile super-cooled liquids. We argue that the activation volume obtained from dielectric relaxation and light-scattering experiments for super-cooled liquids should scale with the Gibbs free energy of activation, with a proportionality constant determined by the isothermal bulk modulus and its pressure derivative, as described by an earlier thermodynamic elastic model. For certain super-cooled liquids the bulk compression transpiring in the local environment, as governed by the isothermal bulk modulus, play a significant role in the reorientational dynamics, with far-field density fluctuations and volume changes avoided by shear deformation.

Magnitude correlations in global seismicity

By employing natural time analysis, we analyze the worldwide seismicity and study the existence of correlations between earthquake magnitudes. We find that global seismicity exhibits nontrivial magnitude correlations for earthquake magnitudes greater than M(w) 6.5.

Natural time analysis of critical phenomena

A quantity exists by which one can identify the approach of a dynamical system to the state of criticality, which is hard to identify otherwise. This quantity is the variance κ(1)(≡<χ(2)> - <χ>(2)) of natural time χ, where <f(χ)> = Σp(k)f(χ(k)) and p(k) is the normalized energy released during the kth event of which the natural time is defined as χ(k) = k/N and N stands for the total number of events. Then we show that κ(1) becomes equal to 0.070 at the critical state for a variety of dynamical systems. This holds for criticality models such as 2D Ising and the Bak-Tang-Wiesenfeld sandpile, which is the standard example of self-organized criticality. This condition of κ(1) = 0.070 holds for experimental results of critical phenomena such as growth of rice piles, seismic electric signals, and the subsequent seismicity before the associated main shock.

Effect of significant data loss on identifying electric signals that precede rupture estimated by detrended fluctuation analysis in natural time

Electric field variations that appear before rupture have been recently studied by employing the detrended fluctuation analysis (DFA) to quantify their long-range temporal correlations. These studies revealed that seismic electric signal (SES) activities exhibit a scale invariant feature with an exponent αDFA≈1 over all scales investigated (around five orders of magnitude). Here, we study what happens upon significant data loss, which is a question of primary practical importance, and show that the DFA applied to the natural time representation of the remaining data still reveals for SES activities an exponent close to 1.0, which markedly exceeds the exponent found in artificial (man-made) noises. This enables the identification of a SES activity with probability of 75% even after a significant (70%) data loss. The probability increases to 90% or larger for 50% data loss.

Nonextensivity and natural time: The case of seismicity

Nonextensive statistical mechanics, pioneered by Tsallis, has recently achieved a generalization of the Gutenberg-Richter law for earthquakes. This remarkable generalization is combined here with natural time analysis, which enables the distinction of two origins of self-similarity, i.e., the process' memory and the process' increments infinite variance. By using also detrended fluctuation analysis for the detection of long-range temporal correlations, we demonstrate the existence of both temporal and magnitude correlations in real seismic data of California and Japan. Natural time analysis reveals that the nonextensivity parameter q , in contrast to some published claims, cannot be considered as a measure of temporal organization, but the Tsallis formulation does achieve a satisfactory description of real seismic data for Japan for q=1.66 when supplemented by long-range temporal correlations.

A new modeling tool for the diffusion of gases in ice or amorphous binary mixture in the polar stratosphere and the upper troposphere

Abstract. To elaborate stratospheric ozone depletion processes, measurements of diffusion coefficients of selected gas phase molecules (i.e. HCl, CH3OH, HCOOH and CH3COOH; Katsambas et al., 1997; Kondratyev and Varotsos, 1996; Varotsos et al., 1994, 1995) in ice in the temperature range 170–195 K have been analyzed with respect to the mechanisms and rates of diffusion. It is argued that the diffusion in ice of these compounds is governed by a vacancy – mediated mechanism, i.e. H2O vacancies are required to diffuse to lattice sites adjacent to these compounds prior to the diffusion of the corresponding molecule into the vacancy sites. In addition, we show that the diffusion coefficients of these compounds exhibit a specific interconnection, i.e. a linear relationship holds between the logarithm of the pre-exponential factor, Do, and the activation energy E. The physical meaning of this interconnection is discussed.

Multiplicative cascades and seismicity in natural time

Natural time chi enables the distinction of two origins of self-similarity, i.e., the process memory and the process increments infinite variance. Employing multiplicative cascades in natural time, the most probable value of the variance kappa(1)(is identical to chi(2)-chi(2))is explicitly related with the parameter b of the Gutenberg-Richter law of randomly shuffled earthquake data. Moreover, the existence of temporal and magnitude correlations is studied in the original earthquake data. Magnitude correlations are larger for closer in time earthquakes, when the maximum interoccurrence time varies from half a day to 1 min.

Detrended fluctuation analysis of the magnetic and electric field variations that precede rupture

Magnetic field variations are detected before rupture in the form of "spikes" of alternating sign. The distinction of these spikes from random noise is of major practical importance since it is easier to conduct magnetic field measurements than electric field ones. Applying detrended fluctuation analysis (DFA), these spikes look to be random at short time lags. On the other hand, long-range correlations prevail at time lags larger than the average time interval between consecutive spikes with a scaling exponent alpha around 0.9. In addition, DFA is applied to recent preseismic electric field variations in long duration (several hours to a couple of days) and reveals a scale invariant feature with an exponent alpha approximately 1 over all scales available (around five orders of magnitude).

Investigation of seismicity after the initiation of a Seismic Electric Signal activity until the main shock

The behavior of seismicity in the area candidate to suffer a main shock is investigated after the observation of the Seismic Electric Signal activity until the impending main shock. This is based on the view that the occurrence of earthquakes is a critical phenomenon to which statistical dynamics may be applied. In the present work, analysing the time series of small earthquakes, the concept of natural time chi was used and the results revealed that the approach to criticality itself can be manifested by the probability density function (PDF) of kappa(1) calculated over an appropriate statistical ensemble. Here, kappa(1) is the variance kappa(1)(=<chi(2)>-<chi>(2)) resulting from the power spectrum of a function defined as Phi(omega)= summation operator(k=1)(N) p(k) exp(iomegachi(k)), where p(k) is the normalized energy of the k-th small earthquake and omega the natural frequency. This PDF exhibits a maximum at kappa(1) asymptotically equal to 0.070 a few days before the main shock. Examples are presented, referring to the magnitude 6 approximately 7 class earthquakes that occurred in Greece.

Investigation of seismicity after the initiation of a Seismic Electric Signal activity until the main shock

The behavior of seismicity in the area candidate to suffer a main shock is investigated after the observation of the Seismic Electric Signal activity until the impending main shock. This is based on the view that the occurrence of earthquakes is a critical phenomenon to which statistical dynamics may be applied. In the present work, analysing the time series of small earthquakes, the concept of natural time chi was used and the results revealed that the approach to criticality itself can be manifested by the probability density function (PDF) of kappa(1) calculated over an appropriate statistical ensemble. Here, kappa(1) is the variance kappa(1)(=-(2)) resulting from the power spectrum of a function defined as Phi(omega)= summation operator(k=1)(N) p(k) exp(iomegachi(k)), where p(k) is the normalized energy of the k-th small earthquake and omega the natural frequency. This PDF exhibits a maximum at kappa(1) asymptotically equal to 0.070 a few days before the main shock. Examples are presented, referring to the magnitude 6 approximately 7 class earthquakes that occurred in Greece.

Technical Note: Long-term memory effect in the atmospheric CO&lt;sub&gt;2&lt;/sub&gt; concentration at Mauna Loa

Abstract. The monthly mean values of the atmospheric carbon dioxide concentration derived from in-situ air samples collected at Mauna Loa Observatory, Hawaii, USA during 1958–2004 (the longest continuous record available in the world) are analyzed by employing the detrended fluctuation analysis to detect scaling behavior in this time series. The main result is that the fluctuations of carbon dioxide concentrations exhibit long-range power-law correlations (long memory) with lag times ranging from four months to eleven years, which correspond to 1/f noise. This result indicates that random perturbations in the carbon dioxide concentrations give rise to noise, characterized by a frequency spectrum following a power-law with exponent that approaches to one; the latter shows that the correlation times grow strongly. This feature is pointing out that a correctly rescaled subset of the original time series of the carbon dioxide concentrations resembles the original time series. Finally, the power-law relationship derived from the real measurements of the carbon dioxide concentrations could also serve as a tool to improve the confidence of the atmospheric chemistry-transport and global climate models.

Long-memory processes in ozone and temperature variations at the region 60° S–60° N

Abstract. Global column ozone and tropospheric temperature observations made by ground-based (1964–2004) and satellite-borne (1978–2004) instrumentation are analyzed. Ozone and temperature fluctuations in small time-intervals are found to be positively correlated to those in larger time-intervals in a power-law fashion. For temperature, the exponent of this dependence is larger in the mid-latitudes than in the tropics at long time scales, while for ozone, the exponent is larger in tropics than in the mid-latitudes. In general, greater persistence could be a result of either stronger positive feedbacks or larger inertia. Therefore, the increased slope of the power distribution of temperature in mid-latitudes at long time scales compared to the slope in the tropics could be connected to the poleward increase in climate sensitivity predicted by the global climate models. The detrended fluctuation analysis of model and observed time series provides a helpful tool for visualizing errors in the treatment of long-range correlations, whose correct modeling would greatly enhance confidence in long-term climate and atmospheric chemistry modeling.

Attempt to distinguish long-range temporal correlations from the statistics of the increments by natural time analysis

Self-similarity may originate from two origins: i.e., the process memory and the process' increments "infinite" variance. A distinction is attempted by employing the natural time chi . Concerning the first origin, we analyze recent data on seismic electric signals, which support the view that they exhibit infinitely ranged temporal correlations. Concerning the second, slowly driven systems that emit bursts of various energies E obeying the power-law distribution--i.e., P(E) approximately E(-gamma)--are studied. An interrelation between the exponent gamma and the variance kappa1(identical with <chi2> - <chi2>) is obtained for the shuffled (randomized) data. For real earthquake data, the most probable value of kappa1 of the shuffled data is found to be approximately equal to that of the original data, the difference most likely arising from temporal correlation. Finally, it is found that the differential entropy associated with the probability P(kappa1) maximizes for gamma around gamma approximately 1.6-1.7 , which is comparable to the value determined experimentally in diverse phenomena: e.g., solar flares, icequakes, dislocation glide in stressed single crystals of ice, etc. It also agrees with the b value in the Gutenberg-Richter law of earthquakes. In addition, the case of multiplicative cascades is studied in the natural time domain.

What happened before the last five strong earthquakes in Greece: Facts and open questions

During the period October 2005 - January 2006, five strong earthquakes occurred in Greece as follows: three magnitude 6.0 consecutive earthquakes with almost the same epicenter in the Aegean Sea close to the western coast of Turkey, one magnitude 6.1 in western Greece and one magnitude 6.9 in southern Greece. In March 2005 and September 2005, intense anomalous geoelectric changes were observed at two different stations respectively: one in the Aegean Sea and the other in western Greece. These changes were immediately reported to international journals well in advance of earthquake occurrences. Natural time analysis of seismicity subsequent to the September changes around the epicenter of the last 6.9 earthquake is made. The results indicate that the occurrence time of the 6.9 earthquake can be specified with a narrow range around two days.