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

Prognostic Properties of Instantaneous Amplitudes Maxima of Earth Surface Tremor

A method is proposed for analyzing the tremor of the earth's surface, measured by GPS, in order to highlight prognostic effects. The method is applied to the analysis of daily time series of vertical displacements in Japan. The network of 1047 stations is divided into 15 clusters. The Huang Empirical Mode Decomposition (EMD) is applied to the time series of the principal components from the clusters, with subsequent calculation of instantaneous amplitudes using the Hilbert transform. To ensure the stability of estimates of the waveforms of the EMD decomposition, 1000 independent additive realizations of white noise of limited amplitude were averaged before the Hilbert transform. Using a parametric model of the intensities of point processes, we analyze the connections between the instants of sequences of times of the largest local maxima of instantaneous amplitudes, averaged over the number of clusters and the times of earthquakes in the vicinity of Japan with minimum magnitude thresholds of 5.5 for the time interval 2012-2023. It is shown that the sequence of the largest local maxima of instantaneous amplitudes significantly more often precedes the moments of time of earthquakes (roughly speaking, has an "influence") than the reverse "influence" of earthquakes on the maxima of amplitudes.

Complexity in Geophysical Time Series of Strain/Fracture at Laboratory and Large Dam Scales: Review

One of the interesting directions of complexity theory is the investigation of the synchronization of mechanical behavior of large-scale systems by weak forcing, which is one of manifestations of nonlinearity/complexity of a system. The effect of periodic weak mechanical or electromagnetic forcing leading to synchronization was studied on the laboratory load-spring system as well as on a big dam's strain data. Due to synchronization, the phase space structure of the forced system strongly depends on the weak forcing intensity-determinism show itself in the recurrence of definite states of the forced system. The nonlinear dynamics of tilts/strains/seismicity near grand dams reflect both the complexity of the mentioned time series, connected with the natural agents (regional and local geodynamics), which were presented even before dam erection, as well as the effects of the water level (WL) variation in the reservoir, which is a quasi-periodic forcing superimposed on the natural geodynamic background. Both these effects are documented by the almost half-century of observations at the large Enguri Dam. The obtained data on the dynamics of strain/seismicity near a large dam can be used for the assessment of the possible risks, connected with the abrupt change of routine dynamics of construction.

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.

Scaling Behavior of Peat Properties during the Holocene: A Case Study from Central European Russia

A better understanding of past climate change is vital to our ability to predict possible future environmental dynamics. This study attempts to investigate the dynamic features of the temporal variability of peat humification, water table depth and air temperature by analyzing palaeoecological data from the Valdai Uplands region (Central European Russia). The regression analysis revealed the presence of a periodicity of about 6000 years in the reconstructed peat humification timeseries. Nonlinear analysis showed that humification time variability, water table depth and air temperature exhibit persistent long-range correlations of 1/f type. This indicates that a fluctuation in these variables in the past is very likely to be followed by a similar one in the future, but is magnified by 1/f power-law. In addition, it dictates that humification, water table depth and temperature are key parameters of a system that implies the existence of a special structure, such as self-organized criticality, operating close to a minimum stability configuration, and achieves it without any fine adjustment by external forcing. These conclusions point to new avenues for modeling future ecosystem disturbances and, in particular, for predicting relevant extreme events.

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.

Nonlinear Statistical Features of the Seismicity in the Subduction Zone of Tehuantepec Isthmus, Southern México

After the M8.2 main-shock occurred on 7 September 2017 at the Isthmus of Tehuantepec, Mexico, the spatial distribution of seismicity has showed a clear clusterization of earthquakes along the collision region of the Tehuantepec Transform/Ridge with the Middle America Trench off Chiapas. Furthermore, nowadays, the temporal rate of occurrence in the number of earthquakes has also showed a pronounced increase. On the basis of this behavior, we studied the sequence of magnitudes of the earthquakes which occurred within the Isthmus of Tehuantepec in southern Mexico from 2010 to 2020. Since big earthquakes are considered as a phase transition, after the M8.2 main-shock, one must expect changes in the Tehuantepec ridge dynamics, which can be observed considering that the b-value in the Gutenberg–Richter law, has also showed changes in time. The goal of this paper is to characterize the behavior of the seismic activity by using the Gutenberg–Richter law, multifractal detrended fluctuation analysis, visibility graph and nowcasting method. Those methods have showed important parameters in order to assess risk, the multifractality and connectivity. Our findings indicate, first that b-value shows a dependency on time, which is clearly described by our analyses based on nowcasting method, multifractality and visibility graph.

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.

Low-Frequency Seismic Noise Properties in the Japanese Islands

The records of seismic noise in Japan for the period of 1997-2020, which includes the Tohoku seismic catastrophe on 11 March 2011, are considered. The following properties of noise are analyzed: The wavelet-based Donoho-Johnston index, the singularity spectrum support width, and the entropy of the wavelet coefficients. The question of whether precursors of strong earthquakes can be formulated on their basis is investigated. Attention is paid to the time interval after the Tohoku mega-earthquake to the trends in the mean properties of low-frequency seismic noise, which reflect the constant simplification of the statistical structure of seismic vibrations. Estimates of two-dimensional probability densities of extreme values are presented, which highlight the places in which extreme values of seismic noise properties are most often realized. The estimates of the probability densities of extreme values coincide with each other and have a maximum in the region: 30° N ≤ Lat ≤ 34° N, 136° E ≤ Lon≤ 140° E. The main conclusions of the conducted studies are that the preparation of a strong earthquake is accompanied by a simplification of the structure of seismic noise. It is shown that bursts of coherence between the time series of the day length and the noise properties within annual time window precede bursts of released seismic energy. The value of the lag in the release of seismic energy relative to bursts of coherence is about 1.5 years, which can be used to declare a time interval of high seismic hazard after reaching the peak of coherence.

New insights and best practices for the successful use of Empirical Mode Decomposition, Iterative Filtering and derived algorithms

Algorithms based on Empirical Mode Decomposition (EMD) and Iterative Filtering (IF) are largely implemented for representing a signal as superposition of simpler well-behaved components called Intrinsic Mode Functions (IMFs). Although they are more suitable than traditional methods for the analysis of nonlinear and nonstationary signals, they could be easily misused if their known limitations, together with the assumptions they rely on, are not carefully considered. In this work, we examine the main pitfalls and provide caveats for the proper use of the EMD- and IF-based algorithms. Specifically, we address the problems related to boundary errors, to the presence of spikes or jumps in the signal and to the decomposition of highly-stochastic signals. The consequences of an improper usage of these techniques are discussed and clarified also by analysing real data and performing numerical simulations. Finally, we provide the reader with the best practices to maximize the quality and meaningfulness of the decomposition produced by these techniques. In particular, a technique for the extension of signal to reduce the boundary effects is proposed; a careful handling of spikes and jumps in the signal is suggested; the concept of multi-scale statistical analysis is presented to treat highly stochastic signals.

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: The Area under the Receiver Operating Characteristic Curve of the Order Parameter Fluctuations Minima Preceding Major Earthquakes

It has been reported that major earthquakes are preceded by Seismic Electric Signals (SES). Observations show that in the natural time analysis of an earthquake (EQ) catalog, an SES activity starts when the fluctuations of the order parameter of seismicity exhibit a minimum. Fifteen distinct minima—observed simultaneously at two different natural time scales and deeper than a certain threshold—are found on analyzing the seismicity of Japan from 1 January 1984 to 11 March 2011 (the time of the M9 Tohoku EQ occurrence) 1 to 3 months before large EQs. Six (out of 15) of these minima preceded all shallow EQs of magnitude 7.6 or larger, while nine are followed by smaller EQs. The latter false positives can be excluded by a proper procedure (J. Geophys. Res. Space Physics 2014, 119, 9192–9206) that considers aspects of EQ networks based on similar activity patterns. These results are studied here by means of the receiver operating characteristics (ROC) technique by focusing on the area under the ROC curve (AUC). If this area, which is currently considered an effective way to summarize the overall diagnostic accuracy of a test, has the value 1, it corresponds to a perfectly accurate test. Here, we find that the AUC is around 0.95 which is evaluated as outstanding.

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.