Complexity measure in natural time analysis identifying the accumulation of stresses before major earthquakes.

Here, we suggest a procedure through which one can identify when the accumulation of stresses before major earthquakes (EQs) (of magnitude M 8.2 or larger) occurs. Analyzing the seismicity in natural time, which is a new concept of time, we study the evolution of the fluctuations of the entropy change of seismicity under time reversal for various scales of different length i (number of events).

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

It has recently been shown in the Eastern Mediterranean that by combining natural time analysis of seismicity with earthquake networks based on similar activity patterns and earthquake nowcasting, an estimate of the epicenter location of a future strong earthquake can be obtained. This is based on the construction of average earthquake potential score maps. Here, we propose a method of obtaining such estimates for a highly seismically active area that includes Southern California, Mexico and part of Central America, i.

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.

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.

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.

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

The observed earthquake scaling laws indicate the existence of phenomena closely associated with the proximity of the system to a critical point. Taking this view that earthquakes are critical phenomena (dynamic phase transitions), here we investigate whether in this case the Lifshitz-Slyozov-Wagner (LSW) theory for phase transitions showing that the characteristic size of the minority phase droplets grows with time as t 1 / 3 is applicable. To achieve this goal, we analyzed the Japanese seismic data in a new time domain termed natural time and find that an LSW behavior is actually obeyed by a precursory change of seismicity and in particular by the fluctuations of the entropy change of seismicity under time reversal before the Tohoku earthquake of magnitude 9.

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

We analyse seismicity during the 6-year period 2012-2017 in the new time domain termed natural time in the Chiapas region where the M8.2 earthquake occurred, Mexico's largest earthquake in more than a century, in order to study the complexity measures associated with fluctuations of entropy as well as with entropy change under time reversal. We find that almost three months before the M8.

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

Using the Japan Meteorological Agency earthquake catalog, we investigate the seismicity variations before major earthquakes in the Japanese region. We apply natural time, the new time frame, for calculating the fluctuations, termed β, of a certain parameter of seismicity, termed κ1. In an earlier study, we found that β calculated for the entire Japanese region showed a minimum a few months before the shallow major earthquakes (magnitude larger than 7.

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

It has been shown that some dynamic features hidden in the time series of complex systems can be uncovered if we analyze them in a time domain called natural time χ. The order parameter of seismicity introduced in this time domain is the variance of χ weighted for normalized energy of each earthquake. Here, we analyze the Japan seismic catalog in natural time from January 1, 1984 to March 11, 2011, the day of the M9 Tohoku earthquake, by considering a sliding natural time window of fixed length comprised of the number of events that would occur in a few months.

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 = 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.

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.

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.

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.

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.

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.

Self-diffusion in sodium under pressure revisited.

The pressure-volume relation in sodium has been measured up to 100 GPa using high-resolution angle-dispersive synchrotron x-ray diffraction (Hanfland et al 2002 Phys. Rev. B 65 184109).

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.

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

Electric signals have been recently recorded at the Earth's surface with amplitudes appreciably larger than those hitherto reported. Their entropy in natural time is smaller than that of a "uniform" distribution. The same holds for their entropy upon time reversal.

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.

Similarity of fluctuations in correlated systems: the case of seismicity.

We report a similarity of fluctuations in equilibrium critical phenomena and nonequilibrium systems, which is based on the concept of natural time. The worldwide seismicity as well as that of the San Andreas fault system and Japan are analyzed. An order parameter is chosen and its fluctuations relative to the standard deviation of the distribution are studied.

Origin of the usefulness of the natural-time representation of complex time series.

The concept of natural time turned out to be useful in revealing dynamical features behind complex time series including electrocardiograms, ionic current fluctuations of membrane channels, seismic electric signals, and seismic event correlation. However, the origin of this empirical usefulness is yet to be clarified. Here, it is shown that this time domain is in fact optimal for enhancing the signals in time-frequency space by employing the Wigner function and measuring its localization property.

Some properties of the entropy in the natural time.

We show that the entropy S , defined as S identical with chi ln chi - chi ln chi [Phys. Rev. E 68, 031106 (2003)] where chi stands for the natural time [Phys.

Natural entropy fluctuations discriminate similar-looking electric signals emitted from systems of different dynamics.

Complexity measures are introduced that quantify the change of the natural entropy fluctuations at different length scales in time series emitted from systems operating far from equilibrium. They identify impending sudden cardiac death (SD) by analyzing 15 min electrocardiograms, and comparing to those of truly healthy humans (H). These measures seem to be complementary to the ones suggested recently [Phys.

Entropy in the natural time domain.

A surrogate data analysis is presented, which is based on the fluctuations of the "entropy" S defined in the natural time domain [Phys. Rev. E 68, 031106 (2003)]].

Electric fields that "arrive" before the time derivative of the magnetic field prior to major earthquakes.

The low frequency electric signals (emitted from the focal area when the stress reaches a critical value) that precede major earthquakes, are recorded at distances approximately 100 km being accompanied by magnetic field variations. The electric field "arrives" 1 to 2 s before the time derivative of the horizontal magnetic field. An explanation, which is still awaiting, should consider, beyond criticality, the large spatial scale as well as that the transmission of the electromagnetic fields (through an inhomogeneous weakly conductive medium like the Earth) obeys diffusion type equations.