Efthimios S. Skordas

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. We find that the scaled distributions fall on the same curve, which interestingly exhibits, over four orders of magnitude, features similar to those in several equilibrium critical phenomena (e.g., two-dimensional Ising model) as well as in nonequilibrium systems (e.g., three-dimensional turbulent flow).

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.

Natural Time Analysis: The New View of Time

Part I Seismic Electric Signals.- 1. Introduction to Seismic Electric Signals-V.- Part II.- 2. Natural Time. Background-F.- 3. Entropy in Natural Time-E.- Part III Natural Time Applications.- 4. Natural Time Analysis of Seismic Electric Signals-AS.- 5. Natural Time Investigation of the Effect of Significant Data Loss on Indentifying Seismic Electric Signals-ASL.- 6. Natural Time Analysis of Seismicity-AEQ.- 7. Indentifying the Occurence Time of an Impending Mainshock-AIM.- 8. Natural Time Analysis of Dynamical Models-AD.- 9. Natural Time Analysis of Electrocardiograms-AEL.- References.

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 of natural time χ, where and pk is the normalized energy released during the kth event of which the natural time is defined as χk = k/N and N stands for the total number of events. Then we show that κ1 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 κ1 = 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.

Fluctuations, under time reversal, of the natural time and the entropy distinguish similar looking electric signals of different dynamics

We show that the scale dependence of the fluctuations of the natural time itself under time reversal provides a useful tool for the discrimination of seismic electric signals (critical dynamics) from noises emitted from man-made sources, as well as for the determination of the scaling exponent. We present recent data of electric signals detected at the Earth’s surface, which confirm that the value of the entropy in natural time as well as its value under time reversal are smaller than that of the entropy of a “uniform” distribution.

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. Rev. E 70, 011106 (2004)]] and altogether enable the classification of individuals into three categories: H, heart disease patients, and SD. All the SD individuals, who exhibit critical dynamics, result in a common behavior.

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. We find that the fluctuations of the order parameter of seismicity exhibit distinct minima a few months before all of the shallow earthquakes of magnitude 7.6 or larger that occurred during this 27-y period in the Japanese area. Among the minima, the minimum before the M9 Tohoku earthquake was the deepest. It appears that there are two kinds of minima, namely precursory and nonprecursory, to large earthquakes.

Scale-specific order parameter fluctuations of seismicity in natural time before mainshocks

We have previously shown that the probability distribution of the order parameter κ1 of seismicity in natural time turns to be bimodal when approaching a mainshock. This reflects that, for various natural time window lengths ending at a given mainshock, the fluctuations of κ1 considerably increase for smaller lengths, i.e., upon approaching a mainshock. Here, as a second step, we investigate the order parameter fluctuations, but when considering a natural time window of a fixed-length sliding through a seismic catalog. We find that when this length becomes comparable with the lead time of Seismic Electric Signals activities (i.e., of the order of a few months), the fluctuations exhibit a global minimum before the strongest mainshock. Thus, the approach of the latter is characterized by two distinct features of the order parameter fluctuations that complement each other.

Order parameter fluctuations of seismicity in natural time before and after mainshocks

It is widely accepted that the observed earthquake scaling laws indicate the proximity of the system to a critical point. Using the order parameter (OP) for seismicity suggested on the basis of natural time as well as the detrended fluctuation analysis of the magnitude time-series, we investigate the behavior of seismicity before and after significant earthquakes. The analysis reveals that the fluctuations of the OP before major earthquakes exhibit a characteristic feature which, if quantified properly, may be used as decision variable to predict the occurrence of a large earthquake in the next time step based solely on the magnitudes of previous earthquakes.

Scale-specific order parameter fluctuations of seismicity before mainshocks: Natural time and Detrended Fluctuation Analysis

The order parameter fluctuations of seismicity are investigated upon considering a natural time window of fixed length sliding through the consecutive earthquakes that occurred in California. We previously found that when this length corresponds to a time period of the order of a few months, the fluctuations exhibit a global minimum before the strongest mainshock. Here, we show that in California, during the twenty five year period 1979–2003, minima of the fluctuations are identified 1 to 5 months before four out of five mainshocks with magnitude M = 7.0 or larger as well as before the M = 6.9 Northridge earthquake. These minima are accompanied by minima of the exponent α of the Detrended Fluctuation Analysis (DFA) of the earthquake magnitude time series, which since α < 0.5 indicate anticorrelated behavior. These results of DFA alone cannot serve for prediction purposes, but do so when combined with the aforementioned minima in the fluctuations of the order parameter of seismicity identified in natural time analysis.