Erratum: A remarkable change of the entropy of seismicity in natural time under time reversal before the super-giant M9 Tohoku earthquake on 11 March 2011

By analyzing the seismicity in the new time domain termed natural time [1],&#160; the entropy changes of seismicity before major earthquakes have been studied. It was found [2-5] that the key quantity is the entropy change &#916;S under time reversal, which is minimized a few months before major earthquakes such as the M9.0 Tohoku earthquake [2] on 11 March 2011 and the M8.2 Chiapas earthquake [3] in Mexico on 7 September 2017; accompanied by an abrupt increase of its fluctuations [4,5]. Here we discuss how these fluctuations may lead to a procedure through which the occurrence time of an impending mainshock can be estimated [6].References1. Varotsos P.A., Sarlis N.V. and Skordas E.S., Natural Time Analysis: The new view of time. Precursory Seismic Electric Signals, Earthquakes and other Complex Time-Series (Springer-Verlag, Berlin Heidelberg) 2011.2. N. V. Sarlis, E. S. Skordas, and P. A. Varotsos, "A remarkable change of the entropy of seismicity in natural time under time reversal before the super-giant M9 Tohoku earthquake on 11 March 2011", EPL (Europhysics Letters), 124 (2018), 29001.3. N. V. Sarlis, E. S. Skordas P. A. Varotsos, A. Ram&#237;rez-Rojas, E. L. Flores-M&#225;rquez, "Natural time analysis: On the deadly Mexico M8.2 earthquake on 7 September 2017", Physica A 506 (2018), 625-634.4. P. A. Varotsos, N. V. Sarlis and E. S. Skordas, "Tsallis Entropy Index q and the Complexity Measure of Seismicity in Natural Time under Time Reversal before the M9 Tohoku Earthquake in 2011", Entropy 20 (2018), 757.5. A. Ram&#237;rez-Rojas, E. L. Flores-M&#225;rquez, N. V. Sarlis and P. A. Varotsos, "The Complexity Measures Associated with the Fluctuations of the Entropy in Natural Time before the Deadly M&#233;xico M8.2 Earthquake on 7 September 2017", Entropy 20 (2018), 477.6. E. S. Skordas, N. V. Sarlis and P. A. Varotsos &#8220;Identifying the occurrence time of an impending major earthquake by means of the fluctuations of the entropy change under time reversal&#8221;, EPL (Europhysics Letters), in press.

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

Entropy ◽

10.3390/e20100757 ◽

2018 ◽

Vol 20 (10) ◽

pp. 757 ◽

Cited By ~ 16

Author(s):

Panayiotis Varotsos ◽

Nicholas Sarlis ◽

Efthimios Skordas

Keyword(s):

Phase Transitions ◽

Time Reversal ◽

Scaling Laws ◽

Tohoku Earthquake ◽

Entropy Change ◽

Characteristic Size ◽

Natural Time ◽

Minority Phase ◽

Earthquake Scaling ◽

Precursory Change

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 9.0 that occurred on 11 March 2011 in Japan. Furthermore, the Tsallis entropic index q is found to exhibit a precursory increase.

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Phenomena preceding major earthquakes interconnected through a physical model

Annales Geophysicae ◽

10.5194/angeo-37-315-2019 ◽

2019 ◽

Vol 37 (3) ◽

pp. 315-324 ◽

Cited By ~ 15

Author(s):

Panayiotis A. Varotsos ◽

Nicholas V. Sarlis ◽

Efthimios S. Skordas

Keyword(s):

Time Series ◽

Physical Model ◽

Order Parameter ◽

Tohoku Earthquake ◽

Entropy Change ◽

Natural Time ◽

Earth Magnetic Field ◽

Preceding Period ◽

Magnetic Field Variations

Abstract. The analysis of earthquake time series in a new time domain termed natural time enables the uncovering of hidden properties in time series of complex systems and has been recently employed as the basis of a method to estimate seismic risk. Natural time also enables the determination of the order parameter of seismicity, which is a quantity by means of which one can identify when the system approaches the critical point (the mainshock occurrence is considered the new phase). Applying this analysis, as an example, to the Japanese seismic data from 1 January 1984 until the super-giant M 9 Tōhoku earthquake on 11 March 2011, we find that almost 3 months before its occurrence the entropy change of seismicity under time reversal is minimized on 22 December 2010, which signals an impending major earthquake. On this date the order parameter fluctuations of seismicity exhibit an abrupt increase. This increase is accompanied by various phenomena; e.g., from this date the horizontal GPS azimuths start to become gradually oriented toward the southern direction, while they had random orientation during the preceding period. Two weeks later, a minimum of the order parameter fluctuations of seismicity appears accompanied by anomalous Earth magnetic field variations and by full alignment of the orientations of GPS azimuths southwards leading to the most intense crust uplift. These phenomena are discussed and found to be in accordance with a physical model which seems to explain on a unified basis anomalous precursory changes observed either in ground-based measurements or in satellite data.

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

Entropy ◽

10.3390/e22070730 ◽

2020 ◽

Vol 22 (7) ◽

pp. 730 ◽

Cited By ~ 1

Author(s):

E. Leticia Flores-Márquez ◽

Alejandro Ramírez-Rojas ◽

Jennifer Perez-Oregon ◽

N. V. Sarlis ◽

E. S. Skordas ◽

...

Keyword(s):

Time Reversal ◽

Order Parameter ◽

Pacific Coast ◽

Entropy Change ◽

North American Plate ◽

Cocos Plate ◽

Mexican Pacific ◽

Flat Slab ◽

The North ◽

Natural Time

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.

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M W9 Tohoku earthquake in 2011 in Japan: precursors uncovered by natural time analysis

Earthquake Science ◽

10.1007/s11589-017-0189-0 ◽

2017 ◽

Vol 30 (4) ◽

pp. 183-191 ◽

Cited By ~ 5

Author(s):

Panayiotis A. Varotsos ◽

Nicholas V. Sarlis ◽

Efthimios S. Skordas ◽

Mary S. Lazaridou-Varotsos

Keyword(s):

Tohoku Earthquake ◽

Time Analysis ◽

Natural Time ◽

Natural Time Analysis

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The change of the entropy in natural time under time-reversal in the Olami–Feder–Christensen earthquake model

Tectonophysics ◽

10.1016/j.tecto.2011.09.025 ◽

2011 ◽

Vol 513 (1-4) ◽

pp. 49-53 ◽

Cited By ~ 36

Author(s):

N.V. Sarlis ◽

E.S. Skordas ◽

P.A. Varotsos

Keyword(s):

Time Reversal ◽

Natural Time ◽

Earthquake Model

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Entropy in Natural Time and the Associated Complexity Measures

10.20944/preprints201704.0097.v1 ◽

2017 ◽

Author(s):

Nicholas V. Sarlis

Keyword(s):

Complex System ◽

Time Domain ◽

Time Reversal ◽

Southern Oscillation ◽

Complexity Measures ◽

Natural Time ◽

Electric Signals ◽

Atmospheric Phenomena ◽

Analysis Of Time Series ◽

New Time

Natural time is a new time domain introduced in 2001. The analysis of time series associated with a complex system in natural time may provide useful information and may reveal properties that are usually hidden when studying the system in conventional time. In this new time domain, an entropy has been defined and complexity measures based on this entropy as well as its value under time-reversal have been introduced and found applications in various complex systems. Here, we review these applications in the electric signals that precede rupture, e.g., earthquakes, in the analysis of electrocardiograms, as well as in global atmospheric phenomena like the El Nino/La Nina Southern Oscillation.

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