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.

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.

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 ß, of a certain parameter of seismicity, termed κ1. In an earlier study, we found that ß calculated for the entire Japanese region showed a minimum a few months before the shallow major earthquakes (magnitude larger than 7.6) that occurred in the region during the period from 1 January 1984 to 11 March 2011. In this study, by dividing the Japanese region into small areas, we carry out the ß calculation on them. It was found that some small areas show ß minimum almost simultaneously with the large area and such small areas clustered within a few hundred kilometers from the actual epicenter of the related main shocks. These results suggest that the present approach may help estimation of the epicentral location of forthcoming major earthquakes.

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

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 M8.2 earthquake, i.e., on 14 June 2017, the complexity measure associated with the fluctuations of entropy change under time reversal shows an abrupt increase, which, however, does not hold for the complexity measure associated with the fluctuations of entropy in forward time. On the same date, the entropy change under time reversal has been previously found to exhibit a minimum [Physica A 506, 625-634 (2018)]; we thus find here that this minimum is also accompanied by increased fluctuations of the entropy change under time reversal. In addition, we find a simultaneous increase of the Tsallis entropic index q.

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.

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.