Identifying the occurrence time of an impending mainshock: A very recent case

TL;DR

This paper reviews a natural time analysis method to identify the imminent mainshock timing using seismicity and electric signals, demonstrated on a 2014 Greece earthquake and discussed with recent SES data.

Contribution

It applies and validates a natural time analysis procedure for predicting mainshock occurrence based on seismic electric signals and seismicity data.

Findings

The 2014 Greece mainshock was predicted to occur early on 15 November 2014.

The method successfully identified the critical point approaching the mainshock.

Recent SES activities are also analyzed in the context of earthquake prediction.

Abstract

The procedure by means of which the occurrence time of an impending mainshock can be identified by analyzing in natural time the seismicity in the candidate area subsequent to the recording of a precursory Seismic Electric Signals (SES) activity is reviewed. Here, we report the application of this procedure to an Mw5.4 mainshock that occurred in Greece on 17 November 2014 and was strongly felt in Athens. This mainshock (which is pretty rare since it is the strongest in that area for more than half a century) was preceded by an SES activity recorded on 27 July 2014 and the results of the natural time analysis reveal that the system approached the critical point (mainshock occurrence) early in the morning on 15 November 2014. SES activities that have been recently recorded are also presented. Furthermore, in a Note we discuss the case of the Mw5.3 earthquake that was also strongly felt in Athens on 19 July 2019 (Parnitha fault).

Equations

$${\kappa }_1=⟨{\chi }^2⟩-⟨\chi {⟩}^2=\sum _{k=1}^N{p}_k({\chi }_k{)}^2-{\left(\sum _{k=1}^N{p}_k{\chi }_k\right)}^2.$$

Full text

I Introduction

Earthquakes (EQs) in general exhibit complex correlations in time, space, and magnitude M which have been investigated by several authors Sornette (2000); Corral (2004); Davidsen and Paczuski (2005); Holliday et al. (2006); Saichev and Sornette (2006); Eichner et al. (2007); Lennartz et al. (2008, 2011); Lippiello et al. (2009, 2012); Sarlis et al. (2009, 2010); Telesca and Lovallo (2009); Bottiglieri et al. (2010); Telesca (2010); Sarlis (2011); Huang and Ding (2012); Sarlis and Christopoulos (2012); Varotsos et al. (2011a); Varotsos et al. (2012). The earthquake scaling laws Turcotte (1997)(Turcotte 1997) indicate the existence of phenomena closely associated with the proximity of the system to a critical point, e.g., see Holliday et al. (2006). Here, we take this view that mainshocks are (non-equilibrium) critical phenomena. Major EQs are preceded by transient changes of the electric field of the Earth termed Seismic Electric Signals (SES) Varotsos and Alexopoulos (1984a, b)(Varotsos and Alexopoulos 1984a,b). A series of such signals recorded within a short time are called SES activities Varotsos and Lazaridou (1991); Varotsos et al. (1993); Varotsos (2005); Varotsos et al. (2009), the average lead time of which is of the order of a few months Varotsos et al. (2011b). It has been suggested that SES are emitted when the stress in the focal area of the impending mainshock reaches a critical value Varotsos and Alexopoulos (1984a, b, 1986); Varotsos et al. (2010). This suggestion is strengthened by the finding Varotsos et al. (2013) that the fluctuations of the order parameter of seismicity defined in the frame of natural time analysis (see the next section) minimize upon the initiation of an SES activity exhibiting long range temporal correlationsVarotsos et al. (2014). Such minima of the fluctuations of the order parameter of seismicity have been identified before all major (M$\geq$7.6) EQs in JapanSarlis et al. (2013, 2015). The identification of the occurrence time of an impending mainshock within a short time window is a challenge. This becomes possible when employing a procedure that combines SES data and natural time analysis of the seismicity Varotsos et al. (2001); Varotsos et al. (2002a, b); Varotsos et al. (2005); Sarlis et al. (2008); Sarlis (2013). In short, the initiation of the SES activity marks the time when the system enters the critical stage and then the natural time analysis of the subsequent seismicity in the candidate area (which is determined on the basis of SES data, e.g., see Varotsos (2005)) identifies when the system approaches the critical point, i.e., the mainshock occurrence, e.g., see Fig.1 of Huang et al. (2015). It is one of the aims of this paper to report a characteristic application of this procedure, which refers to an SES activity that was followed by a pronounced Mw=5.4 mainshock in Greece on 17 November 2014, which is pretty rare as explained later.

II Summary of the procedure to identify the occurrence time of an impending mainshock

Let us first summarize the natural time analysisVarotsos et al. (2002a) in the case of seismicity: In a time series comprising $N$ EQs, the natural time $\chi_{k}=k/N$ serves as an index for the occurrence of the k-th EQ. The combination of this index with the energy $Q_{k}$ released during the k-th EQ of magnitude Mk, i.e., the pair $(\chi_{k},Q_{k})$, is studied in natural time analysis. Alternatively, one studies the pair $(\chi_{k},p_{k})$, where $p_{k}={Q_{k}}/{\sum_{n=1}^{N}Q_{n}}$ stands for the normalized energy released during the k-th EQ. It has been found that the variance of $\chi$ weighted for $p_{k}$ , designated by $\kappa_{1}$, which is given byVarotsos et al. (2001); Varotsos et al. (2002a, b, 2003a, 2003b, 2011b)

[TABLE]

plays a prominent role in natural time analysis. In particular, $\kappa_{1}$ may serve as an order parameter for seismicityVarotsos et al. (2005) and it has been empirically observedVarotsos et al. (2001); Varotsos et al. (2002a, b); Varotsos et al. (2005, 2008); Varotsos et al. (2011b); Sarlis et al. (2008); Sarlis (2013) that $\kappa_{1}$ of the seismicity in the candidate area above a magnitude threshold Mthres subsequent to an SES activity becomes equal to 0.070 when approaching the critical point (mainshock occurrence). Note that $Q_{k}$, and hence $p_{k}$, for earthquakes is estimated through the usual relationKanamori (1978): $Q_{k}\propto 10^{1.5{\rm M}_{k}}$.

Upon the recording of an SES activity, one can estimate an area A within which the impending mainshock is expected to occur. The magnitude M of the expected EQ is estimated through the relation $\log_{10}\left(\frac{\Delta V}{L}\right)\approx 0.3M+{\rm const.}$, e.g., see Varotsos and Lazaridou (1991), where for a given measuring dipole of length $L$ and a given seismic area the SES amplitude $\Delta V/L$ is found from the anomalous variation $\Delta V$ of the potential difference between the corresponding two electrodes. When area A reaches criticality, one expects in general that all its subareas have also reached criticality simultaneously. At that time, therefore, the evolution of seismicity in each of its subareas is expected to result in $\kappa_{1}$ values close to 0.070. Assuming equi-partition of probability among the subareasSarlis et al. (2008), the distribution Prob($\kappa_{1}$) of the $\kappa_{1}$ values of all subareas should be peaked at around 0.070 exhibiting also magnitude threshold invariance. This usually occurs a few days to around one week before the mainshock, thus it enables the prediction of the occurrence time of major EQs with time window of the order of a week or less.

III Application to a pronounced seismic activity in Greece

The SES activity shown in Fig.1(a) was recorded on 27 July 2014 at Keratea (KER) geoelectrical station, the location of which is depicted with the red bullet in Fig.1(b). On the basis of the selectivity map of this station (i.e, the map showing all seismic areas in the past that gave rise to SES recorded at this station, e.g., see Varotsos and Lazaridou (1991) and the ratio of the SES components the candidate area was determined Sarlis et al. (2014). This is depicted here by the rectangle in Fig.1(b) as was designated in the uppermost right part of Fig.2 of the paper uploaded by Sarlis et al. (2014) on 7 August 2014.

We now proceed to the natural time analysis of the seismicity subsequent to the aforementioned SES activity at KER within the candidate area N(37.7-39.0)E(22.6-24.2). The EQ catalogue of the Institute of Geodynamics of the National Observatory of Athens available on 2 February 2015 at http://www.gein.noa.gr/services/current_catalogue.php was used, e.g. see Chouliaras et al. (2013); Mignan and Chouliaras (2014). Figure 2(a) depicts Prob($\kappa_{1}$) versus $\kappa_{1}$ of seismicity for Mthres=2.8 (the data used are compiled in Table 1 of Varotsos et al. (2015)) for the period after 27 October 2014, i.e., almost three weeks before the mainshock occurrence on 17 November 2014. During this period six smaller EQs occurred and we observe that Prob($\kappa_{1}$) maximizes at $\kappa_{1}$ =0.070 upon the occurrence of the last EQ, i.e., the ML=2.8 EQ at 01:01 UTC on 15 November 2014. It is remarkable that the same behavior is observed in Fig.2(b) where in the computation of the $\kappa_{1}$ values we discarded from the seismicity of the candidate area N(37.7-39.0)E(22.6-24.2) the EQs that occurred within the subarea N(37.7-38.3)E(22.6-23.3). This is consistent with the fact that the latter subarea constitutes the preliminary selectivity map of the LOU station, see Fig.1(b), which however did not show any SES activity simultaneously with the one initiated on 27 July 2014 at KER station (alternatively, the area resulting from the subtraction of the above two areas could have been announced as a candidate area for the impending mainshock). To assure that this behavior exhibits also magnitude threshold invariance, we repeated the calculation that resulted in Fig.2(b), but for low magnitude thresholds (so that to have a large number of EQs). In particular, Figs.2(c), (d), (e), (f) depict the corresponding results for Mthres=1.8, 1.9, 2.0, and 2.1, respectively, which do show that Prob($\kappa_{1}$ ) versus $\kappa_{1}$ exhibit local maximum at $\kappa_{1}$=0.070 upon the occurrence of the aforementioned EQ on 15 November 2014 (the seismic data used in order to obtain Figs.2(b) to 2(f) are given in Table 2 of Varotsos et al. (2015)). Actually, almost three days later, i.e, at 23:05 UTC on 17 November 2014, the Mw(USGS)=5.4 EQ occurred with an epicenter at 38.67oN,23.39oE (followed by a smaller Mw(USGS)=5.1 EQ at 23:09 UTC with epicenter at 38.68oN,23.24oE). It should be mentioned that EQs of such magnitude occur there very rarely. In particular, no EQ with Mw(USGS)$\geq$5.4 took place within the coordinates N(38.3-39.0)E(23.0-23.8) since 1965. In view of this very rare occurrence, it is interesting to study this case in the future by employing an approachMoustra et al. (2011) which uses SES and a neural network (trained by relevant data of earlier cases) to predict the magnitude and the occurrence time of the forthcoming EQ.

IV Conclusions

A pronounced Mw(USGS)=5.4 EQ was strongly felt at Athens, Greece, on 17 November 2014. This is pretty rare since it is the strongest EQ that occurred in that area since 1965. The procedure based on natural time analysis of the seismicity subsequent to an SES activity recorded on 27 July 2014 at the KER station close to Athens revealed that the system approached the critical point (mainshock occurrence) just a few days before, i.e., on 15 November 2014.

More recent SES activities: Despite severe experimental difficulties during the current period, it seems that an SES activity of more or less similar polarity has recently been recorded at KER on 15 March 2020 (Fig.4). Natural time analysis of the subsequent seismicity in the area designated by the rectangle in Fig.1(b) was carried out. (Remarkably, such an analysis has just been reported (www.nature.com/articles/s41598-020-59333-4) as being a powerful tool to detect the onset of acceleration as an early warning of an impending failure.) The results of this analysis have been described in the two previous versions of this preprint and followed by the EQs that occurred on 3 September, 11 September, and 2 December 2020 with epicenters at 38.17oN23.99oE, 38.12oN23.18oE, and 38.33oN23.46oE of magnitude Ms(ATH)=4.8, Ms(ATH)=4.7, and Ms(ATH)=4.9, respectively.

Around 18:00 UTC on 8 December 2020 an SES activity appeared on KER station (Fig. 5) obeying the properties described in the main text and the Section 7.2 of Ref.Varotsos et al. (2011b). Beyond the results obtained before the ML(ATH)=6.0 earthquake on 3 March 2021 we report the following: By applying the same analysis in natural time of the subsequent seismicity in the area described above we find that upon the occurrence of the ML(ATH)=2.4 earthquake at 04:15 UTC on 18 March 2021 with an epicenter at 38.30oN23.69oE we find that Prob($\kappa_{1}$ ) versus $\kappa_{1}$ exhibit maximum at $\kappa_{1}$=0.070 upon considering Mthres=2.0 and 2.2 as shown in Figs. 6A and B, respectively. The same holds upon the occurrence of the ML(ATH)=2.1 earthquake at 01:24 UTC on 18 March 2021 with an epicenter at 38.16oN22.91oE as shown in Figs 7A and B upon considering Mthres=2.1 and 2.2.

In continuation of this analysis in the area described above -see Fig. 1(b)- we find that Prob($\kappa_{1}$ ) versus $\kappa_{1}$ exhibit maximum at $\kappa_{1}$=0.070, for Mthres=2.3 and 2.4, upon the occurrence at 08:02 UTC on 24 March 2021 of the ML(ATH)=2.8 EQ with an epicenter at 38.30oN23.68oE (Fig. 8). In addition, a principal peak at $\kappa_{1}$=0.070 is observed upon the occurrence at 06:15 UTC on 25 March 2021 (see Fig. 9 for Mthres=3.0) of the ML(ATH)=3.5 EQ with an epicenter at 38.76oN23.41oE as well as a maximum at $\kappa_{1}$=0.070, for Mthres=2.1 and 2.2, upon the occurrence at 04:15 UTC on 28 March 2021 of a ML(ATH)=2.1 EQ with an epicenter at 38.76oN23.38oE.

On 2 June 2021 an SES activity was recorded at KER geoelectrical station (Fig. 10) as in Fig. 3. In the natural time analysis of the subsequent seismicity in the area described above -see Fig. 1(b)- the critical condition $\kappa_{1}=0.070$ was found to exhibit magnitude threshold invariance in the range $M_{{\rm thres}}=$2.9 to $M_{{\rm thres}}=$3.5, upon the occurrence at 10:08 UTC on 12 September 2021 of the ML(ATH)=3.6 EQ with an epicenter at 38.07oN23.76oE.

On 15 November 2021 an additional SES activity was recorded at KER station (Fig. 11) pointing to the continuation of the process of approaching criticality in the aforementioned region under investigation.

Actually, a ML(ATH)=4.0, i.e., Ms(ATH)=4.5, EQ occurred at 16:13 UTC on 26 December 2021 with an epicenter at 38.10oN23.14oE lying inside the expected rectangular area of Fig. 1(b) felt also in Athens. This EQ was preceded at 17:13 UTC on 25 December 2021 by an ML(ATH)=2.4 event with an epicenter at 38.31oN23.41oE upon the occurrence of which the condition $\kappa_{1}=0.070$ was fulfilled for $M_{{\rm thres}}=$1.7 and 1.8 (Fig. 12). Strikingly, the Ms(ATH)=4.5 EQ was also followed by an ML(ATH)=2.1 event at 20:39 UTC on 26 December 2021 with an epicenter at 38.52oN23.95oE upon the occurrence of which the condition $\kappa_{1}=0.070$ was also fulfilled for $M_{{\rm thres}}=$1.7 and 1.8 (Fig. 13) pointing to the conclusion that the approach to the critical point is still in progress.

On 25 February 2022, upon the occurrence of the ML(ATH)=3.3 EQ at 17:19 UTC with an epicenter at 38.49oN23.61oE, we found that the criticality condition $\kappa_{1}=0.070$ has been obeyed exhibiting magnitude threshold invariance in the range $M_{{\rm thres}}=$2.0 to $M_{{\rm thres}}=$2.5 (Fig.14), which signals the approach of the system to the critical point.

From 5 April 2022 until 8 April 2022, the most wide magnitude threshold invariance of the criticality condition $\kappa_{1}=0.070$ (from $M_{{\rm thres}}=$2.3 to $M_{{\rm thres}}=$3.2, see Fig. 15) concerning the region under investigation has been observed.

Note added on 1 August 2019. In the main text of the previous version of this paperVarotsos et al. (2015), it has been reported that a pronounced Mw(USGS)=5.4 earthquake (EQ) -or ML(ATH)=5.2 EQ, thus Ms(ATH)=ML(ATH)+0.5=5.7 EQ -which was strongly felt at Athens, Greece at 23:05 UTC on 17 November 2014 with an epicenter at 38.64oN 23.40oE has been preceded by an SES activity at Keratea (KER) geoelectrical station uploaded in the arXiv Sarlis et al. (2014) almost three months before, i.e., on 7 August 2014 (only if the expected EQ magnitude Ms(ATH) estimated from the amplitude of the SES activity is comparable with or larger than 6.0, quick report is uploaded before the EQ occurrence as explained in the subsection 7.2 of Ref. Varotsos et al. (2011b)). It has been followed by an EQ of equal magnitude (ML=5.2) almost four minutes later, i.e., at 23:09 UTC on 17 November 2014, practically at the same epicenter, i.e., at 38.64oN 23.41oE.

Here, we report that at 11:13 UTC on 19 July 2019, a Mw(USGS)=5.3 EQ -or ML(ATH)=5.1- was also stongly felt at Athens with an epicenter at 38.12oN 23.53oE. It has been preceded by an SES activity at KER which can be seen in Fig.3. An inspection of this figure shows that it had a different ratio of the SES components compared to the SES activity depicted in Fig.1(a) that preceded the previous EQ in 2014 mentioned above. This explains why (e.g., see Varotsos and Lazaridou (1991)) the recent 19 July 2019 EQ occurred at a different region of the SES selectivity map of the measuring station depicted in Fig. 1(b). Another important difference between these two cases is that the recent event was followed almost 1 hour later, i.e., at 12:11 UTC on 19 July 2019, approximately at the same epicenter, i.e., at 38.10oN 23.58oE, by a smaller EQ with ML=4.3. The study of the evolution of the seismic activity is made by analysing in natural time the events occurring in the candidate area (Fig. 1(b)) subsequent to the SES activity recorded at KER on 19 June 2019 (Fig. 3) by means of the procedure developed in Section II. In view of the complexity of this procedure, which is the most accurate, one may alternatively rely -but only approximately- on the upper time chart depicted in Fig.28 of Ref.Varotsos and Lazaridou (1991), which is explained in simple words in p.35 of Varotsos et al. (1996).

Acknowledgements.

We gratefully acknowledge the continuous supervision and technical support of the geoelectrical stations of the SES telemetric network by Basil Dimitropoulos, Spyros Tzigkos and George Lampithianakis.