Variation of the Earth tide-seismicity compliance parameter during the recent seismic activity in Fthiotida, central Greece

Based on the results of our previous studies concerning the tidal triggering effect on the seismicity in Greece, we consider the confidence level of earthquake occurrence tidal period accordance as an index of tectonic stress criticality, associated with earthquake occurrence. Then, we investigate whether the recent increase in the seismic activity at Fthiotida in Greek mainland indicates faulting maturity and the possible production a stronger earthquake. In this paper we present the results of this inves-


Introduction
Recent analyses on the problem of tidal triggering on earthquakes indicate that this effect is manifested [Heaton 1982, Rydelek et al. 1992, Tsuruoka et al. 1995, Vidale et al. 1998, Wilcock 2001, Tanaka et al. 2002, Tolstoy et al. 2002, Tanaka et al. 2006, Stroup et al. 2007]. In these studies, not only tidal triggering at the global [Tanaka et al. 2002] and local [Tanaka et al. 2006, Contadakis et al. 2012 scales was found. In addition, in the last three studies, an increase in the reliability of the tidalearthquake occurrence correlation was shown to be a precursory phenomenon for strong earthquakes. In the frame to this international effort, applying the Hist(ogram)Cum(ullating) method [van Ruymbecke et al. 2007], we have analyzed the series of the earthquakes occurred in the last 50 years in seismic active areas of Greece. These areas are: (a) the Mygdonian Basin [Contadakis et al. 2009], (b) the Ionian Islands [Contadakis et al. 2012], (c) the Hellenic Arc [Vergos et al. 2015] and (d) the Santorini [Contadakis et al. 2013]. The result of the analysis for all the areas indicate that the monthly variation of the earthquake frequency of is in accordance with the period of the tidal lunar monthly and semi-monthly (Mm and Mf ) variations. Similarly, the same happens with the corresponding daily variations of the earthquake frequency with the diurnal luni-solar (K1) and semidiurnal lunar (M2) tidal variations. In addition the confidence level for the identification of such period accordance between earthquakes frequency and tidal period varies with seismic activity. The higher confidence level corresponds to time periods with stronger seismic activity. These results are in favor of a tidal triggering process on earthquakes when the stress in the focal area is near the critical level. Based on these results, we consider the confidence level of earthquake occurrence -tidal period accordance, p, as an index of tectonic stress criticality for earthquake occurrence. We call it "Earth tide-seismicity compliance parameter". Then we check on posterior weather the variation of the Earth tide-seismicity compliance parameter p, indicate the fault matureness in the case of the recent seismic activity in the prefecture of Fthiotida, central Greece. In this paper we present the results of this test.
aged the activation of a steep, south dipping normal fault. They interpret the Kallidromon seismic sequence as release of extensional seismic strain on secondary steep faults inside the Fokida-Viotia crustal block.   March 31 to April 11, 2013 [Sarlis et al. 2015]. This indicate that the area of central Greece enter to a tectonically critical stage. Then Sarlis et al. [2015] analyzed the earthquake sequence from that moment on up to August 12, 2013, in the natural time domain, using the procedure developed in Varotsos et al. [2005]. They found that the probability Prob(l1) of the l1 values of seismicity in the area of the earthquake of August 7, maximized at l1 = 0.070 at times between 13:10 UT and 19:49 UT of August 9, 2013, exhibiting magnitude threshold invariance in the broad magnitude range M thres =2.6 to 3.6 (which suggests that the system approaches the critical point).
In conclusion, different approaches indicate that the area of Fthiotida is found in tectonic excitation.
For this area we apply the Hi(stogram)Cum(ulating)method in order to see if tidal triggering effect is been detected and if this effect is better traced in the period of the increased microseismicity i.e. the years 2011 -February of 2012.
In our analysis we use the seismological data of the earthquake catalogue of NOA (http://www.gein. noa.gr). The set of data consist of a series of 33281 shallow and 769 of intermediate depth earthquakes with M L ranging from 0.2 to 6.3, occurred within the time interval from January 1964 to December 2013, in an area bounded by 38° ≤ { ≤ 39° and 21° ≤ m ≤ 23°.
However, since 1964 the network of NOA subjected three main upgrades. (1) In 1995 the instrumentation and processing passed from analog-to-digital mode.
(2) Gradually from the end of 2007 to 2011 developed the Hellenic Unified Seismological Network (HUSN), which combined the NOA network to three university networks (Athens, Patras, and Thessaloniki), and (3) in early 2011 the magnitude determination software has been upgraded [Chouliaras 2009, Chouliaras et al. 2013, Mignan and Chouliaras 2014   should be noted that only for the years 1964 and 1965 the total number of earthquakes was less than 30, rendering the results of Shuster's test doubtful.

Tidal effect
Tidal effects on a rigid Earth can be computed theoretically from the ephemerides of the Moon, the Sun and the planets. The Earth tides are the combined effect of the mentioned celestial bodies and the reaction of the solid Earth (like an elastic body) to the tidal forces. The ocean tides follow the law of hydrodynamics, with strong disturbances affecting adjacent seas, so that the ocean loading effect has to be taken into account. Earth tides are discussed extensively in Melchior [1983], Baker [1984], Torge [2001].
The constituents of the Earth tides for the area of Thessaloniki were determined gravimetrically by Arabelos [2002]. Table 2 displays the strongest components of the Earth tides for Thessaloniki. Although the amplitude of the lunar tidal component M1 is equal 27.091 nms -2 (see Arabelos [2002], Table 3), i.e. it is much weaker than the listed components, we consider in addition the possible effect of this constituent by means of the lunar synodic month (i.e. period from new moon to new moon which is 29 d .530589) as well as by lunar anomalistic month (i.e. time period between two successive passages of the moon from perigee which is 27 d .554551). Table 3 displays the actual ocean corrected tidal parameters of O1 and M2 for Sofia, Instabul and Thessaloniki, and the corresponding values from the model of Wahr-Dehant-Zschau [Dehant 1987, Dehant andZchau 1989], expressing the dependency of the tidal parameters on the latitude. As it is shown from Table 3 the amplitude factors of the principal O1 and M2 tidal constituents agree within their error of estimation with the model.
For the latitude of 38° which is the mean latitude of the area under consideration, the extrapolated model amplitude factors for O1 and M2 are equal to 1.156 and 1.158 respectively. Consequently, the amplitudes of O1 and M2 might be changed to about 408 and 591 nms -2 respectively, which are very close to the amplitudes observed in the tidal station of Thessaloniki. However, this estimation does not take into account the actual elastic properties of the lithosphere in the Ionian zone.

Method of analysis
As we have done in previous studies [Contadakis et al. 2009, Contadakis et al. 2012, Vergos et al. 2015, in order to check the possible correlation between Earth tides and earthquake occurrence we investigate the time of occurrence of each earthquake in relation to the sinusoidal variation of Earth tides and investigate the possible correlation of the time distribution of the earthquake events with Earth tides variation. Since the periods of the Earth tides component are very well known and quite accurately predictable in the local coordination system we assign a unique phase angle within the period of variation of a particular tidal component, for which the effect of earthquake triggering is under investigation, with the simple relation: We choose as epoch t o , i.e. as reference date, the time of the upper culmination in Thessaloniki of the new moon of January 7, 1989, which has MJD= 47533.8947453704. Thus the calculated phase angle for all the periods under study has 0 phase angle at the maximum of the corresponding tidal component (of course M2 and S2 has an upper culmination maximum every two cycles). As far as the monthly anomalistic moon concern the corresponding epoch t o is January 14, 1989, which has MJD = 47541.28492. We separate the whole period in 12 bins of 30°a nd stack every event according to its phase angle in the proper bin. Thus we construct a Cumulating Histogram of earthquake events for the tidal period under study.
In order to check the compliance of the earthquake frequency distribution periods with the tidal periods we use the well known Shuster's test [Shuster 1897; see also Tanaka et al. 2002, Tanaka et al. 2006]. In Shuster's test, each earthquake is represented by a unit length vector in the direction of the assigned phase angle ã í . The vectorial sum D is defined as: where N is the number of earthquakes. When a i is distributed randomly, the probability to be the length of a vectorial sum equal or larger than D is given by the equation: Thus, p < 5% represents the significance level at which the null hypothesis that the earthquakes occurred randomly with respect to the tidal phase is rejected. This means that the smaller the p is the greater the confidence level of the results of the Cumulating Histograms is. Finally it should be noted that the total number of the shocks for each year is greater than 30 for all the years since 1966. This means that the normal distribution approach on which Shuster test is based is valid for all the years since 1966.

Results
Figures 3 to 8 display the Cumulating Histogram for the 6291 earthquakes which occurred in the time interval from January 1st, 2013, to December 31, 2013. These figures correspond to the tidal periods of: Anomalistic Monthly period (i.e. time period between two successive passages of the moon from perigee which is 27 d .554551) (Figure 3), Synodic Monthy period (i.e. period from new moon to new moon which is 29 d .530589) (Figure 4), Diurnal luni-solar constituents K1 ( Figure  5), Diurnal luni-solar constituent O1 (Figure 6), Semidiurnal solar constituents S2 (Figure 7), and Semi-diurnal lunar constituent (Figure 8), for the last year of the 50-year analyzed data, i.e. 2013. It is obvious that there is a perfect compliance of tidal and earthquake occurance distribution for Monthly Anomalistic and Synodic period, Diurnal luni-solar K1 and Semi-diurnal solar S2 periods and a smaller compliance for the Diurnal lunisolar O1 and Semidiurnal lunar period. This is shown in    (2) dence levels for all six tidal components for 2013 together with the same quantities for a year of low seismic activity, i.e. 1994 and the mean confidence levels for the 50 years.
Year 1994 was a year with apparently smaller seismic activity than 2013. Table 4 displays the confidence level of earthquake-Earth tide correlation for all earthquakes of the broader area of Fthiotida for the year 2013. In comparison the Mean values of the confidence levels for the last fifty years as well as those for the year 1994, a relatively quiet seismically year. This Table indicates that the confidence level of the compliance of earthquake frequency distribution over the tidal period is very sensitive to the seismicity of the area. This is also shown in Figures 9 to 14. These figures display the variation of the confidence level parameter in the time period 1964 to 2013 together with the earthquakes occurrence for each year. Finally it has to be understood that the confidence level parameter p indicate that the tectonic stress in the area has reached a critical point. This also has been found by Sarlis et al. [2015]. The magnitude of the potential earthquake depends on the tectonic morphology in the stress regime and seismic history of the area.
The high confidence level of the monthly tidal components, despite their small intensity, may indicate that they provide in general favourable conditions for the action of the much stronger tidal components K1 and M2. In this point we may refer to the fact that the monthly tidal barometric variations are quite sensitive to the seismic activity [Arabelos et al. 2008]. Perhaps this peculiar coincidence merits further investigation.

Conclusions
In this paper we investigate the tidal triggering evidence on the earthquakes of the area of Fthiotida in Greece. The result of our analysis using the HiCum method, indicate that the monthly variation of the frequencies of earthquake occurrence is in accordance with the period of the tidal lunar monthly (Mm) variations. The same happens with the corresponding diurnal and EARTH TIDE-SEISMICITY COMPLIANCE PARAMETER IN FTHIOTIDA      semi-diurnal variations of the frequencies of earthquake occurrence with the diurnal (K1), (O1) and semi-diurnal solar (S2) and semidiurnal lunar (M2) tidal variations. The confidence level of the Tidal-Earthquake frequency period compliance is very sensitive to the seismicity of the area and we call it Tidal-Earthquake frequency compliance parameter. We suggest that this parameter may be used in earthquake risk assessment.