Interactive comment on “ Recent seismic activity at Cephalonia island ( Greece ) : a study through candidate electromagnetic precursors in terms of nonlinear dynamics ” by S

1 The preparation process of two recent earthquakes ( EQ ) occurred in Cephalonia (Kefalonia) 2 island, Greece, [(38.22 o N, 20.53 E), 26 January 2014, 6.0 w M = , depth = 21 km], and 3 [(38.25 N, 20.39 E), 3 February 2014, 5.9 w M = , depth = 10 km], respectively, is studied in 4 terms of the critical dynamics revealed in observab les of the involved non-linear processes. 5 Specifically, we show, by means of the method of cr itical fluctuations (MCF), that signatures 6 of critical, as well as tricritical, dynamics were mbedded in the fracture-induced 7 electromagnetic emissions (EME) recorded by two sta tions in locations near the epicenters of 8 these two EQs. It is worth noting that both, the MH z EME recorded by the telemetric stations 9 on the island of Cephalonia and the neighboring isl and of Zante (Zakynthos), reached 10 simultaneously critical condition a few days before th occurrence of each earthquake. The 11 critical characteristics embedded in the EME signal s were further verified using the natural 12 time (NT) method. Moreover, we show, in terms of th e NT method, that the foreshock 13 seismic activity also presented critical characteri s ics before each event. Importantly, the 14 revealed critical process seems to be focused on th e area corresponding to the west 15 Cephalonia zone, following the seismotectonic and h azard zoning of the Ionian Islands area 16 near Cephalonia. 17


Introduction
The possible connection of the electromagnetic (EM) activity that is observed prior to significant earthquakes (EQs) with the corresponding EQ preparation processes, often referred to as seismo-electromagnetics, has been intensively investigated during the last years.Several possible EQ precursors have been suggested in the literature (Uyeda et al., 2009a;Cicerone et al., 2009;Hayakawa, 2013a, b;Varotsos, 2005;Varotsos et al., 2011b) with shallow EQs with magnitude 6 or larger that occurred in land or near coast, has been examined in a series of publications (e.g., Eftaxias et al., 2001Eftaxias et al., , 2004Eftaxias et al., , 2008Eftaxias et al., , 2013;;Kapiris et al., 2004;Karamanos et al., 2006;Papadimitriou et al., 2008;Contoyiannis et al., 2005Contoyiannis et al., , 2013Contoyiannis et al., , 2015;;Eftaxias and Potirakis, 2013;Potirakis et al., 2011Potirakis et al., , 2012aPotirakis et al., , b, c, 2013Potirakis et al., , 2015;;Minadakis et al., 2012a, b), while a four-stage model for the preparation of an EQ by means of its observable EM activity has been recently put forward (Eftaxias and Potirakis, 2013, and references therein;Contoyiannis et al., 2015, and references therein).Note that the specific four-stage model is a suggestion that seems to be supported by the up to now available MHz-kHz observation data and corresponding time-series analyzes, while a rebuttal has not yet appeared in the literature.In summary, the proposed four stages of the last part of EQ preparation process and the associated, appropriately identified, EM observables, specifically EM time series excerpts for which specific features have been identified using appropriate time series analysis methods, appear in the following order (Donner et al., 2015, and references therein): 1st stage: valid MHz anomaly; 2nd stage: kHz anomaly exhibiting tri-critical characteristics; 3rd stage: strong avalanche-like kHz anomaly; 4th stage: electromagnetic quiescence.It is noted that, according to the aforementioned fourstage model, the pre-EQ MHz EM emission is considered to be emitted during the fracture of the part of the Earth's crust that is characterized by high heterogeneity.
During this phase the fracture is non-directional and spans over a large area that surrounds the family of large high-strength entities distributed along the fault sustaining the system.Note that for an EQ of magnitude ∼ 6 the corresponding fracture process extends to a radius of ∼ 120 km (Bowman et al., 1998).
Two strong shallow EQs occurred recently in western Greece (see Fig. 1).On 26 January 2014 (13:55:43 UT) an M w = 6.0 EQ, hereafter also referred to as "EQ1", occurred on the island of Cephalonia (Kefalonia), with epicenter at (38.22 • N, 20.53 • E) and depth of ∼ 16 km.The second significant EQ, M w = 5.9, hereafter also referred to as "EQ2", occurred on the same island on 3 February 2014 (03:08:45 UT), with epicenter at (38.25 • N, 20.40 earthquakes have already been published indicating their seismotectonic importance (Karastathis et al., 2014;Valkaniotis et al., 2014;Papadopoulos et al., 2014;Ganas et al., 2015;Sakkas and Lagios, 2015;Merryman Boncori et al., 2015) as they were located on two different active faults that belong to the same seismic source zone.Two pairs of MHz EM signals were recorded, with a sampling rate of 1 sample s −1 , prior to each one of the above mentioned significant shallow EQs; one pair of simultaneous signals was recorded by two different stations prior to each one of them.On 24 January 2014, two days before the M w = 6.0 Cephalonia EQ (EQ1), two telemetric stations of our EM signal monitoring network (see Fig. 1), the station of Cephalonia, located on the same island (38.18 • N, 20.59 • E), and the station of Zante (Zakynthos), located on a neighboring island belonging to the same (Ionian) island complex (37.77• N, 20.74 • E), simultaneously recorded the first pair of aforementioned signals.The same picture was repeated for the second significant Cephalonia EQ, M w = 5.9 (EQ2).Specifically, both the Cephalonia and the Zante stations simultaneously recorded the second pair of aforementioned signals on 28 January 2014, six days prior to the specific EQ.Note that it has been repeatedly made clear that all the pre-EQ EME signals, which have been observed by our monitoring network, have been recorded only prior to strong shallow EQs, that have taken place on land (or near the coast-line); this fact, in combination to the recently proposed fractal geo-antenna model (Eftaxias et al., 2004;Eftaxias and Potirakis, 2013), explains why they succeed to be transmitted on air.This model gives a good reason for the increased possibility of detection of such EM radiation, since a fractal geo-antenna emits significantly increased power, compared to the power that would be radiated by the same source, if a dipole antenna model was considered.It should also be noted that, none of the recordings of the other monitoring stations of our network (except from the ones of Cephalonia and Zante) presented critical characteristics before these two specific EQs.The analysis of the specific EM time series, using the method of critical fluctuations (MCF) (Contoyiannis and Diakonos, 2000;Contoyiannis et al., 2002Contoyiannis et al., , 2013)), revealed Introduction

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Full critical features, implying that the possibly related underlying geophysical process was at critical state before the occurrence of each one of the EQs of interest.The critical characteristics embedded in the specific time series were further verified by means of the natural time (NT) method (Varotsos et al., 2011a, b;Potirakis et al., 2013Potirakis et al., , 2015)).The presence of the "critical point" during which any two active parts of the system are highly correlated, theoretically even at arbitrarily long distances, in other words when "everything depends on everything else", is consistent with the view that the EQ preparation process during the period that the MHz EME are emitted is a spatially extensive process.Note that this process corresponds to the first stage of the aforementioned four-stage model.
Moreover, we analyzed the foreshock seismic activity using the NT method; the obtained results indicate that seismicity also presented critical characteristics before each one of the two important events.This result implies that the observed EM anomaly and the associated foreshock seismic activity might be considered as "two sides of the same coin".Importantly, the revealed critical process seems to be focused on an area corresponding to the west Cephalonia zone, one of the parts according to the seismotectonic and hazard zone partitioning of the wider area of the Ionian Islands.
Last but not least, one day before the occurrence of EQ2, and five days after the corresponding critical EME signal, tricritical characteristics were revealed in the EME recorded by the Cephalonia station.This finding is also quite important, indicating that the tricritical behavior attributed to the second stage of the aforementioned four-stage model can be identified either in kHz or in MHz EME, leading thus to a revision of the specific four-stage model.Unfortunately, the Zante station was out of order for several hours during the specific day, including the time window during which the tricritical features were identified in the Cephalonia recordings.As a result, we could not cross check whether tricritical signals simultaneously also reached Zante.
The remainder of this manuscript is organized as follows: a brief introduction to the MCF and the NT analysis methods is provided in Sect. 2. The analysis of the EME recordings according to these two methods is presented in Sect.3. Section 4 presents Introduction

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Full the results obtained by the analysis of the foreshock seismic activity using the NT method, while Sect. 5 concludes the manuscript by summarizing and discussing the findings.

Critical dynamics analysis methods
Critical phenomena have been proposed as the likely model to study the origins of EQ related EM fluctuations, suggesting that the theory of phase transitions and critical phenomena may be useful in gaining insight to the mechanism of their complex dynamics (Bowman et al., 1998;Contoyiannis et al., 2004aContoyiannis et al., , 2005Contoyiannis et al., , 2015;;Varotsos et al., 2011a, b).One possible reason for the appropriateness of this model may be the way in which correlations spread thought a disordered medium/system comprised of subunits.From a qualitative/intuitive perspective, according to the specific approach, initially single isolated activated parts emerge in the system which, then, progressively grow and multiply, leading to cooperative effects.Local interactions evolve to longrange correlations, eventually extending along the entire system.A key point in the study of dynamical systems that develop critical phenomena is the identification of the "critical epoch" during which the "short-range" correlations evolve into "long-range" ones.Therefore, the theory of phase transitions and critical phenomena seem to be appropriate for the study of dynamical complex systems in which local interactions evolve to long-range correlations, such as the disordered Earth's crust during the preparation of an EQ.Note that for an EQ of magnitude ∼ 6 the corresponding fracture process extends to a radius of ∼ 120 km (Bowman et al., 1998).
It is worth noting that key characteristics of a critical point in a phase transition of the second order are the existence of highly correlated fluctuations and scale invariance in the statistical properties.By means of experiments on systems presenting this kind of criticality as well as by appropriately designed numerical experiments, it has been confirmed that right at the "critical point" the subunits are highly correlated even at arbitrarily large "distance".At the critical state self-similar structures appear both in time Introduction

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Full and space.This fact is quantitatively manifested by power law expressions describing the distributions of spatial or temporal quantities associated with the aforementioned self-similar structures (Stanley, 1987(Stanley, , 1999)).
The time series analysis methods employed in this paper for the evaluation of the MHz EME recordings and the seismicity around the Cephalonia island in terms of critical dynamics are briefly presented in the following.Specifically, the method of critical fluctuations (MCF) is described in Sect.2.1, while the natural time (NT) method is described in Sect.2.2.
It has been shown (Contoyiannis and Diakonos, 2000) that the dynamics of the order parameter fluctuations φ at the critical state for a second-order phase transition can be theoretically formulated by the non-linear intermittent map: where φ n is the scaled order parameter value at the time interval n; u denotes an effective positive coupling parameter describing the non-linear self-interaction of the order parameter; z stands for a characteristic exponent associated with the isothermal exponent δ for critical systems at thermal equilibrium (z = δ + 1).The marginal fixedpoint of the above map is the zero point, as expected from critical phenomena theory.Introduction

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Full However, it has been shown that in order to quantitatively study a real (or numerical) dynamical system one has to add an unavoidable "noise" term, ε n , to Eq. ( 1), which is produced by all stochastic processes (Contoyiannis and Diakonos, 2007).Note that, from the intermittency mathematical framework point of view, the "noise" term denotes ergodicity in the available phase space.In this respect, the map of Eq. ( 1), for positive values of the order parameter, becomes: Based on the map of Eq. ( 2), MCF has been introduced as a method capable of identifying whether a system is in critical state of intermittent type by analyzing timeseries corresponding to an observable of the specific system.In a few words, MCF is based on the property of maps of intermittent-type, like the ones of Eqs. ( 1) and ( 2), that the distribution of properly defined laminar lengths (waiting times) l follow a powerlaw P (l ) ∼ l −p l (Schuster, 1998), where the exponent p l is p l = 1 + 1 δ (Contoyiannis et al., 2002).However, the distribution of waiting times for a real data time series which is not characterized by critical dynamics follows an exponential decay, rather than a power-law one (Contoyiannis et al., 2004a), due to stochastic noise and finite size effects.Therefore, the dynamics of a real time series can be estimated by forming the distribution of laminar lengths and fitting it to a function ρ(l ) combining both powerlaw and exponential decay (Contoyiannis and Diakonos, 2007): The values of the two exponents p 2 and p 3 , which result after fitting laminar lengths distribution in a log-log scale diagram, reveal the underlying dynamics.Exact critical state calls for p 3 = 0; in such a case it is p 2 = p l > 1.As a result, in order for a real system to be considered to be at critical state, both criticality conditions p 2 > 1 and p 3 ≈ 0 have to be satisfied.
Moreover, a special dynamics case is the one known as "tricritical crossover dynamics".In statistical physics, a tricritical point is a point in the phase diagram Introduction

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Full of a system at which the two basic kinds of phase transition, that is the first order transition and the second order transition, meet (Huang, 1987).A characteristic property of the area around this point is the co-existence of three phases, specifically, the high symmetry phase, the low symmetry phase, and an intermediate "mixing state".A passage through this area, around the tricritical point, from the second order phase transition to the first order phase transition through the intermediate mixing state constitutes a tricritical crossover (Huang, 1987).
The specific dynamics is proved to be expressed by the map (Contoyiannis et al., 2015): where m stands for the order parameter.This map differs from the critical map of Eq. ( 2) in the sigh of the parameter u and exponent z.Note that for reasons of unified formulation we use for these parameters the same notation as in the critical map of Eq. ( 2).At the level of MCF analysis this dynamics is expressed by the estimated values for the two characteristic exponents p 2 , p 3 values, that satisfy the tricriticality condition p 2 < 1, p 3 ≈ 0. These values have been characterized in Contoyiannis and Diakonos (2007) as a signature of tricritical behavior.More details on the application of MCF can be found in several published articles (e.g., Contoyiannis et al., 2002Contoyiannis et al., , 2013Contoyiannis et al., , 2015)), as well as in Sect. 3 where its application on the MHz EM variations is presented.

Natural time method (NT)
The natural time method was originally proposed for the analysis for a point process like DC or ultra-low frequency (≤ 1 Hz) SES (Varotsos et al., 2002;Varotsos, 2005), and has been shown to extract the maximum information possible from a given time series (Abe et al., 2005).The transformation of a time-series of "events" from the conventional time domain to natural time domain is performed by ignoring the time-stamp of each event and retaining only their normalized order (index) of occurrence.Explicitly, in a time Introduction

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Full series of N successive events, the natural time, χ k , of the kth event is the index of occurrence of this event normalized, by dividing by the total number of the considered events, χ k = k/N.On the other hand, the "energy", Q k , of each, kth, event is preserved.We note that the quantity Q k represents different physical quantities for various time series: for EQ time series it has been assigned to a seismic energy released (e.g., seismic moment) (Varotsos et al., 2005;Uyeda et al., 2009b), and for SES signals that are of dichotomous nature it corresponds to SES pulse duration (Varotsos, 2005), while for MHz electromagnetic emission signals that are of non-dichotomous nature, it has been attributed to the energy of fracto-electromagnetic emission events as defined in Potirakis et al. (2013).The transformed time series , where is the natural angular frequency, = 2πφ, with φ the natural frequency, and The study of Π ( ) at close to zero reveals the dynamic evolution of the time series under analysis.This is because all the moments of the distribution of p k can be estimated from Π ( ) at → 0 (Varotsos et al., 2011a).Aiming to that, by the Taylor expansion Π ( ) = 1 − κ 1 2 + κ 2 4 + . .., the quantity κ 1 is defined, where , the variance of χ k weighted for p k characterizing the dispersion of the most significant events within the "rescaled" interval (0, 1).Moreover, the entropy in natural time, S nt , is defined (Varotsos et al., 2006) as (Varotsos et al., 2006(Varotsos et al., , 2011b) ) to the value at q = 1 of the derivative of the fluctuation function F (q) = χ q − χ q with respect to q (while κ 1 corresponds to F (q) for q = 2).It is a dynamic entropy depending on the sequential order of events (Varotsos et al., 2006).The entropy, S nt− , obtained upon considering (Varotsos et al., 2006)  A system is considered to approach criticality when the parameter κ 1 converges to the value κ 1 = 0.070 and at the same time both the entropy in natural time and the entropy under time reversal satisfy the condition S nt , S nt− < S u = ln 2/2 − 1/4 (Sarlis et al., 2011), where S u stands for the entropy of a "uniform" distribution in natural time (Varotsos et al., 2006).
In the special case of natural time analysis of foreshock seismicity (Varotsos et al., 2001(Varotsos et al., , 2005(Varotsos et al., ,2006;;Sarlis et al., 2008), the seismicity is considered to be in a true critical state, a "true coincidence" is achieved, when three additional conditions are satisfied: (i) the "average" distance D between the curves of normalized power spectra Π (φ) of the evolving seismicity and the theoretical estimation of Π (φ) for κ 1 = 0.070 should be smaller than 10 −2 , (ii) the parameter κ 1 should approach the value κ 1 = 0.070 "by descending from above" (Varotsos et al., 2001), (iii) Since the underlying process is expected to be self-similar, the time of the true coincidence should not vary upon changing (within reasonable limits) either the magnitude threshold, M thres , or the area, used in the calculation.
It should be finally clarified that in the case of seismicity analysis, the temporal evolution of the parameters κ 1 , S nt , S nt− , and D is studied as new events that exceed the magnitude threshold M thres are progressively included in the analysis.Specifically, as soon as one more event is included, first the time series (χ k ,Q k ) is rescaled in the natural time domain, since each time the kth event corresponds to a natural time χ k = k/N, where N is the progressively increasing (by each new event inclusion) total number of the considered successive events; then all the parameters involved in the natural time analysis are calculated for this new time series; this process continues until the time of occurrence of the main event.
More details on the application of NT on MHz EME as well as on foreshock seismicity can be found in already published articles (Potirakis et al., 2013(Potirakis et al., , 2015)), as well as in Sects.3 and 4, where its application on the MHz EM variations and foreshock seismicity is presented, respectively.Introduction

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Electromagnetic emissions analysis results
Part of the MHz recordings of the Cephalonia station associated with the M w = 6.0 EQ (EQ1) is shown in Fig. 2a.This was recorded in day of year 24, that is ∼ 2 days before the occurrence of EQ1.This stationary time series excerpt, having a total length of 2.8 h (10 000 samples) starting at 24 January 2014 (12:46:40 UT), was analyzed by the MCF method and was identified to be a "critical window" (CW).CWs are time intervals of the MHz EME signals presenting features analogous to the critical point of a second order phase transition (Contoyiannis et al., 2005).
The main steps of the MCF analysis (e.g., Contoyiannis et al., 2013Contoyiannis et al., , 2015) ) on the specific time series are shown in Fig. 2b-d.First, a distribution of the amplitude values of the analyzed signal was obtained from which, using the method of turning points (Pingel et al., 1999), a fixed-point, that is the start of laminar regions, φ o of about 700 mV was determined.Figure 2c portrays the obtained laminar distribution for the end point φ l = 655 mV, that is the distribution of waiting times, referred to as laminar lengths l , between the fixed-point φ o and the end point φ l , as well as the fitted function f (l ) ∝ l −p 2 e −p 3 l with the corresponding exponents p 2 = 1.35, p 3 = 0.000 with R 2 = 0.999.Finally, Fig. 2d shows the obtained plot of the p 2 , p 3 exponents vs. φ l .From Fig. 2d it is apparent that the criticality conditions, p 2 > 1 and p 3 ≈ 0, are satisfied for a wide range of end points φ l , revealing the power-law decay feature of the time series that proves that the system is characterized by intermittent dynamics; in other words, the MHz time series excerpt of Fig. 2a is indeed a CW.
Part of the MHz recordings of the Zante station associated with EQ1 is shown in Fig. 3a.This was also recorded in day of year 24, that is ∼ 2 days before the occurrence of Cephalonia EQ1.This stationary time series excerpt, having a total length of 2.8 h (10 000 samples) starting at 24 January 2014 (12:46:40 UT), was also analyzed by the MCF method and was identified to be a "critical window" (CW).
The main steps of the MCF analysis (e.g., Contoyiannis et al., 2013Contoyiannis et al., , 2015) ) on the specific time series are shown in Fig. 3b-d values of the analyzed signal was obtained from which, using the method of turning points (Pingel et al., 1999), a fixed-point, that is the start of laminar regions, φ o of about 600 mV was determined.Figure 3c portrays the obtained laminar distribution for the end point φ l = 665 mV, that is the distribution of waiting times, referred to as laminar lengths l , between the fixed-point φ o and the end point φ l , as well as the fitted function f (l ) ∝ l −p 2 e −p 3 l with the corresponding exponents p 2 = 1.49, p 3 = 0.000 with R 2 = 0.999.Finally, Fig. 3d shows the obtained plot of the p 2 , p 3 exponents vs. φ l .
From Fig. 3d it is apparent that the criticality conditions, p 2 > 1 and p 3 ≈ 0, are satisfied for a wide range of end points φ l , revealing the power-law decay feature of the time series that proves that the system is characterized by intermittent dynamics; in other words, the MHz time series excerpt of Fig. 3a is indeed a CW.
After the M w = 6.0 (EQ1), ∼ a week later, the second, M w = 5.9 (EQ2), occurred on the same island with a focal area a few km further than the first one.Six days earlier, both the Cephalonia and Zante stations simultaneously recorded MHz EME.Specifically, a stationary time series excerpt, having a total length of 3.3 h (12 000 samples) starting at 28 January 2014 (05:33:20 UT), from Caphalonia station and a stationary time series excerpt, having a total length of 5 h (18 000 samples) starting at 28 January 2014 (03:53:20 UT), from Zante station were analyzed by the MCF method and both of them were identified to be CWs.Note that the Cephalonia CW was emitted within the time frame in which the Zante CW was emitted.Figures 4 and 5 show the results of the corresponding analyses.
In summary, we conclude that, according to the MCF analysis method, both stations recorded MHz signals that simultaneously presented critical state features two days before the first main event and six days before the second main event.In order to verify this finding, we proceeded to the analysis of all the corresponding MHz signals by means of the NT analysis method, according to the way of application proposed in Potirakis et al. (2013).According to the specific procedure for the application of the NT method on the MHz signals, we performed an exhaustive search seeking for at least one amplitude threshold value (applied over the total length of the analyzed signal), for

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Full which the corresponding fracto-EME events satisfy the natural time method criticality conditions.The idea is that if the MCF gives valid information, and as a consequence the analyzed time series excerpt is indeed in critical condition, then there should be at least one threshold value for which the NT criticality conditions (cf.Sect.2.2) are satisfied.Indeed, as apparent from Fig. 6, all four signals satisfy the criticality conditions according to the NT method for at least one of the considered threshold values, therefore the results obtained by the MCF method are successfully verified.On 2 February 2014, i.e., one day before the occurrence of EQ2, MHz EME presenting tricritical characteristics was recorded by the Cephalonia station.This signal emerged five days after the CWs that were identified in the simultaneously recorded, by the Cephalonia and Zante stations, MHz EME.The specific MHz time series excerpt from Cephalonia station, having a total length of 7.5 h (27 000 samples) starting at 2 February 2014 (07:46:40 UT), was analyzed by means of the MCF method yielding the results shown in Fig. 7.As apparent from the results, this signal satisfies the tricriticality conditions p 2 < 1, p 3 ≈ 0 (cf.Sect.2.1) for a wide range of end points φ l , revealing the intermediate "mixing state" between the second order phase transition to the first order phase transition.Unfortunately, during the time that the Cephalonia station recorded trictitical MHz signal, the Zante station was out of order; actually, it was out of order for several hours during the specific day.
It has been recently found (Contoyiannis et al., 2015) that such a behavior is identified in the kHz EME which usually emerge near the end of the MHz EME when the environment in which the EQ preparation process evolves changes from heterogeneous to less heterogeneous, and before the emergence of the strong avalanche-like kHz EME which have been attributed to the fracture of the asperities sustaining the fault.Actually, this has been proposed as the second stage of the fourstage model for the preparation of an EQ by means of its observable EM activity (Eftaxias and Potirakis, 2013, and references therein;Contoyiannis et al., 2015, and references therein;Donner et al., 2015).The identification of tricritical behavior in MHz EME is a quite important finding, indicating that the tricritical behavior, attributed to the Introduction

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Full second stage of the aforementioned four-stage model, can be identified either in kHz or in MHz EME, leading thus to a revision the specific four-stage model in order to include this case too.As a conclusion, after the first stage of the EQ preparation process where MHz EME with critical features are emitted, a second stage follows where MHz or kHz or both MHz and kHz EME with trictitical features are emitted.As already mentioned (cf.Sect.2.1), in terms of statistical physics the trictitical behavior is an intermediate dynamical state which is developed in region of the phase diagram of a system around the trictitical point, which can be approached either from the edge of the first order phase transition (characterizing the strong avalanche-like kHz EME attributed to the third stage of the four-stage model) or from the edge of the second order phase transition (characterizing the critical MHz EME attributed to the first stage of the four-stage model).Therefore, although it is expected that the trictitical behavior will be rarely observed, as it has already been discussed in (Contoyiannis et al., 2015), it can be found either in MHz time series, following the emission of a critical MHz EME, or in kHz time series preceding the emission of avalanche-like kHz EME.

Foreshock seismic activity analysis results
As already mentioned in Potirakis et al. (2013Potirakis et al. ( , 2015)): "seismicity and pre-fracture EMEs should be two sides of the same coin concerning the EQ generation process.If the MHz EMEs and the corresponding foreshock seismic sequence are observable manifestations of the same complex system at critical state, both should be possible to be described as a critical phenomenon by means of the natural time method".Therefore, we also proceeded to the examination of the corresponding foreshock seismic activity around Cephalonia before each one of the significant EQs of interest in order to verify this suggestion.However, we did not apply the NT method on concentric circles around the epicenter of each EQ, as in Potirakis et al. (2013Potirakis et al. ( , 2015)), but instead Introduction

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Full we decided to study seismicity within areas determined according to seismotectonic and earthquake hazard criteria.
Following the detailed study presented in Vamvakaris et al. (2013), we incorporated the seismic zones proposed there for our area of study.Thus, as it is presented in Fig. 8, we defined five separate seismic zones, based on the criteria explored in Vamvakaris et al. (2013) and the seismic zonation proposed by them.Since the study area, comprises the most seismically active zone in Greece, assigned also the highest value on the Earthquake Building Code for the country, a large number of source, stress and strain studies have been used in their study to establish such definition of zoning.Hence, it was found well justified to follow their zone definition.In Fig. 8, from east to west and north to south, one can identify the zones of Akarnania (area no.1), Lefkada island (area no. 2), east Cephalonia island (area no.3), west Cephalonia island (area no.4), and Zante island (area no.5), respectively, covering the area of the Ionian Sea near Cephalonia island.
Before we proceed to the NT analysis of seismicity, the seismic activity prior to EQ1, as well as between EQ1 and EQ2 is briefly discussed in relation to the above mentioned seismic zones.Earthquake parametric data have been retrieved from the National Observatory of Athens on-line catalogue (http://www.gein.noa.gr/en/seismicity/earthquake-catalogs), while for all the presented maps and calculations the local magnitude (M L ), as provided by the specific earthquake catalog, is used.The Applying the natural time analysis on seismic data (cf.Sect.2.2), the evolution of the time series (χ k , Q k ) was studied for the foreshock seismicity prior to EQ1, where Q k is in this case the seismic energy released during the kth event.The seismic moment, M 0 , as proportional to the seismic energy, is usually considered (Varotsos et al., 2005;Uyeda et al., 2009b;Potirakis et al., 2013Potirakis et al., ,2015)).Our calculations were based on the seismic moment M 0 (in dyn.cm) resulting from the corresponding M L as (Varotsos et al., 2005;Potirakis et al., 2013Potirakis et al., , 2015)), M 0 = 10 0.99M L +11.8 .First, we performed an NT analysis on the seismicity activity of the whole investigated Ionian Sea region during the period from 13 December 2013 00:00:00 to 26 January 2014 13:55:44 UT, i.e., just after the occurrence of EQ1, for different magnitude thresholds, M thres , for which all earthquakes having M L > M thres were included in the analysis.Note that, only M thres ≥ 2 was considered in order to assure data completeness (Chouliaras et al., 2013a, b).
For all the considered threshold values, the result was the same: no indication of criticality was identified (see for example Fig. 10a).Since, as we have already mentioned, the whole investigated area was mainly dominated by the seismic activity in west Cephalonia and the seismic activity in Zante, while an EQ of M L = 4.7 occurred in Zante, we decided to start the NT analysis after the occurrence of the specific Zante EQ, in order to exclude from our analysis possible foreshock activity related to the specific event.As a result, we performed NT analysis for the time period 11 January 2014 04:13:00 (just after the M L = 4.7 Zante EQ) to 26 January 2014 13:55:44 UT, for different magnitude thresholds in three successively enclosed areas: namely, the whole investigated area of Ionian Islands region, both Cephalonia (east and west) zones combined, and the zone of west Cephalonia.Representative examples of these analyses are depicted in Fig. 10b-d.The analysis over the whole investigated area of the Ionian Islands region indicates that seismicity reaches criticality on 19 and 20 January, while the two other progressively narrower areas indicate that the criticality conditions according to NT method are satisfied on 19 and 22 January.These results imply that seismicity was also in critical condition a few days prior to the occurrence of the first studied significant Cephalonia EQ (EQ1).Actually, in the specific case, the Introduction

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Full Before the application of the NT method to the seismic activity prior to EQ2, one should first study the time evolution of the activity between the two significant events of interest, in order to minimize if possible the influence of the first EQ aftershock sequence on the NT analysis.Our first observation about the EQs which occurred during the specific time period was that, all but one had epicenters in west Cephalonia.Only one M L = 2.3 EQ occurred in Zante, at (37.79 • N, 21.00 • E) on 28 January 2014 02:08:27 UT.
Figure 11a shows all the events that were recorded in the whole investigated area of the Ionian Islands region vs. time from just after EQ1 (M w = 6.0) up to the time of EQ2 (M w = 5.9), including EQ2.As it can be seen, if one considers that both significant EQs of interest were main events, it is quite difficult to separate the seismic activity of the specific time period into aftershocks of the first EQ and foreshocks of the second one.However, we observe that up to a specific time point, there is a rapid decrease of the running mean magnitude of the recorded EQs, while after that the long range (75 events) running mean value seems to be almost constant over time with the short range (25 events) one varying around it.We arbitrarily set the 29 January 00:00:00 UT as the time point after which the recorded seismicity is no longer dominated by the aftershocks of EQ1; this by no means implies that the aftershock sequence of the EQ1 stops after that date.It should also be underlined that changing this, arbitrarily selected, date within reasonable limits, does not significantly changes the results of our corresponding NT analysis which are presented next.On the other hand, a significant shift of this limit towards EQ1, i.e., to earlier dates, results to severe changes indicating the domination of the recorded seismicity by the aftershock sequence of EQ1.Accordingly, the considered as foreshock seismic activity before EQ2, i.e., from 29 January 2014 00:00 UT up to the time of occurrence of EQ2, is presented in the map of Fig. 11b for west Cephalonia and analyzed in the following.

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Full Next, we applied the NT method on the seismicity of west Cephalonia for the time period from 29 January 2014 00:00:00 to 3 February 2014 03:08:47 UT.Note that we also applied the NT method on the whole investigated area of the Ionian Islands region, obtaining practically the same results.As we have already mentioned, only one M L = 2.3 EQ occurred outside the west Cephalonia zone, so, on the one hand for magnitude threshold values M thres ≥ 2.3 this event was excluded, while, on the other hand, even for lower threshold values (2 ≤ M thres < 2.3) its inclusion does not change the results significantly.Figure 12 shows the NT analysis results for some threshold values proving that seismicity reaches criticality on 1 or 2 February 2014, that is one or two days before the occurrence of the second significant EQ of interest (M w = 5.9).Actually, in the specific case, the critical condition of seismicity was reached after, but quite close, to the emission of the corresponding MHz signals for which critical behavior was identified (cf.Sect.3).

Discussion -conclusions
Based on the methods of critical fluctuations and natural time, we have shown that the fracture-induced MHz EME recorded by two stations in our network prior to two recent significant EQs occurred in Cephalonia present criticality characteristics, implying that they emerge from a system in critical state.
There are two key points that render these observations unique in the up to now research on the pre-EQ EME: (i) The Cephalonia station is known for being insensitive to EQ preparation processes happening outside of the wider area of Cephalonia island, as well as to EQ preparation processes leading to low magnitude EQs within the area of Cephalonia island.Note that the only signal that has been previously recorded refers to the M = 6 EQ that occurred on the specific island in 2007 (Contoyiannis et al., 2010).

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Full (ii) Prior to each one of the studied significant EQs, two MHz EME time series presenting critical characteristics were recorded simultaneously in two different stations very close to the focal areas, while no other station of our network (cf.Fig. 1) recorded such signals prior to the specific EQs.This indicates that the revealed criticality was not associated with a global phenomenon, such as critical variations in the Ionosphere, but was rather local to the area of the Ionian Islands region, enhancing the hypothesis that these EME were associated with the EQ preparation process taking place prior to the two significant EQs.This feature, combined with the above mentioned sensitivity of the Cephalonia station only to significant EQs occurring on the specific island, could have been considered as an indication of the location of the impending EQs.
EME, as a phenomenon rooted in the damage process, should be an indicator of memory effects.Laboratory studies verify that: during cyclic loading, the level of EME increases significantly when the stress exceeds the maximum previously reached stress level (Kaizer effect).The existence of Kaizer effect predicts the EM silence during the aftershock period (Eftaxias et al., 2013;Eftaxias and Potirakis, 2013, and references therein).Thus, the appearance of the second EM anomaly may reveal that the corresponding preparation of fracture process has been organized in a new barrier.
We note that, according to the view that seismicity and pre-EQ EM emissions should be "two sides of the same coin" concerning the earthquake generation process, the corresponding foreshock seismic activity, as another manifestation of the same complex system, should be at critical state as well, before the occurrence of a main event.We have shown that this really happens for both significant EQs we studied.To be more detailed, the foreshock seismicity associated with the first (M w = 6.0)EQ reached critical condition a few days before the occurrence of the main event.
Specifically, it came to critical condition before, but quite close, to the emission of the corresponding MHz signals for which critical behavior was identified.The seismicity that was considered as foreshock of the second (M w = 5.9) EQ also reached criticality few days before the occurrence of the main event.In contrary to the first EQ case, Introduction

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Full it came to criticality after, but quite close, to the emission of the corresponding MHz signals for which critical behavior was identified.
One more outcome of our study was the identification of tricritical crossover dynamics in the MHz emissions recorded just before the occurrence of the second significant EQ of interest (M w = 5.9).This is considered a quite important finding, since it verifies a theoretically expected situation, namely the approach of the intermediate dynamical state of tricritical crossover, either from the first or from the second order phase transition state.In terms of pre-EQ EME, this leads to a revision of the fourstage model for the preparation of an EQ by means of its observable EM activity.Namely, after the first stage of the EQ preparation process where MHz EME with critical features are emitted, a second stage follows where MHz or kHz or both MHz and kHz EME with trictitical features are emitted.Specifically, the trictitical crossover dynamics can be identified either in MHz time series, following the emission of a critical MHz EME, or in kHz time series preceding the emission of avalanche-like kHz EME.In summary, the proposed four stages of the last part of EQ preparation process and the associated, appropriately identified, EM observables appear in the following order: 1st stage: valid MHz anomaly; 2nd stage: MHz or kHz or MHz and kHz anomaly exhibiting tri-critical characteristics; 3rd stage: strong avalanche-like kHz anomaly; 4th stage: electromagnetic quiescence.Note that the specific four-stage model is a suggestion that seems to be verified by the up to now available MHz-kHz observation data and corresponding time-series analyzes, while a rebuttal has not yet appeared in the literature.However, the understanding of the physical processes involved in the preparation of an EQ and their relation to various available observables is an open scientific issue.Much effort still remains to be paid before one can claim clear understanding of EQ preparation processes and associated possible precursors.
As it has been repeatedly pointed out in previous works (e.g., Eftaxias et al., 2013;Eftaxias and Potirakis, 2013, and references therein), our view is that such observations and the associated analyses offer valuable information for the comprehension of the Earth system processes that take place prior to the occurrence of a significant EQ.As Introduction

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Full it is known, a large number of other precursory phenomena are also observed, both by ground and satellite stations, prior to significant EQs.Only a combined evaluation of our observations with other well documented precursory phenomena could possibly render our observations useful for a reliable short-term forecast solution.Unfortunately, in the cases of the Cephalonia EQs under study this requirement was not fulfilled.To the best of our knowledge, only one paper reporting the emergence of VLF seismic-ionospheric disturbances four days before the first Cephalonia EQ (Skeberis et al., 2015) has been published up to now.It is very important that the specific disturbances, which also correspond to a spatially extensive process as happens with the MHz EME, were recorded during the same time window with the here presented MHz critical signals.
However, more precursory phenomena could have been investigated if appropriate observation data were available.For example, if ground-based magnetic observatories in the area of Greece had available magnetometer data for the time period of interest, EQ-related ULF magnetic field variations, either of lithospheric or ionospheric origin, which are also a result of spatially extensive processes and in other cases have been shown to present critical characteristics prior to EQ occurrence (Hayakawa et al., 2015), could also be investigated.Introduction

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Full  Full during the period from 13 December 2013 00:00:00 to 26 January 2014 13:55:44 UT.Note that the events employed depend on the considered threshold.Moreover, the time (x) axis is not linear in terms of the conventional date of occurrence of the events, since the employed events appear equally spaced relative to x axis, as the natural time representation demands, although they are not equally spaced in conventional time.The horizontal solid light green, solid grey and the grey dashed lines, denote the same quantities as in Fig. 6, while the horizontal solid brown line denotes the limit for D .(For interpretation of the references to colors, the reader is referred to the online version of this paper.)Introduction

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Full 2, 2.6, 2.8, and 3.0, respectively.Note that the events employed depend on the considered threshold.Moreover, the time (x-) axis is not linear in terms of the conventional date of occurrence of the events, since the employed events appear equally spaced relative to x axis, as the natural time representation demands, although they are not equally spaced in conventional time.The horizontal solid light green, solid grey and the grey dashed lines, denote the same quantities as in Fig. 6, while the horizontal solid brown line denotes the limit for D .
(For interpretation of the references to colors, the reader is referred to the online version of this paper.) . The possible relation of the field observed fracture-induced electromagnetic emissions (EME) in the frequency bands of MHz and kHz, associated Discussion Paper | Discussion Paper | Discussion Paper | • E) and depth of ∼ 11 km.Various studies of the two Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | the time reversal T , i.e., T p m = p N−m+1 , is also considered.Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | . First, a distribution of the amplitude Introduction Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | foreshock seismic activity before EQ1 for the whole investigated area of the Ionian Sea region from 13 December 2013 up to the time of occurrence of the main event is shown in the map of Fig.9a.As it can be easily observed from this map, there was a high seismic activity mainly focused on two specific zones: west Cephalonia and Zante.Notably, an EQ of M L = 4.7 occurred in Zante on 11 January 2014 04:12:58, indicated by the black arrow in Fig.9a.No EQs were recorded in Akarnania, while very few events were recorded in Lefkada and east Cephalonia.The events which occurred in west Cephalonia are also shown in a separate map in Fig.9bfor later reference.Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | critical condition of seismicity was reached before, but quite close, to the emission of the corresponding MHz signals for which critical behavior was identified (cf.Sect.3).
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Figure 1 .Figure 6 .Figure 8 .Figure 9 .
Figure1.Map with distribution of stations of the telemetric network that monitors electromagnetic variations in the MHz and kHz bands in Greece, which were operating during the time period of interest.The locations of the Cephalonia and Zante stations are marked by the magenta square and triangle, respectively, while the rest of the remote stations are denoted by red circles and the central data recording server by a blue circle.The epicenters of the two significant EQs of interest are also marked, the first (EQ1, M w = 6.0) by a red cross and the second (EQ2, M w = 5.9) by a green X mark.(For interpretation of the references to colors, the reader is referred to the online version of this paper.) Discussion Paper | Discussion Paper | Discussion Paper | Figure 10.Temporal evolutions of the four natural time (NT) analysis parameters (κ 1 , S nt , S nt− , and D ) for the foreshock seismic activity recorded prior to EQ1: (a) for the activity of the whole investigated area of the Ionian Sea for M L threshold 2.5, during the period from 13 December 2013 00:00:00 to 26 January 2014 13:55:44 UT (just after the occurrence of EQ1); (b) for the activity of the whole investigated area of the Ionian Sea for M L threshold 2.3, during the period from 11 January 2014 04:13:00 (just after the M L = 4.7 occurred in Zante) to 26 January 2014 13:55:44 UT; (c) for the activity of both Cephalonia (east and west) zones combined for M L threshold 2.1, during the period from 13 December 2013 00:00:00 to 26 January 2014 13:55:44 UT; (d) for the activity of the west Cephaloniafor M L threshold 2.1,

Figure 12 .
Figure12.Natural time (NT) analysis results for the seismicity in the partition of west Cephalonia during the time period from 29 January 2014 00:00:00 to 3 February 2014 03:08:47 UT (between EQ1, M w = 6.0, and EQ2, M w = 5.9): (a-d) temporal evolutions of the four natural time analysis parameters (κ 1 , S nt , S nt− , and D ) for the different M L thresholds 2.2, 2.6, 2.8, and 3.0, respectively.Note that the events employed depend on the considered threshold.Moreover, the time (x-) axis is not linear in terms of the conventional date of occurrence of the events, since the employed events appear equally spaced relative to x axis, as the natural time representation demands, although they are not equally spaced in conventional time.The horizontal solid light green, solid grey and the grey dashed lines, denote the same quantities as in Fig.6, while the horizontal solid brown line denotes the limit for D .(For interpretation of the references to colors, the reader is referred to the online version of this paper.)