## 2 Materials and Methods
### Natural Time Analysis: Background  
In a series comprising \(N\) EQ events (which can be considered as a temporal point pattern [5; 92]), natural time \(\chi_{k}\) corresponding to the \(k\)-th EQ of magnitude \(M_{k}\) is defined [20] as \(\chi_{k}=k/N\). Thus, we abandon the notion of conventional time but maintain the EQ energy \(Q_{k}\) (\(\propto 10^{1.5M_{k}}\), see, e.g., [93] and Chapter 6 of [23]) together with the order of occurrence \(k\). In NTA, the pair \((\chi_{k},p_{k})\), where \(p_{k}=Q_{k}/\sum_{n=1}^{N}Q_{n}\) is the normalized energy, is attributed to each event \(k\), and we consider the normalized power spectrum \(\Pi(\omega)\equiv|\Phi(\omega)|^{2}\), where \(\Phi(\omega)=\sum_{k=1}^{N}p_{k}\exp(i\omega\chi_{k})\). The quantities \(p_{k}\) can be considered (see, e.g., Appendix A.3 of [38] and references therein) as probabilities, and hence \(\Phi(\omega)\) with \(\omega\in\mathcal{R}\) corresponds to the characteristic function [94] for \(p_{k}\). This characteristic function provides information for the distribution: for example, the moments \(\langle\chi^{m}\rangle=\sum_{k=1}^{N}\chi_{k}^{m}p_{k}\) that are equal to the derivatives \(d^{m}\Phi(\omega)/d\omega^{m}\) (\(m>0\)) at \(\omega\to 0\). In a similar sense, when considering \(\Pi(\omega)\) in the region of \(\omega\) close to 0, a quantity \(\kappa_{1}\) was obtained from the Maclaurin series  
\[\Pi(\omega)=1-\kappa_{1}\omega^{2}+\kappa_{2}\omega^{4}+\dots, \tag{4}\]  
where  
\[\kappa_{1}=\langle\chi^{2}\rangle-\langle\chi\rangle^{2}=\sum_{k=1}^{N}p_{k} (\chi_{k})^{2}-\left(\sum_{k=1}^{N}p_{k}\chi_{k}\right)^{2}. \tag{5}\]  
For the case of SES activities, mentioned in the Introduction, that exhibit critical dynamics [54], it has been shown [20; 23] that the corresponding \(\Pi(\omega)\) takes the form:  
\[\Pi_{crit}(\omega)=\frac{18}{5\omega^{2}}-\frac{6\cos\omega}{5\omega^{2}}- \frac{12\sin\omega}{5\omega^{3}}. \tag{6}\]  
Figure 3: The tectonic settings of the Anatolian region along with the epicenters (yellow stars) and the focal mechanisms of the two catastrophic EQs of \(M_{w}=7.8\) at 01:17:34 UTC and \(M_{w}=7.5\) at 10:24:48 UTC on 6 February 2023. The red arrows indicate the movement of the tectonic plates, and the black arrows indicate the direction of movement along the major fault zones; see [89] and references therein (cf. for a review of the historical seismicity in the region, see [91]). Moreover, it has been shown that  
\[\kappa_{1}\approx 0.070 \tag{7}\]  
at criticality for various dynamical systems [20; 23; 38; 95] that include SES activities; see, e.g., Table 8.1 on page 343 of [23]. In general, \(\kappa_{1}\) is suitable for identifying the approach to a critical point. Especially, in NTA of EQs, \(\kappa_{1}\) can be thought of [23; 38] as an order parameter (OP) for seismicity because its value diminishes abruptly when a strong EQ takes place, while the statistics of its fluctuations share properties observed in well-known critical systems [96]. One of the advantages of NTA is that it allows for monitoring the fluctuations of the OP of seismicity within an EQ catalog. For this purpose, we consider an excerpt of this catalog consisting of \(W\) successive events. We then deduce the totality of \(\kappa_{1}\) values resulting from subexcerpts of the successive 6 to \(W\) EQs. For this set of \(\kappa_{1}\) values, we calculate the mean value \(\mu(\kappa_{1})\) and the standard deviation \(\sigma(\kappa_{1})\), leading to the variability of \(\kappa_{1}\):  
\[\beta_{W}=\frac{\sigma(\kappa_{1})}{\mu(\kappa_{1})} \tag{8}\]  
that quantifies the \(\kappa_{1}\) fluctuations within this EQ catalog excerpt. The quantity \(\beta_{W}\) of Equation (8) is interrelated with the square root of the Ginzburg criterion (cf. Equation (6.25) of [97]) whose usefulness in the physics of EQs has been explained by [PERSON] et al. [98].