## 3 Results and Discussion
Indicative results of such a study are shown in Figure 5. This two-week time lag would have been the estimation of the occurrence time of the Kahramanmaras-Gaziantep \(M_{w}\)7.8 Pazarcik EQ by means of NTA if we did not proceed to the combination of NTA with NESM in [5; 74]. [PERSON] et al. [5; 74] suggested that in order to improve the estimate of the occurrence time of an impending EQ, one should also study the time-series of \(S_{q}\) and \(\Delta S_{i}\) of seismicity within the area to suffer the strong EQ, at comparable scales of \(i\) consecutive events, in order  
Figure 5: The values of \(x_{1}\), \(S\), \(S\), \(-\), and \(\langle D\rangle\) (left scale) as they evolve event after event for the seismicity inside the \(3^{\circ}\times 3^{\circ}\) area around the Kahramanmaras-Gaziantep \(M_{w}\)7.8 Pazarcik EQ epicenter. The EQs reported by AFAD are shown with the black candlesticks ending at circles, the magnitude \(M\) of which can be read in the right scale. Panels (**a–d**) correspond to \(M_{thres}=2.0\), \(2.2\), \(3.0\), and \(3.2\), respectively. to identify similar transient changes. The necessity of such a similarity has been discussed in detail in Section 5 of [74] and mainly stems from the fact that as we approach the strong EQ, fluctuations increase, making their presence evident in both NTA and NESM. The time-series of the Tsallis entropy \(S_{q}\) together with the entropy change \(\Delta S_{i}\) in natural time under time reversal are shown in Figure 6 for the time period after the true coincidence (17 to 21 January 2023) until the Kahramanmaras-Gaziantep \(M_{w}\)7.8 Pazarcik EQ. An inspection of Figure 6 reveals a similar transient behavior indicated by the red arrows that lasts from 29 January to 3 February 2023, i.e., almost three days before the Kahramanmaras-Gaziantep \(M_{w}\)7.8 Pazarcik EQ. We observe that the combination of NTA with NESM may provide an improved estimate of the occurrence time of the Kahramanmaras-Gaziantep \(M_{w}\)7.8 Pazarcik EQ by a significant factor, i.e., from almost two weeks to almost three days. This, i.e., the improvement of the estimate of the occurrence time of an impending strong EQ, is compatible with the results found for the 2011 M9 Tohoku, Japan, EQ [5], the 2017 M8.2 Chiapas, Mexico, EQ [74], and the 2019 \(M\)7.1 Ridgecrest EQ [74]. In our view, it is this point that stresses the importance of fluctuations before strong EQs, which should be also studied in the future for other catastrophic EQs. As already mentioned, there were no SES data before the Kahramanmaras, Turkey, EQ doublet. In such cases, NTA may provide an estimate of the epicentral area of the impending EQ by means of a spatiotemporal study, see, e.g., Chapter 3 of [38] and references therein. However, such an analysis is possible when the local EQ catalog used fully covers the study area, which is rarely possible when national boundaries exist in this area. In these cases, our group has suggested [124; 125; 129] that the average EPS maps based on Equation (15) may provide an estimate of the epicentral location of the impending EQ. The calculation of the \(\langle\)EPS\(\rangle\) map should be made on the date of the variability minimum \(\beta_{W,min}\) identified before the strong EQ. Following [PERSON] et al. [124] and Section 2.6, we depict in Figure 7a  
Figure 6: The quantities (upper panel) \(\Delta S_{i}\) in NTA and (lower panel) Tsallis entropy \(S_{q}\) of NESM versus the conventional time (UTC) inside the 3\({}^{\circ}\times\) 3\({}^{\circ}\) area around the Kahramanmaras-Gaziantep \(M_{w}\)7.8 Pazarcik EQ epicenter. The red arrows indicate the simultaneous transient changes of \(\Delta S_{i}\) and \(S_{q}\) after the validity of the criticality condition \(\kappa_{1}=0.070\). They start and end upon the occurrence of two EQs of magnitudes 4.4 and 4.6, respectively.