## 4 Discussion  
The results presented here are showing a small, but positive correlation between the occurrence of earthquakes and the anomalous variations of ionospheric scintillation. The confusion matrix shows the values for the True Positives, True Negatives, False Negatives, and False Positives integrated for all the days in the period studied. The positives (P) show the number of pixels with at least one earthquake within the radius distance, and it is only varying when this parameter changes. For example, in Table 3, is 363 for all cases, as the radius is always 100 km. It is observed that when the \(\Delta S_{4}\) threshold (\(s4\_th\)) increases, the number of true positives (TP) and false positives (FP) both decrease. The relative ratio of change is studied with the ROC curves. Larger values of the TPR with respect to the FPR for the same threshold mean that is more probable that a positive in the predicted condition (ionospheric anomaly) is associated with an earthquake event, than it is not, and they will be represented by curves above the diagonal. Figure 13 shows the ROC for the three magnitude intervals. All of them show a small, but positive indicator, with curves above the main diagonal for almost all the threshold values selected. What is also very interesting is that, as the magnitude of the earthquakes increases, the curves are further from the diagonal, and also they separate from each other. In the last graph (Figure 13c), for magnitudes larger than 6, curves for \(d\_margin=+3\) and \(d\_margin=+6\) are above their corresponding negatives values. This means that for the  
Figure 14: ROC curves for three magnitude intervals using \(radius=50\) km. Figure 15: ROC curves for three magnitude intervals using \(radius=100\) km. largest earthquakes a better correlation is observed when the anomalies are recorded a few days (3 to 6) before the earthquakes. Similar results show the ROC curves in Figures 14 and 15, which have been drawn using a coarser s4_th interval. In this case, for the 50 km radius and magnitudes larger than 6 (Figure 14c), we observe that only the one corresponding to the \(d\_margin=+6\) is separating from the main diagonal. Here we can see that the correlation is less when the radius decreases from 100 km to 50 km. The values of the ROC-AUC are also a good indicator of the performance of the correlation. Please note that in all the ROC curves shown before in Figure 13, none of their values reach the point (1,1) even that the sensitivity parameter, s4_th, has been swept from 0 to 0.03 or 0.04. \(s4\_th=0\) is the one closer to the (1,1), but decreasing this value under 0 makes no sense as it would mean considering a detection when the average \(S_{4}\) during the last 7 days has been larger than a value lower than the last 2-month average. Then, the ROC-AUC has been computed using the data points shown in the curves, and adding the points (0,0) and (1,1), doing a linear extrapolation. The resulting areas are shown in Tables 5 and 6. Table 5 for \(radius=100\) km identifies the magnitude larger than 6, as the set of curves with larger ROC-AUC values in general, being the largest one, 0.5766, when the interval for \(d\_margin\) is \([0,+3]\), closely followed by the \(d\_margin=[+3,+6]\). The rest of the table exhibits values around 0.52, very similar among them, remarking the similarity among the curves for the lowest two magnitude intervals in Figure 13.  
Table 6 shows the results of the ROC-AUC for \(radius=50\) km. In the case of the largest magnitude interval (above 6), as observed in Figure 14 the ROC lines are closer to the main diagonal, or even under it, resulting in ROC-AUC values under 0.5. In this case, the better results in terms of ROC-AUC values are for the lower magnitude intervals, [5-5.9] and [4-4.9]. This may be an indicator that smaller earthquakes may produce perturbations at smaller distances from the epicenter. Another way to analyze the correlation between both events is through the statistics extracted from the CM.