## 6 Aftershock Sequence Analysis in Relation with Temporal Variations of \(b\) Value
Then, for each dataset, we recomputed the magnitude of completeness with the same method, since it is more appropriate than the goodness of fit method for small sample sizes (\(N^{*}\leq 200\)), which is the case here. A correction factor of +0.2 is considered in order to avoid biased results in the \(b\) value estimation, since the \(M_{c}\) tends to be underestimated [33; 37]. Table 4 summarizes the details of the two datasets. In both cases, the magnitude bin with the highest frequency corresponds to \(M=1.3\), so the completeness magnitude after the addition of the correction factor \(+0.2\) is \(M_{c}=1.5\), leading to \(N_{pre}=94\) events before the main shock and \(N_{aft}=226\) aftershocks (see Figure S1 for the GR law distribution of both datasets). Then, a sample window of size \(n_{pre}\) and \(n_{aft}\) is determined for the datasets before and after the main shock, respectively, for which we iteratively estimated the \(b\) values moving at each iteration one event forward. A minimum number of events for the sample size \(n_{thr}=50\) is defined, which is the threshold for an approximately 15% error in the estimation of the \(b\) value [35]. In this way, we achieved statistically reliable results. Figure 7: (**a**) Earthquake magnitudes, \(M\geq M_{c}\), as a function of time, (**b**) incremental (red triangles) and logarithm of the cumulative frequency (blue triangles) as a function of magnitude. The black line is the GR law fit with \(M_{c}=1.3\) according to maximum curvature (MAXC). We tested different sample sizes in order to examine the dependency of the results on the choice of the free parameters, \(n_{pre}\) and \(n_{aft}\) (Figure 8). The time-varying evolution of the \(b\) value does not significantly depend on the choice of these parameters in the size ranges (50, 85). We set \(n_{pre}=50\) and \(n_{aft}=70\), with 45 and 157 number of samples, respectively. However, we stress that with any other combination, the same conclusions would have been reached. In our case, the magnitude completeness is assumed constant, however, it is generally suggested to reevaluate it at each step since it can change in time, due to seismic network modifications or detection limitations. We keep the same initially estimated completeness threshold for two reasons. Firstly, the dataset covers a short period with relatively few events since it concerns the aftershock sequence of a moderate size main shock, which must be taken into account with caution for a robust estimation of the \(b\) value while evaluating iteratively the completeness threshold (many samples fall under the minimum value \(n_{thr}\)). Secondly, we verified that the geometry of the seismic network during the study period was stable, meanwhile, we are highly confident about the monitoring analysis quality since it was under our surveillance for the entire time interval. Nevertheless, we tested the temporal fluctuations of the \(b\) values both with constant and moving magnitude completeness thresholds and we did not observe significant variations through time (Figures S2 and S3). In all cases, the main observation of decreasing \(b\) values after the \(M4.5\) foreshock (dashed black line in Figure 8) compared to the increasing ones just after the main shock held true, therefore, in our analysis, we continued with a constant threshold that let us include more samples. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Datasets** & **Time Interval** & **N** & \(M_{c}\) & \(N_{c}\) & \(a\) & \(b\) \\ \hline Pre-main shock & 4/2/2018–5/2/2019 & 122 & 1.5 & 94 & 2.84 & 0.58 \\ \hline After-main shock & 5/2/2019–8/10/2019 & 298 & 1.5 & 226 & 3.48 & 0.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Information on the two datasets used in the study. Figure 8: Time-series of the \(b\) value for different sample sizes. The number of shocks (n) of each sample is written at the left top corner of each box and it is the same for both the pre-main shock and after-main shock datasets.