## 5 Discussion  
By adopting the newly developed procedure, we can consider a much larger dataset for estimating the parameters of the tapered Gutenberg-Richter distribution, as catalog should not be declustered and different magnitude of completeness can be adopted in an older time, extending the temporal coverture of the catalog. This allows a deeper analysis of the Gutenberg-Richter distribution, also considering possible variations in sub-catalogs. We applied this principle to the seismicity of the Atlantic ridge, obtaining a much-improved description of its seismicity. In particular, the different shapes of the confidence regions obtained considering the whole catalog and the sub-catalogs clearly demonstrate that a mixture of different types of events (i.e., with different focal mechanisms) with different statistical properties for the Gutenberg-Richter distribution can lead to an untrustworthy estimation of its parameters, artificially enlarging their confidence bounds, in particular for the corner magnitude. We find instead that the corner magnitude for both normal and strike-slip events is well constrained, and incompatible with an unbounded Guttenberg-Richter distribution. This is in agreement with the observation that the size of such a structure is rather limited in the case of oceanic ridges [15]. The estimation of the corner magnitude for the normal event is particularly low (\(C_{M}=5.78\)), but it is in line with the estimation obtained by [PERSON] et al. [15] for oceanic spreading ridge earthquakes (\(C_{M}=5.83\)). Conversely, the undifferentiated catalog provides an averaged corner magnitude (biased with respect to both sub-catalogs), with an open confidence region that is compatible with unbounded distribution. Notably, the sub-catalogs almost completely cover the entire catalog, and the thrust and unclassified events not only represent a small subset of events, but also cannot influence the estimation of the corner magnitude, as the maximum observed magnitude for these events is considerably smaller than the one of the whole catalog (6.31 vs. 7.10). The slope parameter \(\beta\) for strike-slip event is similar to the one of [PERSON] et al. [29] for the global catalog; on the contrary, the \(\beta\) for the normal events is very high (1.08), corresponding to a b-value equal to 1.62; however, this estimation is quite uncertain (see Figure 7, green curve), with the 95% confidence region for \(\beta\) ranging from 0.90 to 1.25. This large confidence region is compatible with the \(\beta\) estimated by [PERSON] and [PERSON] [16] for the normal event in the oceanic spreading ridge (\(\beta=0.91\)). The results are pretty independent of the selected completeness. In the Supplementary Material, we perform the same estimation shown in Figure 7, but using a more conservative magnitude of completeness, obtaining very similar results, and thus demonstrating that these results are robust and do not depend on the chosen completeness thresholds. As discussed above, the newly developed estimation method allows increasing the input dataset by not requiring declustering and by allowing a variation through time of the completeness level. While the largest reduction is due to no declustering, we not \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **Corner Magnitude (MLE)** & \(\beta\) **(MLE)** \\ \hline Whole catalog & 7.25 & 0.92 \\ \hline Normal events & 5.78 & 1.08 \\ \hline Strike-slip events & 7.01 & 0.66 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Maximum likely estimation MLE of the corner magnitude and the slope \(\beta\), for the whole catalog and for the two sub-catalogs. that also the possibility of considering different completeness levels has a considerable impact. In Figure 8 we show the specific impact of the use of different completeness thresholds through time, allowed by the newly developed estimation method. The results are compared with the classical estimation method, in which one level of completeness for the whole catalog is used (Mw 5.5 from 1980 to 2019).