**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 muchimproved 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 agreemen<sup>t</sup> 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 Bird 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 *β* for strike-slip event is similar to the one of Schorlemmer et al. [29] for the global catalog; on the contrary, the *β* 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 *β* ranging from 0.90 to 1.25. This large confidence region is compatible with the *β* estimated by Bird and Kagan [16] for the normal event in the oceanic spreading ridge (*β* = 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 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). The lower number of events available using only one level of completeness leads to larger confidence regions. In particular, for normal events, the confidence region computed with the classical method (light green curve in Figure 8) is much bigger than the one computed with the new method (green curve in Figure 8). As expected, a larger amount of available information leads to smaller uncertainties in the estimated parameters, especially in this case. Notably, central values (MLEs) also change, correcting potential biases. For example, the MLE for the entire catalog results outside the confidence bounds defined using more data.

**Figure 8.** 95% Confidence region estimation (curves) and maximum likelihood estimations MLEs (dots) for the classical estimation approach (light colors: gray, pink, and light green) and the new estimation approach (dark colors: black, red, and green). As in Figure 7, we report both results using for the whole catalog (gray and black), and the sub-catalogs with strike-slip events (pink and red), and with normal events (light green and green).

The different shapes of the confidence region considering the whole catalog and the sub-catalogs show the importance of separating the contribution of different classes of earthquakes to correctly interpret their behavior. Indeed, the averaged behavior estimated from the complete catalog is substantially incompatible with the actual behavior of each single seismicity class. Indeed, by applying the global statistics (obtained by the full catalog) to each individual class, we would implement the wrong statistics to different classes, impacting the hazard in a different way. In our case study for the Atlantic ridge, we would artificially increase the probability of high magnitude normal events. On the contrary, compared with strike-slip events, we demonstrated that normal earthquakes have a significantly smaller corner magnitude coupled with a significantly larger b-value, resulting in a smaller probability of high magnitude normal events.

This not only may complicate the interpretation of the parameter estimation, but also may have a significant impact on hazard quantifications. For example, most of the recent ground motion prediction equations to estimate the attenuation of seismic waves from the source to target are dependent on faulting mechanisms, applying different attenuation laws to the different mechanisms (e.g., [30]). This is probably even more impacting is tsunami hazard, where different mechanisms have a different capability of deforming the sea bottom, resulting in different tsunamigenic capabilities (e.g., [31]). For example, normal events are typically more tsunamigenic than strike-slip events. For not introducing artificial bias in hazard quantification, it will be therefore fundamental to individuate potential mechanism-dependent variation of earthquake statistics and apply hazard models allowing for the aggregation of multiple classes of seismicity (e.g., [32]).
