**4. Results**

We estimate the corner magnitude and the *β* of the tapered Pareto distribution both for the whole catalog and for two sub-catalogs: the one containing only normal events and the one containing only the strike-slip events. To select the event in the sub-catalogs, we use the classical Aki-Richards convention for rake: we consider as normal the events with the rake of both nodal planes of the CMT catalog in the range from −45◦ to <sup>−</sup>135◦, and as strike-slip the events with the rake of both nodal planes of the CMT catalog in the range from −45◦ to 45◦ or 135◦ to 180◦ or −180◦ to <sup>−</sup>135◦. When the two nodal planes have different classifications, the event is not classified. The results of this classification are reported in Table 2. Notably, thrust and undefined events, not contained in either subcatalog, represent only a small part of the events. We underline that in our computation we do not take into account possible uncertainties in the focal mechanism estimation of the CMT catalog; future development of the method will try to introduce these uncertainties in the estimation process.

**Table 2.** Number of events, percentage (over the whole catalog), and maximum observed magnitude for the different sub-catalogs.


In Figure 7 we show the results of the estimation for the whole catalog (black curve and dot), for the normal events (green curve and dot), and strike-slip events (red curve and dot); the curves represent the estimated 95% confidence regions (corresponding to 2 standard deviations in normal distributions), while the dots represent the MLE. In the case of distributions with two parameters, the confidence intervals became confidence regions (see Figure 4), to properly capture the 2D nature of these uncertainties.

**Figure 7.** 95% Confidence region estimation (curves) and maximum likelihood estimations MLEs (dots) for the whole catalog (black), and the sub-catalogs with strike-slip events (red), and with normal events (green).

Looking at the shape of the confidence regions, it is evident that the two parameters result fairly uncorrelated. Both for normal and strike-slip events we obtain closed confidence regions, i.e., the confidence regions define a finite area for the uncertainty, showing

a well-constrained estimation for all parameters; conversely, for the whole catalog, the confidence region is open toward large corner magnitudes, indicating an unconstrained estimation of the corner magnitude [7,8]. These results are compatible with an infinite corner magnitude corresponding to an unbounded Gutenberg-Richter. We also obtain a clear distinction of the *β* values for the two sub-catalogs, which results averaged when the whole catalog is used. In Table 3 we show all the MLE for the corner magnitude and *β* parameters.

**Table 3.** Maximum likely estimation MLE of the corner magnitude and the slope *β* , for the whole catalog and for the two sub-catalogs.

