## 2 Data  
I used three different earthquake catalogs. The first was the ISC-GEM catalog ver 6.0 [12; 13; 14]; the second was that produced by the Southern California Earthquake Center [15]; the third was the Italian CPTI15 [16], with numerous additions that I illustrate in detail. The ISC-GEM catalog is a worldwide instrumental catalog, spanning from 1904 to 2015. The main set I selected (DS1) considers magnitude M \(\geq\) 6.00 and depth D \(\leq\) 60 km. The time interval goes from 1950 to 2015, as 1950 seemed to represent a turning point in the completeness of the catalog such that, for the purposes of this paper, the set could be considered to be complete. A few tens of events, however, had to be discarded, as many large events were, in fact, multiple events; global catalogs often fail to detect these, and the completeness in such cases is almost null. An example I am personally aware of [17] is the 1980 Irpinia earthquake, which was a multiple event composed of three different M \(>\) 6 earthquakes which took place, spaced about 20 s one from the other, along different faults located a few tens of kilometers from each other. The global catalogs, including the ISC-GEM one, consider this earthquake to be a single event. However, there are some cases when the multiple events in ISC-GEM are reported separately. Consequently, I eliminated the second earthquake from the dataset, whenever two events were spaced less than twice the sum of the length of their faults (computed according to Reference [18]) and had a time interval consistent with a rupture propagation speed of at least 500 m/s. After this operation, 6921 events remained. There was another reason. Most of the solutions, in terms of magnitude, in the ISC-GEM were from the GCM catalog [19; 20]; the latter does not distinguish between two proximal events, being a spectral method, and includes the sum (in terms of moment) of both events. The second dataset (DS2) also originated from the ISC-GEM catalog, and it is composed of events with magnitude M \(\geq\) 8.50 and depth D \(\leq\) 60 km. The time interval goes from 1918 to 2015. There are 16 events in it. The third dataset (DS3) is the de-clustered version of DS2, which is made up by 14 events. The fourth dataset (DS4) is composed of all the earthquakes reported by the Southern California Earthquake Center with magnitude M \(\geq\) 3.00 between 1980 and 2018. It is made up of 11,852 events. I chose this magnitude threshold for two reasons; it ensures completeness also in the most peripheral areas--particularly offshore--and it does the same for the aftermath of the largest events. The fifth dataset (DS5) is composed by 64 events which caused noticeable damage in Italian territories from 1600 to 2016. They yield magnitude M \(\geq\) 6.00 and depth D presumably \(\leq\)45 km. Of these events, 61 are from the CPTI15, which ends in 2014, while the last three (all occurring in 2016) are from the GCM catalog. One event, the 1743 Ionian Sea, was excluded, even though it caused heavy damage in southern Puglia, since its epicentral location was very far offshore [21] and, at that distance, only very large events could be detected; the seismic record in that area, therefore, is surely not complete. DS5 was a validated set, but it did not pass even a simple completeness _Gutenberg_--_Richter_ test. I devised a way to complete it, from a statistical viewpoint, which formed the sixth and last dataset (DS6) (see File S1 in supplementary). The rationale is that the vast majority of the missing events were already reported in the catalog; however, for some reason, their magnitude was underestimated. Obviously, it could also occur that events with M \(\geq\) 6.00 were overestimated. I believed, however, that the true solution was hidden in this dataset. In particular, I split the 27 March 1638 event into two events, according to Reference [22]. Then, I chose all the events reported in the CPTI15 catalog that may have represented underestimated events.