## 2 The Algorithm for Identification of Multiple Events  
A special algorithm for the search of multiple events in a seismic catalog was created to use it as metrics in the comparison between the simulator results and the observed seismicity of the studied region. The computer code is \"customer-built\" and it was already introduced by [PERSON] et al. [7]. There is no specific definition of \"sequence with multiple main shocks\", nor any fixed magnitude values. We give here a brief description for a better understanding of its use. At its first level, the algorithm systematically analyzes time-ordered couples of events to check if they meet some constitutive conditions. Once matching couples are found, they are then used as elements for ordered noncyclic graph construction. These graphs can be 'traversed' to find in them the searched multiple events groups. In accordance with the above definitions, we developed a method based on four criteria for our comparisons among couples of events (Table 1):  
1. There is a minimum magnitude threshold for the first event of the group (hereafter called \"pivot\");
2. The magnitude of any other main shocks of the sequence must lay in a predefined neighborhood of the pivot's magnitude;
3. The events' time differences must be less than a threshold time, which is a function of event magnitudes (subject to criteria #1 and #2);
4. For any event, a magnitude dependent distance (a radius) is defined and the distance between the epicentres must be smaller than a proper function of those radii.  
The values associated to the criteria #1 and #2 are selected by the user and based on needs, expert judgment and/or knowledge of the instrumental-historical seismicity of the area. The relations for time (#3) and distance (#4) thresholds as a function of event magnitudes were derived from [PERSON] and [PERSON] [5] empiric tables and as epicentre distance threshold. Notice that the criterion #3 does not provide for a choice, while the criterion #4 provides for the choice among three different ways of applying the formulas of [PERSON] and [PERSON] [5]. In this study, we used the sum of the radii. Once launched, the algorithm parses the catalog through a cyclic, the three-step analysis procedure is repeated until the end of the file:* The first step starts with the selection of the next pivot event and the definition of a pool of eligible events (if they exist). They are found using criterion #3;
* The second phase is a thorough analysis of all useful couples taken from the pool, checked for fulfillment of criteria #1, #2 and #4;
* The last step is the construction of the graph, its traversal for the multiplets group search, its eventual output in the output buffer, and the flagging of used events to not reuse them after the next pivot search.  
Table 1 summarizes the formulas, explaining the rationale by which they were used in this study, and lists our choices for the threshold values.  
Even if the algorithm cannot be called \"optimal\" in principle, since it is based on an arbitrary choice among possible criteria, it is, however, quite effective, and its importance lays in the metrics it represents for comparison among seismic catalogs.