## 3 Validation of the Improved KF Version
To give an example, we explored the case of the 2012 earthquake, an area that was almost 0.5\({}^{\circ}\)\(\times\) 0.5\({}^{\circ}\), precisely 47 lines in latitude by 51 rows in longitude. Since we were using only another parameter, this computation is extremely fast, but in cases where we are exploring seven or eight parameters, using hundreds of intensity points, this computation rapidly approaches levels of CPU time that are simply not affordable. This means that it is necessary to follow a refinement approach. Moreover, there is a maximum distance for the application of this method that is about 100 km, the distance in Italy for which we have direct S-wave propagation using an elastic half-space; this implies that we need to keep the number of intensity points that falls within the 100 km range at each step constant. This distance within 100 km obviously depends on epicentral locations, fault lengths, and strikes. Since  
Figure 2: SA and SB: best representatives of two families of solutions for the 20 May 2012 event; blue polygon: area of maximum deformation after [16]; red lines are known thrusts (all dipping southward) [36]. at each refinement step, the parameter range is reduced, this introduces another source of strong nonlinearity. This is tantamount to saying that there is a small but non-negligible degree of subjectivity in defining an optimal solution. This is another reason why we will, in general, identify a few families of possible solutions, represented by the best one for each family, and then we will try to select the preferred one on the basis of tectonic considerations and not on the basis of residuals only. It would be natural to test this approach on some modern event where the source is well known. However, none of those with M \(>\) 6 shows a full range of intensity values. The event we selected, however, yields intensities from I\({}_{\text{MCS}}\) = 2 to I\({}_{\text{MCS}}\) = 9 and has an instrumental magnitude estimate (M\({}_{\text{wp}}\) = 6.09) that is not dissimilar to the macroseismic-based one (M\({}_{\text{wp}}\) = 5.99) [1]. The epicentral area of the M\({}_{\text{wp}}\)6 earthquake of 27 March 1928 (Table 2) is located in the central part of the Italian Region of Friuli Venezia Giulia (Figure 3), in the eastern portion of the Southern Alps. The area (Figure 4) of the 1928 M\({}_{\text{wp}}\)6 earthquake is located at the boundary between the fold and thrust belt of the Southern Alps and the Venetian Friulian plain and follows the Pliocene-Quaternary front of the eastern Southalpine Chain [37]. Figure 4: **(a)** The 27 March 1928 macroseismic field [1,2]. **(b)** Zoom in of **(a)** that encompasses the macroseismic epicentral area and the Gémona alluvial fan. Locality names refer to those cited in the text. The eastern part of the Southern Alps is affected by high seismicity, the highest in the entire Alpine chain. The shortening and thickening of the crust are still active and the most seismic activity has been recorded along the southern edge of the eastern Southalpine Chain. The seismicity is almost exclusively due to the activation of compressional sources, with the main compression oriented between NNW-SSE and N-S [38]; associated with the evolution of the S-SE verging trending overthrust fronts, focal mechanisms of strike-slip characterize the western Slovenian territory [39; 40] and the Alto Tagliamento area north of Tolmezzo [38; 39; 40; 41; 42]. The central part of eastern Southern Alps Chain--the area affected by the 1928 earthquake--is located in the transition zone between the Southern Alps and the Dinarides. The transition is marked by the southern front or Periadriatic Lineament [43]. The geological units of the area consist mainly of limestones and carbonate rocks from Triassic to Cretaceous, which belong to the thick shelf complex of the Friuli Platform [44]. Flysch and molasse compose the Cenozoic and Quaternary deposits.