## 5 Results and Discussion  
A total of 15 plots of the volumetric strain at the free surface have been computed for the modeled faults, inferring a different sense of slip (Figure 6a-q). Being inferred by inversions of intensity data, the source MF (Figure 6e,l,q) obviously shows a good fit with the map of intensities and the location of the earthquake. However, the performance of the strain modeling of this source is limited, with no agreement between observed hydrological changes and the expected pattern of strain, independent of the style of faulting adopted. Additionally, there is no close association between the location of this source and the distribution of the other effects observed following the earthquake, all located northwest of the fault. When we impose pure normal kinematics to all of the seismogenic sources investigated (Figure 6a-e), we obtain a limited agreement between the predicted pattern of strain and the location of the hydrological changes. In particular, the noticeable increase in discharge of the Gari springs observed in Cassino constantly falls in an area of expected dilatation. Conversely, if we impose a lateral component of the slip on the five sources, we find more satisfactory solutions for data merging. In general, oblique left-lateral sources display a better fit between strain and hydrological signatures; in particular, PF (Figure 6h) and SF (Figure 6g,i) show the best fit for the observations in Cassino (increase in discharge/expected compression) and Isola Liri (decrease in discharge/expected dilatation). The potential source of the 1654 earthquake is inferred through the cross-analysis between the results from modeling and the other pieces of evidence described above (see chapter 3). Though there is a fairly good fit from strain modeling shown by the Balsorano fault with rake \(-130^{\circ}\) (only for the two observations in Isola Liri, Figure 6m), we exclude this source from the group of most likely causative faults of the 1654 earthquake because (1) there is no agreement between its location and the map of the intensities (see Figure 2);  
Figure 6: Comparison between the calculated coseismic strain fields along five potential sources and the observed hydrological effects produced by the 1654 earthquake. The calculation of strain was made using Coulomb 3.4 [27,28]. Plots ‘(**a**–**e**)’ show the calculations for normal sources (rake \(-90^{\circ}\)), plots ‘(**f**–**i**)I’ show the calculations for oblique left-lateral sources (rake \(-50^{\circ}\)), and plots ‘(**m**–**q**)’ show the calculations for oblique right-lateral sources (rake \(-130^{\circ}\)). In the plots of strain, blue shading indicates areas in compression and red shading indicates areas in dilatation. Units: \(10^{-5}\). A red rectangle indicates the surface projection of the fault plane; a green line is the intersection of the updip projection of the fault with the surface. Streamflow changes are indicated by circles (black/discharge increase; white/discharge decrease). (2) oblique-right lateral source seems to be an infrequent style of faulting in this sector of the Central Apennines based on seismological and geodetic data [11; 29]; and (3) the epicenter of the 1654 quake is located 15 km from the southern tip of the BF. With regard to the Posta-Fibreno fault, its location fits better than the Balsorano fault when compared with the 1654 epicenter and distribution of macroseismic intensities, and an oblique left-lateral sense of slip along this fault (Figure 6h) displays a good fit with the distribution of the hydrological changes (effects 1, 2, and 3 in Figure 5 and Table 1). However, given the present mapping, the magnitude of a seismic event along this fault (M6.1-6.2, see also Table 2) would be underestimated when compared with the M6.3 magnitude presently reported for the 1654 event in the Catalogue (see Table 2). The results from the strain calculations suggest that the Sora fault, when modeled with a left-lateral component of slip, is the most probable candidate fault of the 1654 earthquake.