## 3 Methods and Fault-Slip Data
### Fault Slip-Data  
In the present study, fault-slip data (Appendix A) used by [32] for defining the paleostress history in the Voltri Massif of the Ligurian Alps (Figure 1a) are re-analyzed for un-raveling the paleostress history through a different approach. They are 92 fault-slip data in total, and they have been recorded in five structural stations (SS), i.e., SS2, SS3, SS6, SS7, and SS11 from Pra' Vallarino to Tiglieta. These SSs are located along an ENE-WSW to NE-SW boundary that separates the overlying Erro-Tobbio Unit in the north from the underlying Beigua Unit in the south (Figure 1b, and SS location details in Figure 2 of [32]). Both units belong to the Voltri Massif, and according to [32], there is no big fault in this area like the Sestri-Voltaggio fault (SVF) (see Figure 1 and Figure 2 in [32]). In contrast, [60] suggested that the contact is a large detachment fault (Figure 1b). From the 92 fault-slip data, only one that dips at less than \(50^{\circ}\) towards NNW with extensional displacement (FED_1, Appendix A) at SS2 might be similar to the detachment geometry and kinematics. Fifty-one (51) fault-slip data are extensional, and 41 are contractional, based on whether the slip along the fault surface is uplifting or subsiding the hanging wall against the football block, and considering the horizontal plane as a reference level. Interestingly, 56 fault surfaces display pitch (pt) \(\leq 30^{\circ}\), 22 have \(30^{\circ}<\) pt \(<60^{\circ}\), and 14 have pt \(\geq 60^{\circ}\), indicating the predominance of the strike-slip and oblique-slip fault motions over the dip-slip, which in turn does not favor the precise estimation of the least or greatest principal stress axis of the resolved stress tensors. We follow the stress types classification for the stress regimes of [79]. Finally, we chose these data for analysis and applied a different approach by defining both'site' stress tensors at each SS and 'bulk' stress tensors from the whole fault-slip dataset to compare our results with their results. Furthermore, the two most remote SSs are at a distance of no more than 10 km from each other (Figure 1, and SS location details in Figure 2 of [32]), describing a rock volume that is small compared to the known large structures of the region like the SVF, and far apart from them, so that it can be considered as a small cubical element for the regional stress regimes [18; 80]. In this study, the present analysis includes six stages, starting by examining the possible heterogeneity of the fault-slip data [32] at each SS (Figure 1b) by applying another best-fit stress inversion method, i.e., the 'Minimized Shear Stress Variation,' which uses the algorithm of [81; 82] with the aid of MyFault software (Table 1). The authors in [81; 82], in estimating the regional stresses, made the simplifying assumption that the magnitude of the slip stress on the fault is similar for all faults in the set at the time of slip. Thus, minimizing the variations in slip stress among the faults leads to an overdetermined set of linear equations. These equations are solved using the standard eigenvector method, giving the three principal stresses and their direction. Because the mean stress during the slip is generally unknown, the principal stresses are normalized, assuming that the maximum stress is 1 and the minimum is 0. The stress ratio is equal to intermediate stress. The fault-slip data for which the obtained MA is greater than \(30^{\circ}\) under the resolved stress tensor were excluded at each station. However, if any of the excluded fault-slip data under the new resolved stress tensor obtain a new MA that is smaller or equal to \(30^{\circ}\), they are reconsidered in the final solution. Figure 2: _Cont._  
Figure 2: The TRM application [44] to the fault-slip data presented at the different SSs by [32].