## 6 Conclusions  
In this study, we calculated two new IPEs based on the ESI-07 scale, specifically for onshore normal fault earthquakes in the 5.4-7.4 M\({}_{\rm w}\) range. First, we calculated the D\({}_{\rm Epi}\)-based IPE using a dataset of 26 global earthquakes and employing the epicentral distance. Subsequently, we calculated the D\({}_{\rm RupX}\)-based IPE using a subset of 10 earthquakes, which generated surface rupture, from the same dataset. In both cases, we employed the IDP-based analysis methodology. Additionally, we analyzed the influence of the input data on the final results, with particular reference to the 1980 Irpinia-Basilicata earthquake. The use of macroseismic intensity as a parameter for seismic hazard is widely accepted internationally, with many countries evaluating hazards exclusively in terms of intensity [69]. Seismic hazard maps are generally correlated with the predicted intensity at a site and its attenuation with distance. The ESI-07 scale has already been identified as a useful tool for hazard assessment (e.g., [70]), thus we consider it appropriate to implement IPEs based on this scale. The chosen methodology is easily replicable, and alongside the widely used D\({}_{\rm Epi}\), we include D\({}_{\rm RupX}\), a distance that can be easily calculated for both historical and recent earthquakes provided that they generate surface faulting. It is important to remark that the ESI-07 scale has good assets to calculate the attenuation or to complete the results calculated with other macroseismic scales. Therefore, this research aims to provide an additional contribution to the calculation of new IPEs, with the goal of improving our knowledge of seismic hazards in specific contexts. Among the limitations of this approach is the applicability of the new IPEs, which is limited to a few tens of kilometers from the epicenter/fault. This limitation is due to the fact that the ESI-07 scale offers a certain reliability in the process of assessing macroseismic intensities in the epicentral area, while it tends not to accurately describe such values in the far field [26]. Indeed, we consider the proposed equations reliable up to 40 km and do not recommend extrapolation beyond these limits. Additionally, the proposed IPEs are valid for normal faults only, given the wider availability of ESI-07 data for such settings. We believe that the development of ESI-07-based IPEs can be further refined and improved. Among future prospects, we consider the development of new IPEs based on 3D D\({}_{\rm Rup}\), i.e., the distance perpendicular to the fault plane, the analysis of anisotropy along and across the strike of the fault rupture, and the derivation of IPEs for other fault kinematics. M.P., conceptualization, methodology, formal analysis, and preparation of the draft manuscript; F.F., conceptualization, methodology, data validation, and review; P.L., conceptualization, supervision, and review; A.M.M., supervision and writing--review and editing; M.M.V.-B. and S.P., writing--review and editing. All authors have read and approved the published version of the manuscript. Figure 9: Representation of the proposed new IPEs: those based on D\({}_{\rm Epi}\) and D\({}_{\rm RupX}\) up to \(\Delta\)I = 5 are shown in red, while those up to \(\Delta\)I = 4 are shown in black. The trend was derived using a log-linear fit [10]. **Funding:** This research was supported by the European Union--Next Generation EU--Mission 4 \"Education and Research\"--Component 2 \"From Research to Business\"--Investment 3.1 \"Fund for the realization of an integrated system of research an innovation infrastructure\"--Project IR0000037--GeoSciences IR. **Insituational Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable.