## 5 Discussion
Consequently, this work demonstrates that the quality of the input data has a more significant impact on the final output than the statistical and methodological choices used for fitting the data. Additionally, it is important to consider that most of the intensity prediction equations (IPEs) currently available were developed several years ago. This implies the need for systematic updates of these equations over time. For example, in the Italian geological context, these equations generally predate the significant seismic events of 2009 in L'Aquila and 2016 in Central Italy [31, 32, 62, 63, 64, 65]. These equations usually refer to the MCS scale and adopt hypocentral or epicentral distances. An update was proposed by [PERSON] et al. (2024) [66], who developed attenuation models specific to Italy. These models are calibrated in terms of magnitude (M\({}_{\text{w}}\)) and are based on an empirical relationship between macroseismic intensity and energy. This study, based on post-1900 Italian earthquakes, uses the hypocentral distance as a descriptor. Since its inception, the ESI-07 scale has been immediately considered for the analyses of macroseismic attenuation models due to its ease of use and its ability to provide homogeneous data across both historical and recent earthquakes, allowing for comparative analyses [26, 43]. However, to date, only one IPE based on the ESI-07 scale has been proposed, calculated specifically for the Apennines region of Italy [10]. Indeed, this work aims, on the one hand, to update the existing IPEs and, on the other hand, to further explore the use of the ESI-07 scale for hazard purposes. Analyzing the D\({}_{\text{Epi}}\)-based IPE, Figure 6b,c shows that comparing the attenuation relationship we obtained with that calculated by [PERSON] et al. (2020) [10], the attenuation trend is similar, but the curve calculated in this study has a steeper slope. These results, and consequently the differences with the attenuation calculated by [PERSON] et al. (2020) [10], can be explained by the epistemic uncertainty, the input data, and the nature of intensity scales themselves. Certainly, it is possible to refer to the quality of the input data but also to a component of uncertainty related to macroseismic scales. Indeed, these observations can be influenced by various factors and uncertainties, such as cumulative effects and the overlap of effects across different degrees, leading to a certain level of disparity between the theoretical expectations and observed realities due to assumptions and subjective evaluations of the researchers [67]. Another possible explanation relates to the data's spatial distribution. The majority of IDPs are located in the epicenter area or, at most, within a few tens of kilometers from it (74% within 25 km). This is because larger effects are more easily catalogued than smaller ones, and the ESI-07 scale is not entirely accurate in describing effects located in the far field [26; 60]. Additionally, the level of urbanization in the earthquake-affected area is significant; although the ESI-07 scale is unrelated to the anthropogenic environment, the lack of a population in certain areas, especially in the far field, can result in not observing any effects, particularly those of lower intensity. In this research, we analyzed countries with different population densities, with the consequence that this parameter may have partly affected the final number of IDPs available for each earthquake. Indeed, i.e., Italy, analyzed by [PERSON] et al. (2020) [10], nowadays has a significantly higher density, compared to Spain, Greece, and Mexico. Additionally, the local geology can contribute to these differences, actively influencing the spatial distribution of the seismo-induced effects. The geological, geomechanical, and morphological characteristics of a site can attenuate or amplify earthquake effects. Consequently, there may be minimal effects or intensities lower than expected in areas near the epicenter, while significant effects may occur in the far field.