## 3 Data and Methods
### Aim 2: Normal Faulting IPE with Global Validity (Epicentral Distance)  
We addressed the second issue, the exportability of the Italian Apennine IPE to other settings by collecting a dataset of normal faulting earthquakes with available IDPs (Table 1). We applied the same method of [PERSON] et al. (2020) [10] to derive an updated IPE valid on a global scale: the attenuation was computed from the IDPs, employing the \"intensity binning\" methodology introduced by [PERSON] and [PERSON] (1997) [27] and considering the median epicentral distance of each intensity class. Prior to computing the attenuation relations, data were decimated to avoid the incompleteness bias in the far field. We adopted the method described by [PERSON] (2001; Equation (1)) [31] and already used in [PERSON] et al. (2020) [10], building a preliminary attenuation to estimate the distance at which the intensity falls below a given threshold, which here, was set to ESI-07 \(\geq\) V.  
Using all the IDPs contained in the dataset, we calculated the median distance for each intensity class. The median distance for the threshold value of ESI-07 = V was determined to be 65 km. Accordingly, we excluded all data points with distances exceeding this value. Data points corresponding to half-degrees were also removed. Considering that the analyzed earthquakes have different epicentral intensities (I\({}_{0}\)), we used \(\Delta\)I [31] to calculate an IPE for the entire dataset:  
\[\Delta\)I = I\({}_{0}-\) I\({}_{i} \tag{1}\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Event** & **Country** & **Date** & **Lat.** & **Long.** & **Magnitude** & **ESI-07 I\({}_{0}\)** & **N\({}^{\circ}\) IDPs** & **Ref. ESI-07 Data** \\ \hline Sannio & Italy & 5 June 1688 & 41.28 & 14.56 & 7.1 & X & 11 & [37] \\ \hline Avola & Italy & 11 January 1693 & 37.12 & 14.93 & 7.4 & X & 4 & [39] \\ \hline Irpinia-Basilica & Italy & 8 September 1694 & 40.86 & 15.41 & 6.7 & X & 6 & [37] \\ \hline Norcia & Italy & 14 January 1703 & 42.71 & 13.07 & 6.8 & X & 4 & [39] \\ \hline L’Aquila & Italy & 2 February 1703 & 42.43 & 13.29 & 6.6 & X & 7 & [39] \\ \hline Puglia & Italy & 20 February 1743 & 39.85 & 18.77 & 7.1 & XI & 2 & [40] \\ \hline Estubeny & Spain & 23 March 1748 & 39.03 & \(-\)0.63 & 6.2 & IX & 32 & [41] \\ \hline Calabria & Italy & 5 February 1783 & 38.30 & 15.97 & 7.1 & XI & 34 & [42] \\ \hline Molise & Italy & 26 July 1805 & 41.50 & 14.47 & 6.7 & X & 38 & [37] \\ \hline Basilicta & Italy & 16 December 1857 & 40.35 & 15.84 & 7.1 & X & 41 & [39] \\ \hline
**Atalanti** & Greece & 27 April 1894 & 38.63 & 23.10 & 6.8 & X & 19 & [43] \\ \hline Messina & Italy & 28 December 1908 & 38.15 & 15.69 & 7.1 & XI & 59 & [44] \\ \hline
**Acambay** & Mexico & 19 November 1912 & 19.98 & \(-\)99.83 & 6.9 & X & 54 & [45] \\ \hline
**Fucino** & Italy & 13 January 1915 & 42.01 & 13.53 & 7.1 & X & 9 & [39] \\ \hline Irpinia & Italy & 23 July 1930 & 41.07 & 15.32 & 6.7 & X & 29 & [37] \\ \hline
**Sofades** & Greece & 30 April 1954 & 39.28 & 22.29 & 6.8 & IX-X & 6 & [46] \\ \hline Albolote & Spain & 19 April 1956 & 37.15 & \(-\)3.39 & 5.4 & VIII & 8 & [47] \\ \hline
**Thessaloniki** & Greece & 20 June 1978 & 40.70 & 23.30 & 6.5 & IX & 22 & [43] \\ \hline
**Irpinia** & Italy & 23 November 1980 & 40.84 & 15.28 & 6.9 & X & 534 & [38] \\ \hline Kalamata & Greece & 13 September 1986 & 37.11 & 22.14 & 6.1 & IX & 51 & [48] \\ \hline Pyrgos & Greece & 26 March 1993 & 37.68 & 21.46 & 5.7 & VII-VIII & 7 & [26] \\ \hline
**Kozani** & Greece & 13 May 1995 & 40.16 & 21.68 & 6.5 & IX & 19 & [43] \\ \hline
**Coliforito** & Italy & 26 September 1997 & 43.01 & 12.85 & 6.0 & IX & 23 & [39] \\ \hline
**L’Aquila** & Italy & 6 April 2009 & 42.31 & 13.51 & 6.3 & IX & 27 & [39] \\ \hline
**Amatice** & Italy & 24 August 2016 & 42.70 & 13.23 & 6.2 & IX & 14 & [10] \\ \hline Samos & Greece & 30 October 2020 & 37.76 & 26.81 & 7.0 & IX & 46 & [49] \\ \hline \hline \end{tabular}
\end{table}