###### Abstract  
Earthquake environmental effects may significantly contribute to the damage caused by seismic events; similar to ground motion, the environmental effects are globally stronger in the vicinity and decrease moving away from the epicenter or seismogenic source. To date, a single intensity prediction equation (IPE) has been proposed in the Italian Apennines for intensity scale dealings with environmental effects: the Environmental Seismic Intensity (ESI-07). Here, we evaluate the sensitivity of the IPE with respect to input data and methodological choices and we propose IPEs with global validity for crustal normal faults. We show the strong influence of input data on the obtained attenuation investigating the 1980 Iripnia-Basilicata (Southern Italy) earthquake. We exploit a dataset of 26 earthquakes to build an IPE considering the epicentral distance. We also propose an IPE considering the distance from the fault rupture, which is derived from a dataset of 10 earthquakes. The proposed equations are valid for normal faults up to 40 km from the epicenter/fault and may flank other models predicting ground motion or damage to the built environment. Our work thus contributes to the use of the ESI-07 scale for hazard purposes. intensity attenuation; ESI-07 scale; intensity prediction equations; earthquake; normal fault +
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have been published (e.g., [5,6]), predicting the expected level of Peak Ground Acceleration (PGA), Peak Ground Velocity (PGV), or Spectral Acceleration (SA). Regarding intensity, several tens of intensity prediction equations (IPEs) are available for different territorial settings [4, 7, 8, 9], mostly based on the Mercalli-Cancani-Sieberg (MCS) intensity scale in Italy and on the Modified Mercalli (MM) scale worldwide. [PERSON] et al. (2020) [10] introduced the first IPE based on the Environmental Seismic Intensity scale (ESI-07), a macrosiseismic scale where the Earthquakes Environmental Effects (EEEs) are the only descriptors [11, 12, 13]. In the last decades, several earthquakes have shown that EEEs are a relevant source of hazard, which may be even more prominent than ground shaking. Examples include the 2008 M\({}_{\rm w}\) 7.9 Wenchuan, China, the 2010 M\({}_{\rm w}\) 7.1 South Island, New Zealand, the 2011 M\({}_{\rm w}\) 9.0 Tohoku, Japan, and the 2023 M\({}_{\rm w}\) 7.8 and M\({}_{\rm w}\) 7.5 Turkey-Syria earthquakes [14, 15, 16]. Concurrently, in the last years, several initiatives were undertaken to develop high-resolution datasets of EEEs or in the systematic collection of such data (e.g., [17, 18, 19, 20]). Furthermore, as demonstrated in specific studies, EEEs are considered good descriptors for the re-evaluation of historical earthquakes and, because of their homogeneous nature, can also be used for comparison between such earthquakes and modern ones (e.g., [21, 22, 23]). The ESI-07 scale provides good objectivity in the assessment of macrosise intensities, especially in the epicentral area, compared to traditional intensity scales influenced by human factors such as local economy, culture, and the enforcement of building seismic codes. Moreover, the ESI-07 scale does not saturate at high intensity levels and is independent of the location and distribution of settlements and the construction quality of buildings. Therefore, it enables the comparison of earthquake effects across different regions and time periods, which is crucial for hazard evaluation [24, 25, 26]. However, to date, only one IPE based on the ESI-07 scale has been proposed, and it is specific to a localized territorial setting (i.e., [PERSON] et al., 2020, [10] in the Italian Apennines). Here, we analyze and discuss the application of the ESI-07 scale for seismic hazard purposes. The aims of this article are three-fold:  
1. Investigating the role of the resolution and uncertainty of the input data (e.g., number and accuracy of the EEE sites) and of methodological choices in the derivation of the ESI-07 IPE.