## 2 Materials and Methods
### Logic Tree Approach/Structure and PSHA Calculations  
Seismic hazard was evaluated by computing PGA and PGV values for a return period of 475 and 950 years for all groups considering rock conditions (V\({}_{\mathrm{s}30}\) > 760 m/s). Moreover, S\({}_{\mathrm{a}}\) values were calculated in order to construct Uniform Hazard Spectra for a return period of 475 for Athens, Methana, and the capital of each island, taking into account local soil conditions. In the absence of V\({}_{\mathrm{s}30}\) profiles that could be used for the accurate representation of each site, we used topographic slope data from digital elevation models (DEMs) [91]. V\({}_{\mathrm{s}30}\) derived from topographic data may not have the accuracy of in situ measurements; however, it can be used as a first-order proxy for site classification purposes at a regional scale [92]. The sampling interval was set to 10 km in sub-area 1 (Attica peninsula) and 1 km in the remaining sub-areas. Due to the inherent complexities characterizing earthquakes and wave propagation, a wide range of uncertainties may be associated with PSHA calculations. As a result, it was essential to properly treat uncertainties in our approach in an effort to reduce them as much as possible. The most commonly used method to deal with uncertainties is the designation of a logic tree formulation to include alternative models in the analysis [93; 94; 95]. Logic tree approaches have become a crucial framework in modern PSHA studies in an effort to account for the aleatory variability as well as the epistemic uncertainties in the analysis. It provides a structured approach to combine different seismological models, GMPEs, and input parameters, allowing for a comprehensive exploration of the range of possible outcomes. It starts with a main branch representing the seismotectonic model, and it typically incorporates multiple alternative models or approaches, each representing a different interpretation or assumption. Secondary branches emerge to account for additional uncertainties, as they consider different GMPEs to capture the range of possible PGA, PGV, and S\({}_{\mathrm{a}}\) estimates. Each branch of the logic tree is assigned a weight based on expert judgment or statistical analysis, reflecting the confidence of each alternative. The final results were obtained using a non-equal logic tree, where each minor branch represented a weighted GMPE (except for MARG2002 [76]), whereas each primary branch corresponded to a different seismotectonic model (Figure 2). By assigning multiple weighted GMPEs per area source, we managed to create a sophisticated logic tree that contained minor logic trees for each area source. Consequently, by creating a large number of logic tree paths, the epistemic uncertainties were qualitatively reduced. The weight factors of 0.86 and 0.14 were determined for major crustal and slab branches, respectively, based on the number of earthquakes within the crustal and slab environments from the catalog that was used. The reason for assigning equal weights to the crustal primary branches was that neither of the two area source models was deemed superior. The zones of ESHM13 cover smaller areas, indicating that dissimilar seismotectonic characteristics, such as focal mechanisms, are less likely to be grouped. On the other hand, the ESHM20 model employs larger seismotectonic zones, which may reflect potential seismotectonic uncertainties but benefits from a greater number of earthquakes within each source. The latter implies that b-values are computed with a smaller Root Mean Squared Error (RMSE) and that the difference between the M\({}_{\mathrm{u}}\) and M\({}_{\mathrm{c}}\), which is proportional to the accuracy of the b-value estimations, is likely to be increased. The hazard assessment was performed through the latest version of the R-CRISIS software (V20.0) [67].