# Probabilistic Seismic Hazard Assessment of the Southwestern Region of Saudi Arabia
## 2 Methodology
### Estimation of Seismic Hazard by Using a Logic Tree  
Following the methodology described by [88], contemporary earthquake hazard assessment procedures must take uncertainties in the location, magnitude, and frequency of seismic events into consideration because these variables have a direct impact on the ground shaking levels felt at a given location [89]. Logic trees, which give distinct subjective weights to various estimations for every input parameter, are used to handle some of these uncertainties. Using a logic tree approach makes it possible to include and measure what is referred to as epistemic uncertainty in the hazard estimation [90; 91]. A lack of understanding about the inputs used in the hazard assessment gives rise to epistemic uncertainty. In this assessment for southwestern Saudi Arabia, addressing potential uncertainties associated with specific input parameters was paramount, leading to the adoption of a logic tree design (Figure 3). A sensitivity analysis was initially conducted to identify the most critical parameters and models for hazard computation and to understand their impact on the final PSHA results. To conduct this analysis and evaluate the parameters significant for PSHA, some sites were selected for a detailed inspection. For these selected sites, PGA values for a return period of 475 years were computed considering all the different input parameter options (Mmin, Mmax, \(\lambda\)-value, b-value, GMPEs). As a result, notable differences in the PGA results were observed, while the Mmax, b-values, and GMPEs were varied. This indicates that these three parameters are the most critical factors in the hazard assessment, based on the proposed seismic source model. Accordingly, three essential components for the logic tree scheme were found by this thorough sensitivity analysis of the input parameters: the chosen GMPEs, the expected maximum magnitude, and the Gutenberg-Richter \(b\)-value. Here, the utilized logic tree comprises a total of 27 branches, each one representing a different seismic hazard scenario. For the Gutenberg-Richter \(b\)-value, three branches were established to consider the uncertainty linked to its estimation. The mean value carried a higher weight (0.6), while lower weights (0.2) were assigned to the other two branches (b + \(\sigma\) and b \(-\)\(\sigma\) values). Similarly, for the expected maximum magnitude, three branches with varying weights (0.7 for the mean estimated Mmax value, and 0.15 for both Mmax + \(\sigma\) and Mmax \(-\)\(\sigma\) values) were incorporated. The subjective weights were determined based on previous studies for consistency [70; 71; 72; 73; 74; 92; 93; 94]. In the final node of the logic tree, three NGA-West2 attenuation equations [75; 76; 77] were selected for application alternately in the context of shallow crustal seismic sources. Equal weight (0.33) was assigned to each branch, in line with criteria from previous literature [70; 71; 72; 73; 95; 96], indicating an equal level of user confidence. The rationale behind assigning equal weight to the selected NGA-West2 GMPEs follows practices in similar publications worldwide [70; 71; 72; 95; 96]. These GMPEs were chosen due to their strong scientific credibility, broad acceptance in the seismological community, and relevance to the tectonic setting of the study area. By weighting them equally, we aimed to ensure a balanced and unbiased representation of ground motion predictions, thereby enhancing the robustness of the PSHA results. Considering that the weights assigned to the branches in the designed logic tree reflect our subjective confidence based on and following several published articles [70; 71; 72; 95; 96], assigning different weights to these branches in a seismic hazard assessment will directly impact the final hazard estimates. This adjustment will change the relative importance of various seismic source models, GMPEs, and other parameters, potentially resulting in variations in the calculated seismic hazard levels.