# Probabilistic Seismic Hazard Assessment for United Arab Emirates, Qatar and Bahrain
## 6 Logic Tree Framework and Seismic Hazard Computations  
Due to the incomplete understanding of the phenomena of earthquakes, several sources of uncertainties are usually associated with any seismic hazard assessment. In the current assessment, and in order to handle and treat such sources of uncertainties in an appropriate way, a logic-tree design has been implemented. After several considerations for the different input parameters, only four elements/inputs were considered in the logic-tree framework. They are the used seismic source model, the Gutenberg-Richter \(b\)-value, the maximum expected magnitude, and the used ground-motion attenuation models [75; 81; 82] for the active shallow crustal regions (Figure 5). In total, 54 branches for the designed logic tree were implemented, with each of them representing an alternative seismic hazard scenario. Considering the seismic source model, three different alternatives have been setup. They are the area source model by [PERSON] et al. [2], the spatially-smoothed seismicity model using the same catalog and seismicity parameters published by [PERSON] et al. [2; 6], and the area source model by [PERSON] et al. [65] that was used recently by [PERSON] et al. [21] and [PERSON] et al. [96] for assessing the seismic hazard for the Arabian Peninsula and Oman, respectively. The assumed subjective weights for the three alternatives are 0.4, 0.4, and 0.2, respectively (Figure 5). A higher weight (0.4) was given to the first couple of models because it is the outcome of the hazard analyst opinion that the model by [PERSON] et al. [2] is developed specifically and more representative for the region under study rather than the regional model [65] developed for the Arabian Peninsula. Considering the \(b\)-value, the same design and weights as in several publications e.g., [19; 97] has been followed (Figure 5). The preferred mean \(b\)-value was given a higher weight (0.6) in comparison with the other two alternatives (\(b\)-value \(\pm\)\(\sigma\)) with lower weights (0.2). Two additional branches were setup for the third parameter, the maximum expected magnitude, with a given weight of 0.75 (for the mean value) and 0.25 (for M\({}_{\text{max}}\) + \(\sigma\)), using in this case a conservative criterion. For the final input element, the selected ground-motion prediction models for the shallow active crustal seismic sources, it is common to apply an equal weight for different branches, e.g., [60; 97; 98; 99], that represents equal levels of the modeler's confidence. So, in the current assessment, three equal-weighted branches (0.33 for each) were implemented for the [PERSON] et al. [81], the [PERSON] et al. [82], and the [PERSON] et al. [75] models (see Figure 5). During the subjective weighting process, we tried as possible to select weights that reflect our confidence in the different input parameters and variables, as well as following some published works, e.g., [19; 21; 60; 97; 98; 99; 100]. Based on the [PERSON] [101] PSHA methodology, the followed seismic hazard assessment procedure in the current appraisal is the standard one. Seismic hazard was computed applying the well-known total probability theorem and expressed in terms of the rate of exceedance for a specific level of ground motion for the considered site condition. Among several available open-source PSHA software codes (e.g., OpenSHA [102], OpenQuake [103], and EqHaz [104]), the validated and verified R-CRISIS [94] was chosen for this assessment. R-CRISIS [94] provides a friendly graphical interface environment to facilitates data input and compute the seismic hazard. The computations were performed for grid points covering all the studied region at a spacing of \(0.1^{\circ}\times 0.1^{\circ}\) (about \(10\) km \(\times\) 10 km). In order to run the assessment, several input parameters for each individual seismic source (and accordingly in each logic-tree branch) were necessary to be included in R-CRISIS [94].