# Probabilistic Seismic Hazard Assessment of the Southwestern Region of Saudi Arabia
## 2 Methodology
### Ground Motion Prediction Equations  
In regions where data are limited, selecting appropriate GMPEs is not straightforward. Developing robust, region-specific GMPEs may not be feasible in such cases. Therefore, it becomes necessary to choose models developed for other regions while filtering out candidate models based on specific criteria [68]. Recently published GMPEs incorporate terms accounting for various factors beyond just magnitude and distance. Faulting style, site effects (both shallow and deep site effects), hanging wall effect, and an aleatory uncertainty model are some of these factors [69]. The selection of a GMPE should be closely aligned with the predominant seismo-tectonic conditions in the area under study [70; 71]. In light of the seismotectonic setting, GMPEs that have been created globally can be broadly divided into three groups [72; 73; 74]: (i) models appropriate for locations with active crustal tectonics, such as [75; 76; 77] models, where shallow crustal earthquakes are common; (ii) models developed for regions with active subduction tectonics, [78; 79; 80; 81] models, and (iii) models appropriate for stable continental regions, such as [82; 83; 84] models. In the present work, taking into account both the faulting mechanism data and the prevailing regional tectonic conditions, the proposed source models align with the first category, i.e., active shallow crustal sources. For the current assessment, globally recognized GMPEs are essential because there are not locally developed GMPEs for the study area. Then, three models from the Next-Generation Attenuation (NGA) West 2 models were selected in accordance with the selection criteria for GMPEs as stated in [68; 85]. This decision was taken to mitigate potential uncertainties stemming from incomplete knowledge of attenuation characteristics for shallow seismic sources. Several guidelines were proposed in [68] for selecting GMPEs in PSHA. The authors' approach suggests that selection should not be influenced by familiarity with specific GMPEs or their creators, nor by personal preferences of the analyst. Instead, the hazard analyst should start with a comprehensive list of equations meeting standard scientific criteria from international peer-reviewed journals. Criteria for exclusion include the following: (a) models derived for inappropriate tectonic environments, (b) models not published in Thomson Reuters ISI-listed peer-reviewed journals, (c) lack of accessible datasets used in model derivation, (d) supersession by more recent publications, (e) inability to provide spectral predictions across adequate response periods, (f) absence of non-linear magnitude dependence or magnitude-dependent decay with distance, (g) models not derived using appropriate statistical approaches (one- or two-stage maximum likelihood or random effects), (h) inappropriate definitions of explanatory variables or neglect of site effects, (i) limited applicability range for necessary extrapolations in PSHA (magnitude and distance), and (j) constraints from insufficient dataset sizes (fewer than 10 earthquakes per magnitude unit or fewer than 100 records per 100 km distance). These criteria aim to ensure that the selected GMPEs are robust, suitable for the specific boundary conditions of the PSHA, and scientifically sound. Accordingly, the three selected models from NGA West 2 [75, 76, 77] were chosen for their robust datasets, statistical methodologies, and comprehensive predictive capabilities across varied response periods, aligning well with our study's seismic hazard analysis needs. Taking into account such criteria, the selected attenuation models for modeling shallow crustal earthquakes, those of [75, 76, 77], were integrated into a logic tree scheme. It was determined that these models were the most suitable due to the incorporation of magnitude ranges, oscillation periods, distance intervals, and soil type classifications. The attenuation model [75] is designed exclusively for shallow crustal earthquakes with magnitudes ranging from Mw 3.0 to 8.5.