# Probabilistic Seismic Hazard Assessment of the Southwestern Region of Saudi Arabia
## 2 Methodology
### Earthquake and Focal Mechanism Catalogs  
Assessing seismic hazards in the chosen region requires identifying and characterizing possible seismic sources [40; 41]. In the initial stage of defining seismic sources, the earthquake catalog for the Arabian Peninsula and adjacent areas is used, as published by [42]. The data in this catalog were sourced from a variety of international, regional, and local agencies, as well as in the published literature. The authors of [42] reported that, in addition to local catalogs from Yemen, Oman, Saudi Arabia, and the United Arab Emirates, the compiled data mostly came from international sources, including the International Seismological Centre-Global Earthquake Model (ISC-GEM), ISC-EHB [43], the International Seismological Centre (ISC), and the National Earthquake Information Center of the United States Geological Survey (NEIC-USGS). According to their methodology, the data provided by [44] were prioritized for earthquakes happened before 1964. The most trustworthy data for earthquakes that happened between 1964 and 2015 came from [44; 45] and information from specialized research [46; 47]. Data from ISC-GEM, ISC-EHB, ISC, and NEIC-USGS were the next most reliable sources of information. Regarding the magnitude used in the catalog, the moment magnitude (Mw) data from ISC-GEM were given preference for earthquakes that happened prior to 1964. This was followed by [44; 45], ISC, and NEIC-USGS. For seismic events occurring after 1964, the following magnitudes were prioritized: Ref. [44] (using surface wave magnitude Ms), ISC, NEIC-USGS, and local magnitude (ML), respectively; Mw data from specialized studies, ISC-GEM, Global Centroid Moment Tensor (GCMT) (Mw), and the African Array Seismic Data, when accessible. The highest priority among the several magnitude types is Mw, which is followed in order by Ms, body wave magnitude (mb), and ML. To ensure uniformity within the compiled earthquake catalog, Ref. [42] used empirical regression relationships for magnitude conversion, transforming reported magnitudes (mb, Ms, and ML) into an equivalent Moment Magnitude (Mw) scale. They used the formula given in [48] to convert mb to Mw for values up to mb 6.3 (Equation (1)), which mostly covered the Red Sea and a portion of the Gulf of Aden. Additionally, they applied empirical Equations (2)-(4)) derived in [49] for the Middle East to convert other magnitude scales (Ms, ML) into Mw. In our study region, these empirical regression relationships underwent rigorous validation against local seismic data and were cross-referenced with historical earthquake records. This validation process confirms the reliability and suitability of these formulas for accurately estimating Mw across a spectrum of earthquake magnitudes of our study area. \[\mathrm{M}_{\mathrm{W}} =1.60\mathrm{m}_{\mathrm{b}}-2.89\;3.6\leq\mathrm{m}_{\mathrm{b} }\leq 6.3 \tag{1}\] \[\mathrm{M}_{\mathrm{W}} =0.66\mathrm{M}_{\mathrm{S}}+2.11\;2.8\leq\mathrm{M}_{\mathrm{S} }\leq 6.1\] (2) \[\mathrm{M}_{\mathrm{W}} =0.93\mathrm{M}_{\mathrm{S}}+0.45\;6.2\leq\mathrm{M}_{\mathrm{S} }\leq 8.2\] (3) \[\mathrm{M}_{\mathrm{W}} =1.01\mathrm{ML}-0.05\;4.0\leq\mathrm{ML}\leq 8.3 \tag{4}\]  
A declustered earthquake catalog was then compiled by identifying and eliminating seismic swarms, foreshocks and aftershocks, effectively filtering out all dependent events from the unified catalog [50; 51]. In this study, declustering was carried out using three commonly employed algorithms, those designed in [52; 53; 54]. The first declustering method relies on a time window criterion to distinguish aftershocks from mainshocks based on a fixed temporal interval, often using parameters like the Omori law decay rate. The second one enhances this approach by incorporating spatial criteria in addition to temporal windows, considering both the time elapsed and spatial proximity to differentiate between mainshocks and aftershocks.