# Probabilistic Seismic Hazard Assessment of the Southwestern Region of Saudi Arabia
## 2 Methodology
### Ground Motion Prediction Equations
It is applicable to rupture distances (Rrup) of up to 300 km and oscillation durations of up to 10.0 s. The ground motion dataset was chosen from the NGA-West2 database [86]. This attenuation model was developed using a strong-motion dataset comprising 15,750 recordings derived from 326 earthquakes. Among these, 221 events are strike-slip, 79 are reverse events, encompassing the full range of magnitudes, and 26 are predominantly normal events falling within the magnitude range of 4.6 to 6.0. China, Japan, Taiwan, Europe, the Middle East, and California were among the regions from which the earthquake data were gathered. In this attenuation model, recordings from regions with limited sampling are restricted to a maximum distance of 80 km, whereas recordings from California, China, Taiwan, and Japan extend up to 400 km. Beyond 80 km, variations in crustal structure significantly influence ground motion, impacting attenuation over long distances. Accordingly, regional disparities are incorporated into the GMPE to accommodate these variations. The two parameters that this model employs to characterize the site conditions are the shear wave velocity (Vs,30) value and the depth to the Vs,30 value equal to 1.0 km/s. Although the largest magnitude in the NGA dataset is M 7.9, this selected GMPE model can be reliably applicable and extrapolated to M 8.5. Regarding site conditions, the model is considered suitable for Vs,30 values among 180 m/s and 1000 m/s. In order to predict the horizontal ground motion amplitudes resulting from shallow crustal earthquakes, [PERSON]. [77] introduced an NGA model. The empirical dataset used to generate this model was also chosen from the NGA-West2 ground motion database [86]. In order to account for fault dip and rupture directivity effects, it includes terms related to faulting style, scaling with sediment thickness, depth-dependent scaling to the rupture's top, and extra terms. This second model is considered suitable for earthquakes with magnitudes between Mw 3.5 and 8.5 for the case of strike-slip events, and between Mw 3.5 and 8.0 in the case of reverse and normal faulting earthquakes. Additionally, it is appropriate for Vs,30 spanning from 180 to 1500 m/s, and Rrup up to 300 km. Concerning the applicability and limitations of this selected model, in comparison to the [87] model, the lower limit of the applicable magnitude range was reduced to M 3.5 due to the large number of small earthquakes included in this update; also, the upper limit of the applicable distance range was increased from 200 km to 300 km because of the extensive data available for distances between these two distances. Using an extended Pacific Earthquake Engineering Research Center-NGA-West2 database, Ref. [76] created a novel GMPE for the average horizontally component of the PGA, PGV, and pseudo-absolute acceleration response spectra throughout 21 periods ranging from 0.01 s to 10 s. The employed ground motion database in this model is a subset of the PEER NGA-West2 database [86], which was updated to include earthquakes up to 2011. The NGA-West2 database contains over 21,000 three-component recordings from earthquakes in California and worldwide, with Mw ranging from 3.0 to 7.9. Most of the recordings used in the database represent free-field site conditions. In active tectonic environments, this attenuation model is thought to be appropriate for measuring horizontal ground motion caused by shallow crustal earthquakes. Depending on the underlying process, it encompasses Rrup up to 300 km and Mw values from 3.3 to 7.5-8.5. NEHRP site classifications B, C, D and E correspond to a range of Vs,30 values between 150 and 1500 m/s, for which the model is suitable. This ground motion model is considered valid under the following general conditions: maximum magnitudes of M \(\leq\) 8.5 for strike-slip faults, M \(\leq\) 8.0 for reverse and reverse-oblique faults, and M \(\leq\) 7.5 for normal and normal-oblique faults.