## 5 Results and Discussions
### Frequency-Magnitude Distribution Analysis
The Red Sea area was partitioned into distinct seismic source zones for a focused analysis of seismicity. These zones include the Gulf of Suez, the Gulf of Aqaba, the Northern Red Sea, the Central Red Sea, and the Southern Red Sea Seismic Source Zones. This segmentation facilitates a detailed and region-specific study of seismic parameters, enabling a comprehensive understanding of the seismic behavior in each of these zones. As a preliminary step to estimate the \(b\)-value, it is crucial to determine the magnitude of completeness (\(M_{c}\)). This is the threshold above which all earthquakes in a region are detected and below which some smaller earthquakes might be missed. The magnitude of completeness is a crucial parameter in seismology as it signifies the lowest magnitude at which 100% of the events in a dataset are detected. In this study, the Maximum Curvature method (MAXC), delineated by [35], was utilized. The point of maximum curvature on the plot corresponds to the magnitude of completeness. Mathematically, this is where the second derivative of the earthquake frequency with respect to magnitude is at a maximum. Figure 9 illustrates the \(M_{c}\) values obtained for the entire area, including the Gulf of Suez (Figure 9b), the Gulf of Aqaba (Figure 9c), the Northern Red Sea (Figure 9d), the Central Red Sea (Figure 9e), and the Southern Red Sea (Figure 9f). The variation in the magnitude of completeness (\(M_{c}\)) across different regions suggests differences in seismic network sensitivity, seismicity rates, or both. The Gulf of Aqaba area has the lowest (\(M_{c}\approx 0.8\)), indicating that the seismic network in this region is able to detect and record  
very small earthquakes. This could be due to a dense network of high-quality seismometers or high seismic activity that allows for a better statistical representation of smaller events. In contrast, the Southern Red Sea area has the highest (\(M_{c}\approxeq 3.4\)), which suggests that only larger earthquakes are being reliably detected. This could be due to fewer or less sensitive instruments in the region, greater distances between the seismic sources and the detectors, or a lower seismicity rate, meaning that there are naturally fewer small magnitude earthquakes to detect. The \(M_{c}\) values in the other regions fall between the two extremes mentioned above. These values indicate a moderate level of detection capability, where the network is able to record earthquakes of small to moderate size. The comparative uniformity of \(M_{c}\) values in these areas suggests a level of consistency in seismic detection capabilities and/or earthquake occurrence rates. The \(b\)-value, a statistical parameter derived from the frequency-magnitude relationship delineated by [36], serves as a pivotal metric for characterizing seismic activity and offers significant insights into seismotectonic configurations and the potential seismic hazards within the Red Sea area. This parameter is extensively applied across various magnitude scales to assess seismic phenomena, particularly within the context of differing tectonic environments, stress heterogeneity, and anisotropic media. The spatial distribution of \(b\)-values, which ranges from low to high, correlates with the accumulation of stress, indica  
Figure 9: Magnitude of completeness (\(M_{c}\)) of Seismic Activity in the Red Sea Spanning Various region. tive of structural heterogeneities. These heterogeneities are often attributed to the presence of cracks with varying orientations. A high \(b\)-value is typically associated with seismicity dominated by smaller magnitude events, whereas a low \(b\)-value suggests a comparative prevalence of larger earthquakes relative to smaller ones, as elucidated by [38]. The distribution of \(b\)-values, as depicted in Figure 10, exhibits a considerable range of variation, extending from 0.55 to 0.93.