## 5 Statistical Characterization of Seismic Activity
### Spatial Distribution  
Understanding seismicity patterns is fundamentally linked to the spatial distribution of earthquake moment magnitudes (\(M_{w}\)) and the variability of depth in relation to latitude and longitude, as depicted in Figure 5. Moment magnitude combined with depth offers crucial insight into the geodynamic processes that shape the Earth's crust. Figure 4: Temporal distribution of earthquakes in the Red Sea across different time scales. Each subplot illustrates the frequency of earthquakes over a specific period: (**a**) daily, (**b**) weekly, (**c**) monthly, and (**d**) yearly. Horizontal dashed lines in each subplot indicate the minimum (red), maximum (green), and mean (blue) counts for that time scale. Figure 5: Multifaceted analysis of spatial earthquake distribution characteristics in the Red Sea: (**a**,**c**) showing the distribution of earthquake magnitudes across latitudinal and longitudinal ranges. (**b**,**d**) depicting the depth distribution of earthquakes along latitudinal and longitudinal coordinates. (**e**) A 3D histogram illustrating the frequency of earthquakes across varying magnitudes and depths. Figure 5 displays a density plot that illustrates the distribution of earthquake moment magnitudes (\(M_{w}\)) and depths in relation to either latitude or longitude. Figure 5a illustrates a concentration of seismic events with magnitudes predominantly clustered between latitudes of 24 and 28 degrees, indicating a zone of heightened seismic activity within this range. The accompanying marginal histogram exhibits pronounced peaks that correspond to the densest areas, revealing that most earthquakes occur with magnitudes between 1.5 and 3.0 \(M_{w}\). These observations suggest that seismic activity is not uniformly distributed but is instead focused in specific regions, potentially aligning with underlying geological structures such as tectonic plate boundaries or rift zones. Figure 5b indicates that the deepest earthquakes are concentrated around latitudes of 25 to 26 degrees and 28 to 29 degrees, hinting at a potential correlation with geologically active events. The marginal histograms demonstrate that the majority of seismic events take place at depths of less than 10 km, with a decline in frequency at greater depths. Figure 5c highlights a notable concentration of seismic activity, particularly of lower magnitudes, around a 35-degree longitude. The marginal histograms exhibit a pronounced spike at this longitude, indicating that the majority of earthquakes recorded in this dataset have magnitudes just above 2.0 \(M_{w}\). Figure 5d depicts a seismic depth distribution chart by longitude in the Red Sea region, revealing a considerable aggregation of events at shallower depths around a 35-degree longitude, indicating geological activity in this longitudinal range. The marginal plots display a significant peak at a 35-degree longitude, predominantly at depths of less than 10 km, with a gradual decrease in the number of events at greater depths. This pattern suggests the presence of specific zones within the Red Sea region that exhibit heightened seismic activity, especially at shallower depths. From Figure 5e, it is evident that most earthquakes in the dataset are of relatively low magnitude, clustering around 2.0 to 3.0 \(M_{w}\), and occur at shallow depths, primarily less than 15 km. There is a noticeable decrease in earthquake frequency with increasing magnitude and depth. The highest frequency of events is found at lower magnitudes and shallow depths. The prevalence of shallower earthquakes can be associated with crustal movements, while the presence of deeper events may signal subduction zones or other profound tectonic activities. The observed patterns indicate that seismic activity is indeed concentrated within specific latitudinal and longitudinal bands, but the depth of these earthquakes varies within these bands, suggesting a more complex seismic profile.