## 5 Statistical Characterization of Seismic Activity
### Progression of Earthquake Activity
#### 5.3.5 Local Variations and Concentrated Areas in Seismic Activity  
The geostatistical characterization of seismic activity in the Red Sea region has been augmented through the integration of univariate Local Indicators of Spatial Association (LISA) [44] and Getis-Ord \(G^{\bullet}\)[62; 63] statistics. This method offers a thorough insight into localized variations and clusters, enabling the identification of concentrated areas with heightened seismic activity. An analysis of Local Indicators of Spatial Association (LISA) maps was performed to identify clusters and statistically significant seismicity data. The goal was to generate cluster maps using spatial autocorrelation data, as described in [PERSON]'s 2009 work on OpenGeoDa [64]. This analysis aimed to pinpoint spatial patterns of earthquake events, including earthquake clusters, as well as to understand the spatiotemporal dynamics, mechanisms, and characteristics of seismic activity. Figures 7 and 8 display the outcomes of a Local Indicators of Spatial Association (LISA) analysis, examining seismic events in the Red Sea region over four distinct time frames: 1997-2002 (Figure 7a), 2002-2008 (Figure 7b), 2008-2014 (Figure 8a), and 2014-2020 (Figure 8b). This analysis categorizes earthquake events into distinct clusters \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Magnitude** & \multirow{2}{*}{**LMI Index**} & **Mean** & \multirow{2}{*}{**Z-Score**} & \multirow{2}{*}{\(p\)-Value**} & **Detected** \\
**Range** & & **Magnitude** & & & **Pattern** \\ \hline
1.00–1.55 & 0.123003 & 1.183140 & 0.224410 & 0.005188 & Clustered \\
1.55–2.10 & 0.090980 & 1.863986 & 0.175247 & 0.007915 & Clustered \\
2.10–2.65 & 0.029216 & 2.310083 & 0.063909 & 0.001094 & Clustered \\
2.65–3.20 & 0.062832 & 2.852866 & 0.083825 & 0.006475 & Clustered \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Local Moran’s I (GMI) analysis of seismic event patterns categorized by both magnitude range. based on their spatial correlations and magnitudes. This temporal segmentation facilitates the examination of evolving or consistent seismic patterns. The analysis categorizes seismic spatial patterns into four clusters: high-high (HH), indicating regions of frequent, intense seismic activity; low-low (LL), denoting areas with minimal seismic events; and two types of spatial outliers, high-low (HL) and low-high (LH), which identify areas where seismic magnitudes significantly diverge from their immediate environments. HH clusters suggest seismicity clustering, potentially linked to active tectonic features, while LL clusters imply areas of relative tectonic inactivity. The HL and LH outliers may signal localized geophysical anomalies or tectonic complexities, where observed seismic activities markedly differ from those of surrounding areas. Figure 7: Spatial distribution of Local Indicators of Spatial Association (LISA) clusters and corresponding significance maps for two distinct periods: 1997–2002 and 2002–2008. Figure 8: Spatial distribution of Local Indicators of Spatial Association (LISA) clusters and corresponding significance maps for two distinct periods: 2008–2014 and 2014–2020. Adjacent to these cluster maps, the figures also illustrate the statistical significance of the identified clusters, employing \(p\)-value thresholds to challenge the hypothesis of random spatial distribution. Clusters with significant \(p\)-values, especially along the central axis of the Red Sea, highlight a spatially correlated pattern that could be connected to the region's tectonic structure. Conversely, clusters lacking statistical significance might represent either random distributions or an insufficiency of data to establish a discernible pattern. The aggregation of significant clusters along the Red Sea's central axis is particularly salient, possibly indicating a correlation with the seafloor spreading center and related earthquake activities.