## 5 Statistical Characterization of Seismic Activity
### Progression of Earthquake Activity
#### 5.3.3 Global Moran's I (GMI)  
The queen contiguity criterion is employed to establish adjacency relationships among spatial units. In this context, spatial units are considered neighbors if they share any boundary or vertex. Formally, the spatial weight matrix (W) is constructed by assigning binary weights of 1 to neighboring units and 0 to non-neighboring units. The resultant matrix encapsulates the spatial relationships inherent in the geographical distribution of the observed seismic activity as outlined in Equation (5). Global Moran's I (GMI) constitutes a statistical index of spatial autocorrelation [61], signifying the degree of correlation among seismic occurrences within proximate spatial locales [60]. The spatial analysis of seismic activity in the Red Sea region, as indicated by the GMI index, is presented in Table 5. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \begin{tabular}{c} **Magnitude** \\ **Range** \\ \end{tabular} & \begin{tabular}{c} **GMI Index** \\ **Magnitude** \\ \end{tabular} & \begin{tabular}{c} **Mean** \\ **Z-Score** \\ \end{tabular} & \
\begin{tabular}{c} **\(p\)-Value** \\ **Pature** \\ \end{tabular} &
\begin{tabular}{c} **Detected** \\ **Pattern** \\ \end{tabular} \\ \hline
1.00–1.55 & 0.143011 & 1.183140 & 24.870270 & 0.000001 & Clustered \\
1.55–2.10 & 0.107987 & 1.863986 & 17.478009 & 0.000003 & Clustered \\
2.10–2.65 & 0.042225 & 2.310083 & 3.895662 & 0.000098 & Clustered \\
2.65–3.20 & 0.067881 & 2.852866 & 3.408918 & 0.000652 & Clustered \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Global Moran’s I (GMI) analysis of seismic event patterns categorized by both magnitude range. The GMI Index, detailed in Table 3, shows significant clustering in seismic activity across various magnitude ranges in the Red Sea region. The lowest magnitude range (1.0-1.55) has a GMI Index of 0.143011, with a high \(Z\)-score of 24.870270 and a \(p\)-value of practically zero, indicating strong clustering. This clustering diminishes slightly but remains significant in higher magnitudes: 1.55-2.1 range has a GMI of 0.107987, 2.1-2.65 a GMI of 0.042225, and 2.65-3.2 a GMI of 0.067881. Even as the \(Z\)-scores decrease (to 3.408918 in the highest magnitude range), they stay high, underscoring the clustered nature of seismic events. The consistently low \(p\)-values across all ranges further support the non-randomness of this pattern. This clustering trend, as highlighted in previous studies like [14], is crucial for understanding seismic risks and preparing for potential disasters in the Red Sea region. To validate the interpretations derived from the estimated GMI values in Table 3, scatter plots depicting the distribution of earthquake magnitudes and their spatial lags were created, as illustrated in Figure 6. These GMI scatter plots provide an extensive quantitative analysis of spatial autocorrelation in earthquake magnitudes specific to the Red Sea region. The scatter plots show data points primarily clustering around the mean, indicating a consistent spatial pattern across different magnitude ranges. Positive GMI values suggest that areas with similar magnitude earthquakes are geographically close, a significant observation for the tectonically active Red Sea rift. Supporting this, studies by [14,60] and [31] have independently confirmed similar findings, validating the effectiveness and reliability of the GMI method in spatial analysis of Red Sea seismicity. Figure 6: Global Moran’s I (GMI) scatter plots depicting spatial autocorrelation across distinct earthquake magnitude ranges. Each plot is partitioned into quadrants by blue dashed lines, representing the respective means of magnitude and spatial lag of magnitude. Red line represents the fitting of a regression between magnitude and the spatial lag of magnitude. This regression fitting is crucial for illustrating the relationship between the magnitude of seismic events and their corresponding spatial lags.