## 5 Statistical Characterization of Seismic Activity
### Progression of Earthquake Activity
#### 5.3.2 Quadrat Count Analysis (QCA)  
The outcomes of the QCA, detailed in Table 4, were obtained from both earthquake magnitude intervals and annual data. These results provide crucial insights into the spatial and temporal dynamics of seismic activity in the studied region. The QCA of the earthquake dataset revealed distinct patterns in magnitude and temporal distributions. In magnitude, significant clustering was observed in lower ranges \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Magnitude Range** & **Mean** & **Variance** & \(\mathbf{Z}\)**-Score** & \(\mathbf{p}\)**-Value** & **Detected Pattern** \\ \hline
1.00–1.55 & 1.1831 & 0.0342 & 75.3441 & 0.000023 & Clustering \\
1.55–2.10 & 1.8640 & 0.0248 & 54.2673 & 0.000016 & Clustering \\
2.10–2.65 & 2.3101 & 0.0255 & \(-\)47.4820 & 0.000056 & Dispersion \\
2.65–3.20 & 2.8529 & 0.0194 & \(-\)82.7884 & 0.000079 & Dispersion \\ \hline \multicolumn{5}{c}{Year Range} \\ \hline
1997–2002 & 2000 & 0.9385 & \(-\)43.6551 & 0.000035 & Dispersion \\
2002–2008 & 2004 & 2.0619 & 121.4927 & 0.000054 & Clustering \\
2008–2014 & 2010 & 2.1741 & 20.37150 & 0.000044 & Clustering \\
2014–2020 & 2016 & 3.1774 & \(-\)88.4000 & 0.000022 & Dispersion \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Quadrat Count Analysis (QCA) of seismic event patterns categorized by magnitude and year ranges. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Magnitude Range** &
\begin{tabular}{c} **ANN** \\ **Distance** \\ \end{tabular} & **Mean** & **Z-Score** & \(\mathbf{p}\)**-Value** & **Detected Pattern** \\ \hline
1.00–1.55 & 0.00647 & 0.02350 & \(-\)307.93 & 0.000013 & Clustered \\
1.55–2.10 & 0.00776 & 0.02633 & \(-\)294.62 & 0.000059 & Clustered \\
2.10–2.65 & 0.01656 & 0.04702 & \(-\)158.48 & 0.000071 & Clustered \\
2.65–3.20 & 0.03031 & 0.08822 & \(-\)86.970 & 0.000066 & Clustered \\ \hline \multicolumn{5}{c}{Year Range} \\ \hline
1997–2002 & 0.00962 & 0.04228 & \(-\)140.66 & 0.000020 & Clustered \\
2002–2008 & 0.00564 & 0.02282 & \(-\)393.49 & 0.000009 & Clustered \\
2008–2014 & 0.01034 & 0.03084 & \(-\)252.56 & 0.000081 & Clustered \\
2014–2020 & 0.03012 & 0.10284 & \(-\)66.440 & 0.000063 & Clustered \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average Nearest Neighbor (ANN) analysis of seismic event patterns categorized by both magnitude and year ranges. (1.00-1.55 and 1.55-2.10) with high positive z-scores and low \(p\)-values, indicating a higher frequency of smaller earthquakes. Conversely, higher magnitude ranges (2.10-2.65 and 2.65-3.20) showed dispersion, with negative z-scores and \(p\)-values near zero, suggesting fewer large earthquakes. Temporally, the years 2002-2008 and 2008-2014 demonstrated significant clustering (high positive z-scores and low \(p\)-values), indicating more frequent seismic activity, whereas 1997-2002 and 2014-2020 showed dispersion, suggesting less activity. These results indicate a complex interplay of geological and tectonic factors influencing the distribution and frequency of earthquakes. The frequent occurrence of smaller quakes is consistent with global seismic trends, and the observed temporal clustering could reflect regional geological changes. The _VTMR_ and ANN analyses (Tables 3 and 4) distinctively evaluate the spatial distribution of seismic events. The _VTMR_, focusing on frequency distribution within the Red Sea area, is sensitive to event clusters such as aftershocks or swarms, as it assesses the variability of seismic occurrences. This method is susceptible to skewness from localized event density increases. In contrast, the ANN index, by measuring distances between seismic events, provides insights into spatial uniformity, capturing spatial distribution patterns less apparent in _VTMR_'s frequency distribution analysis. The ANN analysis, using a pairwise distance metric, provides a clear understanding of spatial relationships in seismic events. This approach is less affected by anomalies or dense clusters, giving a comprehensive view of how earthquakes are distributed.