## 3 Anomaly Detection and Quantification of Seismicity Parameters  
Anomaly detection in seismic activity, particularly through the application of Isolation Forest algorithms, represents a critical frontier in seismology, offering a nuanced approach to identifying irregular patterns indicative of seismic events. The Isolation Forest method, distinct from traditional anomaly detection techniques, operates on the principle of isolating anomalies instead of profiling normal data points. This is achieved through a mechanism akin to the random forest algorithm, utilizing numerous decision trees. Each tree isolates  
Figure 1: (**a**) Tectonic Divisions and Geological Characteristics of the Red Sea Region Derived from [27; 31]. (**b**) Spatial Distribution of Seismic Activity in the Red Sea Region as Recorded by Various Saudi Arabian Seismic Networks. a data point by randomly selecting a feature and then randomly selecting a split value between the maximum and minimum values of the chosen feature. The fundamental premise rests on the notion that anomalies are 'easier' to isolate due to their inherent differences from normal observations. This leads to shorter paths in the tree structure for anomalies. Mathematically, this can be represented as the path length \(h(x)\) for a data point \(x\), where anomalies will, on average, have shorter path lengths. The anomaly score is computed using the equation [11]:  
\[s(x,n)=2^{-\frac{E(h(x))}{c(n)}} \tag{1}\]  
where \(E(h(x))\) is the average path length of \(x\) over all the trees in the forest, \(n\) is the number of external nodes, and \(c(n)\) is the normalization factor to standardize the path length. In the context of seismic activity, this methodology allows for the swift and effective identification of seismic events that deviate from established patterns, thereby facilitating timely and informed responses to potential seismic hazards. By employing this technique, seismologists can efficiently sift through vast datasets to pinpoint potential seismic anomalies, which are crucial for early warning systems and risk assessment. The application of the Isolation Forest algorithm for anomaly detection in seismic activity leverages its unique approach to identify irregular seismic patterns, which significantly deviates from conventional methods. Unlike standard anomaly detection techniques that focus on modeling the normal data points, the Isolation Forest algorithm isolates anomalies. This isolation is executed through the construction of binary trees. For each tree in the forest, the algorithm randomly selects a feature and then randomly chooses a split value between the maximum and minimum values of that feature. This process partitions the data space, and the path length from the root node to the terminal node becomes a measure of normality [11]. In an Isolation Forest comprising multiple trees, the path length \(h(x)\) for a data point \(x\) is shorter for anomalies. This is quantified as:  
\[s(x,n)=2^{-\frac{E(h(x))}{c(n)}} \tag{2}\]  
where \(s(x,n)\) is the anomaly score, \(E(h(x))\) is the expected path length of \(x\), and \(c(n)\) is the normalization factor, calculated as  
\[c(n)=2H(n-1)-\frac{2(n-1)}{n} \tag{3}\]  
with \(H(i)\) being the harmonic number. In seismic data analysis, this technique can identify outliers which could signify unusual seismic activity. The algorithm's efficiency stems from its ability to handle multi-dimensional data, making it adept at processing complex seismic datasets. The average path length becomes a critical metric, as shorter paths indicate anomalies. This is especially pertinent in seismology, where early detection of such anomalies can lead to timely interventions and potentially mitigate the risks associated with seismic events. The Isolation Forest thus serves as a robust tool in the arsenal of seismologists, enabling them to discern and react to aberrant seismic patterns with greater accuracy and speed.