# Detection of Electromagnetic Seismic Precursors from Swarm Data by Enhanced Martingale Analytics
## 4 Quantitative Experiment
Within each plot, a comprehensive examination of observable EMF characteristics is conducted. We meticulously document instances of positive and negative spikes, indicating notable increases and decreases in intensity values, respectively. These spikes are scrutinized to discern their significance within the broader context of the plot, considering factors such as magnitude and duration. Additionally, the temporal proximity of each spike to the seismic event is meticulously annotated, employing vertical reference lines to denote specific time intervals (e.g., 3 months prior and 3 months post-event). This in-depth annotation facilitates a detailed temporal analysis, allowing for the identification of potential precursory EMF patterns preceding seismic events and their evolution over time. The same method is applied in each instance. Using Equation (10), we form a sequence of time-series data, wherein each data point is the mean of \(|\overrightarrow{B}|\) values occurring over a day's orbit(s). From this, we form two time-series sequences by varying the geospatial bound to \(500\times 300\) km and \(1000\times 800\) km. These are our ground truth data. The grid size will contribute significantly to the calculated \(|\overrightarrow{B}|\) values because of its size as it changes the number of data points available over each day. We then examine the results of the conventional Martingale approach and compare them with the results of the proposed \(z\)-Martingale approach to determine which of the two methods is more accurate. Within our case studies, the dataset \(T\) encompasses values spanning from one year preceding the seismic event to three months following it. This extensive temporal scope allows us to capture the dynamics of electromagnetic field (EMF) activity leading up to and after the seismic event, providing a comprehensive understanding of the pre-seismic and post-seismic EMF behavior. By including this wide range of temporal data, we aim to analyze and identify any discernible patterns, anomalies, or fluctuations in EMF intensity that may serve as potential precursors or indicators of seismic activity. This approach enables us to explore not only the immediate events surrounding the seismic occurrence but also the broader context and temporal evolution of EMF phenomena, thereby enhancing our ability to detect and interpret anomalies in the EMF data with greater depth and accuracy. Our overarching objective encompasses not only the detection of anomalies within the data but also the assessment of their significance. As we progress through each case study, we meticulously evaluate the anomalies detected by our algorithms, aiming to discern their relevance and potential implications. By scrutinizing the detected anomalies, we seek to identify those that exhibit notable characteristics or patterns, indicating a departure from expected behavior. Our assessment includes considerations such as the magnitude, frequency, and temporal distribution of anomalies, as well as their spatial correlation with known seismic events or geological features. Furthermore, we delve into the context surrounding each anomaly, exploring factors such as its proximity to seismic activity, its alignment with historical events, and its correlation with environmental or anthropogenic factors. Through this comprehensive analysis, we endeavor to distinguish between anomalies of genuine interest and those that may arise from noise or artifacts in the data. Ultimately, our goal is to not only detect anomalies but also to interpret their significance within the broader context of seismic monitoring and environmental surveillance. By identifying and characterizing anomalies of particular interest, we aim to advance our understanding of electromagnetic phenomena and contribute valuable insights to the field of geoscience.