# Detection of Electromagnetic Seismic Precursors from Swarm Data by Enhanced Martingale Analytics
## 4 Quantitative Experiment  
As discussed earlier, Swarm satellites generate a significant amount of data at second intervals, accumulating a large dataset since project inception and the initial report observations. For our study, we have chosen to focus on a limited time frame--specifically, one year prior to the seismic event--including the day of the seismic event itself and 3-month aftershocks. However, in future studies, we may extend our observations further into the past. Based on the success of our algorithm in the first experiment, we can assert that our algorithm is capable of detecting anomalies with a high degree of accuracy and correctness, with our hypothesis being that our algorithmic system is transferable into this problem domain. Building upon this, we examine the EMF activity in relation to time preceding the seismic event, such as three months, six months, and twelve months, as well as three months post-seismic event. To refine our analysis, we narrow down the dataset by imposing a geospatial constraint, meaning only data within predefined latitude and longitude grids are considered for forming the time-series analyzed by our algorithm. Specifically, we utilize two grids: a 1000 km \(\times\) 800 km grid and a 500 km \(\times\) 300 km grid, respectively. The Swarm satellite constellation, comprising satellites Alpha, Beta, and Charlie [26], operates with distinct orbits: A and C travel at an altitude of approximately 450 km in parallel, while B orbits at around a 550 km altitude, perpendicular to Alpha and Charlie. These satellites record Vector Field Magnetometer (VFM) readings, capturing three-axis bounded values denoted as \(b_{x}^{2}\), \(b_{y}^{2}\), and \(b_{z}^{2}\). To simplify analysis, we reduce the data dimensionality in a 1-dimensional intensity \(|\overrightarrow{B}|\) value defined as  
\[|\overrightarrow{B}|=\sqrt{b_{x}^{2}+b_{y}^{2}+b_{z}^{2}} \tag{10}\]  
This transformation enables a more streamlined approach to analyzing the magnetic field data, facilitating subsequent interpretation for various applications, such as seismic \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Dataset** & **Accuracy (\%)** & **Precision (\%)** & **R-Rank (\%)** \\ \hline Chfdb\_chf01\_275\_f1 & 0.91 & 0.79 & 0.26 \\ Chfdb\_chf01\_275\_f2 & 0.87 & 0.74 & 0.80 \\ Chfdb\_chf13\_45590\_f1 & 0.91 & 0.55 & 0.26 \\ Chfdb\_chf13\_45590\_f2 & 0.94 & 0.75 & 0.28 \\ Data4 & 0.96 & 0.93 & 0.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of original Martingale. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Dataset** & **Accuracy (\%)** & **Precision (\%)** & **R-Rank (\%)** \\ \hline Chfdb\_chf01\_275\_f1 & 0.91 & 0.75 & 0.62 \\ Chfdb\_chf01\_275\_f2 & 0.89 & 0.75 & 0.81 \\ Chfdb\_chf13\_45590\_f1 & 0.91 & 0.57 & 0.64 \\ Chfdb\_chf13\_45590\_f2 & 0.94 & 1.0 & 0.55 \\ Data4 & 0.97 & 0.94 & 0.39 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of \(Z\)-score enhanced Martingale. event detection. Utilizing (10), we define the magnitude of the intensity values across a single day of samples \(N\) as  
\[\bar{B}=\sum_{i=1}^{N}|\overrightarrow{B}|_{i} \tag{11}\]  
Taking (11), we can further define the average intensity value over multiple days (complying with our algorithmic \(T\)) as  
\[T=\left\{\frac{1}{N_{j}}\bar{B}_{j}\mid j=1,2,\ldots,I\right\} \tag{12}\]  
Our final time-series, per satellite, comprises data points representing the mean average across the orbits of a given day. It is important to note that non-orbit days are excluded from the final time-series. This ensures that our analysis focuses on data captured during satellite orbits, providing a more accurate representation of the electromagnetic field activity. Furthermore, by constraining our analysis to specific geospatial grids, we aim to enhance the precision of our findings by focusing solely on regions of interest where seismic activity is most likely to occur.