# Detection of Electromagnetic Seismic Precursors from Swarm Data by Enhanced Martingale Analytics
## 4 Quantitative Experiment
### Greece 2020
#### 4.2.1 \(500\times 300\) km  
Figure 10 showcases the EMF intensity activity across a \(500\times 300\) km area before and after the seismic event. Each data point represents the mean intensity value per day, calculated using Equation (10). The figure consists of two sub-figures: Figure 10a,b.  
In Figure 10a, the unmodified time-series obtained from the \(500\times 300\) km grid is depicted. It is noticeable that approximately \(1\) year prior to the event date, the values obtained for Beta exhibit errors, showing zero values for \(b_{x}\), \(b_{y}\), and \(b_{z}\). To enhance visual clarity, Figure 10b displays only the time-series of Alpha and Charlie. It is important to highlight that although we modified the plot in Figure 10b to exclude Beta, we did not exclude Beta from our analysis. We believe both the original Martingale and \(z\)-Martingale systems to be robust enough to handle such errors appropriately.  
Figure 8 shows the results from both the Martingale and \(z\)-Martingale systems operating over the data shown in Figure 10a. Figure 8a shows the results obtained from the original Martingale system, with only Beta and Charlie producing anomalies. Beta produces roughly five anomaly detections just prior to the event date, while Charlie produces a number of anomalies through its time-series from roughly \(10\) months prior to \(2\) months post the seismic event with a large spike occurring near the same position as the anomalies detected by Charlie. Interestingly, we can observe an unusual waveform in Beta at the rough location of the erroneous data, the impact of which was minimized by the Martingale process but suggests the potential exploration of shape-based encoding [19] for future work.  
Figure 8b shows the results of our \(z\)-Martingale, with all three satellites (Alpha, Beta, and Charlie) exhibiting anomalies in their time-series. The Alpha time-series produces anomalies at roughly \(6\) and \(3\) months prior to the seismic event; however, we note rapid fluctuations in EMF intensity lasting for long periods of time. Beta produces anomalies approximately \(3\) months post the event data, which is in contrast to Figure 8a where Beta produces anomalies just before the event date; again, as in Figure 8a, we can observe an unusual waveform pattern for Beta at the time of the erroneous data sampling. The time series of Charlie appears to follow a similar pattern to Charlie of Figure 8a but with fewer anomalies.  
Figure 9: Comparison of Martingale and \(z\)-Martingale values within the \(1000\times 800\) km grid for the Greece case study. The color coding is Alpha (red), Beta (green), and Charlie (blue). **(a)** Martingale value data plotted within the \(1000\times 800\) km grid obtained using the original Swarm satellite data alongside Equation (3). It is observable that this approach detects fewer anomalies compared to the \(z\)-Martingale **(b)** method. **(b)**\(z\)-Martingale value data plotted within the \(1000\times 800\) km grid obtained using the original Swarm satellite data alongside Equation (7). It is observable that the \(z\)-Martingale scores produce more anomaly detections than the regular Martingale method **(a)** method.