# Detection of Electromagnetic Seismic Precursors from Swarm Data by Enhanced Martingale Analytics
## 4 Quantitative Experiment
### Mexico 2017
#### 4.1.2 \(1000\times 800\) km  
Figure 6 presents the EMF intensity activity over a larger area of \(1000\times 800\) km, both preceding and following the seismic event. Each data point in the graph represents the mean intensity values calculated using Equation (10) for a single day. A distinct shift in EMF behavior is observable compared to the \(500\times 300\) km grid depicted in Figure 4. Across all members of the satellite constellation--Alpha, Beta, and Charlie--more pronounced waveform behavior shifts are evident leading up to and following the seismic event. This divergence arises from the expanded coverage area of our geospatial boundary, resulting in a greater number of data samples.  
Figure 7a shows the results obtained using the original Martingale system with the data plotted in Figure 6 for each of the satellite time-series. Starting with Alpha, we see a number of anomalies detected up to 16 months prior to the seismic event data until roughly 5 months prior, followed by a period of no detection until 1 month post the event date; it is noteworthy that Alpha exhibits a series of large spikes causing anomaly detection, which are sustained for long periods of time. Beta begins to exhibit triggering behavior at approximately 9 months prior to the event data, with strong spiking activity over a long duration of time until 3 months prior to the event data; no further anomalies are detected  
Figure 5: Comparison of Martingale and \(z\)-Martingale values within the \(500\times 300\) km grid for the Mexico case study. The color coding is Alpha (red), Beta (green), and Charlie (blue). **(a)** Martingale value data plotted within the \(500\times 300\) 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 \(500\times 300\) 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.  
afterwards. Charlie only exhibits anomalies approximately 1 year prior to the event data and remains untriggered, with no anomalies detected for the remainder of the time-series.  
We do note that, although no anomalies are detected near the event data, the time-series themselves show some spiking activity with long durations just before and after the event data for all three satellites when processed with \(z\)-Martingale.  
Figure 7b depicts the outcomes derived from employing our \(z\)-Martingale system with the data plotted in Figure 6 for each of the satellite time-series. In comparison to the original Martingale system (Figure 7a), we observe fewer anomalies for Alpha, with none detected approximately 1 year before the seismic event. Regarding Beta, the results closely resemble those obtained in Figure 7a, albeit with the \(z\)-Martingale system producing fewer anomalies but larger spikes in magnitude. Similarly, anomalies for Charlie appear similar to those in Figure 7a, although the spikes exhibit greater power in terms of magnitude. Additionally, the time-series produces anomalies just after the event date.  
We do note that, as before, the time-series themselves show some spiking activity with long durations just before and after the event data for all three satellites when processed with \(z\)-Martingale.  
Figure 6: A plot of the original data occurring within the \(1000\times 800\) km grid obtained using the original Swarm alongside Equation (10). The color coding is Alpha (red), Beta (green), and Charlie (blue).  
Figure 7: _Cont._