# Successful Tests on Detecting Pre-Earthquake Magnetic Field Signals from Space
## 3 Results and Discussion
### Magnitude-duration correlation  
According to Figure 3, which is obtained from the detailed analysis, there is a logarithmic relationship between the duration of the magnetic anomaly appearing in the components of the magnetic field (y-axis) and the magnitude of the earthquake, generally as Mw (x-axis). Confidence intervals are marked with thin black lines and mean data are marked with thick black lines. In Figure 3a, all data are used without considering geomagnetic indices. As shown in this figure, the obtained relationship can be expressed as follows:  
\[M=(1.414\pm 0.771)\times\ \ln(Du)+(1.29\pm 0.678) \tag{2}\]  
where \(M\) is the magnitude of the earthquake and \(Du\) is the duration of the anomaly (in seconds). Consequently, the greater the magnitude of the earthquake, the longer the duration of the anomaly. This issue can be seen in Figures 2 and S2-S4, and the other figures in the Supplementary Material.  
Figure 2: **Identified magnetic anomalies.** Anomalous event detected on 22 April 2015 by SW-A, which was three days before the 25 April 2015, Mw = 7.8 Nepal earthquake. The anomalous satellite-detected event occurred at a distance of 279 km from the epicenter. The epicenter is indicated by a green star, and a green oval surrounding it (the oval shape is because of the projection; it would be actually a circle over the earth’s surface and at satellite altitude), representing the Dobrovolsky area. The red line illustrates the path of the satellite. At the top of the figure, relevant information is provided, including the satellite name (Alpha = A, Charlie = C), the date and time of the satellite passing through the specified area, the date and time of the earthquake, the satellite track number, geomagnetic indices (Dst, Kp, F10.7), and the closest distance of the orbit from the epicenter of the earthquake. The direction of satellite movement is indicated by a black arrow, with the upward direction represented by an arrow pointing upwards (ascending) and the downward direction represented by an arrow pointing downwards (descending). In this case, the orbit is descending. The red point depicts another M5+ earthquake occurring in the same spatio-temporal interval.  
In Equation (2), the R-square of the fit is equal to 0.976, which shows that the model can predict the results very well. The corresponding error value is equal to R-mse = 0.125, so comparable to the typical error associated with the magnitude when estimated from seismograms. In Figure 3b, the effect of geomagnetic indices on the relationship is investigated. In this panel, the condition of the geomagnetic indices being in a quiet state has been applied to the data (i.e., all three conditions are checked simultaneously: Kp \(\leq\) 3 AND \(\mid\)Dist \(\mid\)\(\leq\) 20 nT AND F10.7 \(\leq\) 150). As can be seen, the relationship has not changed drastically and has remained stable, and it can be said that the R-square and the error rate have remained almost constant. In two other investigations, anomalies with a signal-to-noise ratio greater than two (Figure 3c) and values greater than five (Figure 3d) have been selected. As evident from the comparison between the results for the general state of the data (Figure 3a) and those with the signal-to-noise ratio selection (Figure 3c,d), it is clear that considering this ratio has further improved the stability of the results, although the coefficients of the relationship do not change significantly.