# Successful Tests on Detecting Pre-Earthquake Magnetic Field Signals from Space
## 3 Results and Discussion
### Magnitude-Energy correlation
For example, see Figures S13 and S14, which are related to the Mw = 7.3 China earthquake that occurred on 21 May 2021 (Earthquake number 762 in Table S1). In Figure S13, an anomaly was detected 8 days before the earthquake that occurred at a distance of 992 km on track number 42010 of the SW-C satellite for 37 s in the Z component of the magnetic field. In Figure S14, an anomaly was detected 1 day before the occurrence of the same earthquake at a distance of 833 km in track number 42117 of the SW-C satellite. The anomaly was recorded for 60 s. As we can see, despite the fact that the distance of both orbits to the epicenter of the earthquake does not differ significantly, track 42117, which experienced an earthquake one day prior, exhibits the anomaly for a longer duration. Therefore, the effect of time on the duration of the anomaly can be shown in Figure S7. The x-axis is the earthquake's magnitude, and the y-axis is the natural logarithm duration of the anomaly in time. According to Figure S7a, plotted for all the data, there is a natural logarithmic relationship between magnitude \(M\) and duration \(Du\) in seconds as follows:  
\[M=(1.449\pm 0.918)\times\ln(Du\times Time)+(-1.113\pm 0.739) \tag{5}\]  
where \(Time\) is the time in days before the earthquake. The R-square of the system is also equal to 0.89, and the error value is equal to 0.256. In Figure S7b, the effect of geomagnetic indicators on the system is investigated. As observed, the stability of the system (R-square = 0.78) and the error values (R-mse = 0.35) have been somewhat affected, and this could be due to the limited time period we considered before the earthquake (only 10 days). Another test was performed on the system (Figure S7c,d) in which the signal-to-noise ratio for values higher than two (Figure S7c) and values higher than five (Figure S7d) is applied to the data. As observed, the error rate increases (R-mse = 0.32), and the system's stability decreases (R-square = 0.84). As mentioned earlier, this could be due to the limited time interval that was considered before each earthquake. In particular, once a satellite anomaly is identified, Equations (2)-(5) allow for the estimation of three crucial precursor parameters, i.e., time, distance, and magnitude. These estimations are made possible through the measurement of anomaly duration, amplitude (\"energy\"), and distance of satellite data from the impending earthquake epicenter. We recognize that identifying a precursor alone does not provide full confidence in predicting earthquake occurrences, as the region of the event would require multiple precursors for a more reliable assessment [19; 49]. However, we will show that the established correlations between some anomaly features and earthquake magnitude can serve as the base for an OEPS. We will not exclude that the next valuable outcome in precursor discussions could be a key component in future multi-parameter methodologies for an improved earthquake prediction method when including satellite magnetic field measurements.