# Feasibility Study on Earthquake Prediction Based on Imending Geomagnetic Anomalies
## 2 Methods for Observing and Capturing Geomagnetic Anomalies
### Extraction of Geomagnetic Anomaly Signals Caused by Earthquakes  
Due to the complex environment of modern human life with various electrical equipment and stations, there are various electromagnetic interferences around monitoring points. The magnetic intensity sensor in the magnetic sensor network in this experiment does not use any shielding interference device, so it will be subject to various interferences. Generally, the geomagnetic anomaly of small earthquakes is very weak, and may be submerged in environmental noise. In order to extract the geomagnetic anomaly in this environment, it is necessary to filter out all kinds of magnetic anomalies or background noise not caused by earthquakes. The magnetic interference around the observation environment mainly includes the following categories:  
1. Random interference: surrounding electrical appliances, vehicles, and lightning. This interference only causes short-term interference to individual stations. 2. Static interference: high-voltage stations, communication base stations, underground metal pipelines, etc. in the environment, which only cause long-term interference to individual stations. 3. The annual and daily variations from the solar system and the Earth's magnetic field can be corrected by the geomagnetic correction method. The idea of our algorithm for geomagnetic anomaly capturing is as follows:  
1. Interpretation of anomaly: using the window-based magnetic anomaly judgment method, when the average number in a period exceeds a certain threshold, it is considered as the abnormal magnetic field strength, referred to as a geomagnetic anomaly in short. This algorithm can eliminate short-term spike anomalies, such as magnetic anomalies caused by automobile passing and electrical switches. 2. Similarity judgment: ignoring the anomalies of individual stations, which is recognized as a geomagnetic anomaly when the data from multiple stations have similar changes during the same time period which may last for a few days. 3. Using the energy integration method to improve the signal-to-noise ratio is as follows:  
Figure 2: Magnetic magnitude waveform and synchronous enhancement before earthquakes. In this algorithm, the magnetic intensity signal is considered a stationary random process, and its mean is obtained by calculating the cumulative mean, which is the arithmetic mean \(\mu(0)\) of all the magnetic intensity sample values in one day, and then it is averaged using the previous day's mean to obtain the daily average \(\mu(i)\) as the following:  
\[\mu(i)=\frac{1}{2}[\mu(i-1)+\mu(0)] \tag{3}\]  
The daily observation time is divided into many observation windows, for example, \(N\), where the window length is \(T\). We newly define \(F\) as the total geomagnetic field after removing the variation of daily and annual magnetic field, and \(\Delta F\) as the anomalous intensity of the net geomagnetic field only caused by earthquakes or other geological factors, for example, the iron ones. Especially, within a time window of length \(T\), we define \(E=\Delta F^{2}\times T\) as a new measure of the geomagnetic field observation, i.e., the cumulative geomagnetic anomaly energy, which can enhance the pre-earthquake geomagnetic anomaly signal, eliminate random interference from the surrounding environment, and highlight weak pre-earthquake geomagnetic anomaly change signals. We prove the above conclusion as follows:  
First, we assume that within kth time window the geomagnetic anomaly energy at discrete time \(k\) is \(E(k)\), the noise energy is \(N(k)\). The signal-to-noise ratio in this time window can be expressed as follows:  
\[SNR=\frac{E(k)}{N(k)}=\frac{\Delta F^{2}\times T}{\mu_{k}^{2}\times T} \tag{4}\]  
where \(\mu_{k}\) is the mean of the random noise at time \(k\). When the geomagnetic field is stable, the fluctuation in the magnetic field is usually less than 50 nT, that is \(\Delta F<\) 50 nT, \(E(k)\) tends to stabilize and can be approximated as a constant.