# An Earthquake Forecast Model Based on Multi-Station PCA Algorithm
## 2 Related Work  
Current earthquake prediction methods contain statistics methods and precursory anomalies analysis methods. The statistics methods pay attention to the historical earthquakes and the structure of potential sources, and they use statistical and geological theories to analyze the relationship between the historical earthquakes and the potential earthquakes in the future. These works [3; 4; 5] use Gutenberg-Richter law to analyze the law of earthquakes in a large area and over a long term. The method uses a statistical law that the magnitude M and the number N of earthquakes whose magnitude is upon M in a specific area and time, \(log_{10}N=a-bM\), and \(a\), \(b\) are constants. This method could only analyze earthquake risk in the long term, so it can not guide humans to avoid disaster. The precursory anomalies analysis method is based on a law that there will be some anomalies behind an earthquake. [PERSON] surveyed the published scientific literature to identify each kind of earthquake precursor and to explore the proposed physical models to explain each earthquake precursor [6]. [PERSON] analyzes probabilities for an anomalous signal of various geophysical elements to be related to a forthcoming earthquake, which are estimated based on the existing data of precursors [7], finding that precursors can be detected further from the epicenter as the mainshock magnitude becomes larger [8]. [PERSON] finds that there seems to be a close relationship between these gravity variations and the occurrences of earthquakes [9]. [PERSON] finds that observable precursors may exist before large earthquakes from the 1 April 2014 Chile event [10]. These works showed that there are usually some precursor signals before a burst earthquake, such as land deformation revealed by geodetic survey and tide-gauge observation, ground tilt observed by a water-tube tiltmeter, anomalous seismic activity, and geomagnetic field change, and they proved that this method could show a risk of some earthquakes in an acceptable time range, instead of a long-term analysis according to the Gutenberg-Richter law or other statistical laws. However, earthquake precursory anomalies are complex and uncertain, which makes it difficult to analyze them. As a common method, PCA shows high performance in feature extraction, and we use it to extract our data. LightGBM is a kind of powerful model in machine learning based on the decision tree, which is stable and quick with high accuracy and prediction ability [11]. The PCA algorithm is more widely used in the geomagnetic research field. [PERSON] applied Principal Component Analysis to study the daily variation of geomagnetism after harmonic approximation at three stations and found that the proportion of the second principal component fluctuated several times in one month before the earthquake (the 2000 Izu Islands earthquake). [PERSON] and [PERSON] applied Principal Component Analysis to the horizontal magnetic field component data of electromagnetic observation at Jinggu, Lijiang, and Datong, and they found that the proportion of the second principal component, which could be related to the local underground electrical structure change and electromagnetic disturbance, increased significantly about two weeks before the earthquake (Jinggu earthquake in 2015) [12]. [PERSON] has performed statistical studies on the electromagnetic data observed at the AETA station using a modified PCA method. They concluded that 80% of AETA stations have a significant relationship between electromagnetic anomalies and local earthquakes [13]. [PERSON] and [PERSON] used the sliding Principal Component Analysis (PCA) method to study the ionospheric electron concentration with daily periodic variation and achieved some reflective effect on the 2011 Honshu M9.0 earthquake in Japan [14]. [PERSON] used this method to analyze the electromagnetic signals of some AETA stations and found clear anomalies before and after the Juzhaigou earthquake in 2017 [15].