# Exploring the Dynamics of Global Plate Motion Based on the Granger Causality Test
## 3 Data Analysis and Results  
### Data Preparation  
The International Seismological Center-Global Earthquake Model (ISC-GEM) provides a global earthquake catalog that has been widely used in a broad range of studies, such as tectonics, seismicity assessment, and determination of seismic hazard [47]. In addition to this catalog, there are several other international centers that provide earthquake record data, such as the National Earthquake Information Center (NEIC) and the International Data Center (IDC). [PERSON] [48] compared the numbers of events against magnitude based on the three catalogs and found that the numbers of events with magnitudes (a characterization of earthquake intensity) greater than five are similar. In other words, these databases from the three centers have the same recording capabilities for large earthquakes. Therefore, in this paper, a global database of earthquake records acquired from ISC was used, and the time period ranged from 1904 to 2014. Before any scientific analysis of the earthquake catalog, an important procedure for most studies related to seismicity is to assess the consistency, quality, and homogeneity of the data. In the research, one specific aspect of quality control was addressed, which was determining the minimum magnitude of complete recording, \(M_{c}\). This value was considered the lowest magnitude at which all of the earthquakes in a space-time volume were detected [49; 50]. Here, the frequency-magnitude distribution (FMD) [51], which is one of the most popular methods to describe the relationship between the frequency and magnitude of an earthquake, was used to estimate \(M_{c}\). The data were plotted as Log[\(N\)(\(>\)\(M\))] against \(M\) and fitted with a linear function by the least-squares method (Figure 1). Based on the catalog earthquakes with magnitudes above 5.6, a general linear trend implied a power-law-frequency-size relationship between Log\(N\) and \(M\). The result gives Log[\(N\)(\(>\)\(M\))] = 15.66-2.69 \(M\), with \(R^{2}\) = 0.992. Therefore, M\({}_{0}\) = 5.6 was set as a threshold magnitude considering the completeness of the earthquake catalog, which included 24,650 large earthquakes from 1904 to 2014. For demonstration purposes, the locations of earthquake events with magnitudes greater than 5.6 are shown in Figure 2. A global set of plate boundaries that contains 52 plates is presented by [PERSON] in digital form [52]. However, the dataset is too meticulous to meet the needs of this study because it contains many small plates that do not have enough earthquake events. Thus, based on the dataset, new plate boundaries are formulated based on the USGS ([[http://volcanoes.usgs.gov/about/edu/dynamicplanet](http://volcanoes.usgs.gov/about/edu/dynamicplanet)]([http://volcanoes.usgs.gov/about/edu/dynamicplanet](http://volcanoes.usgs.gov/about/edu/dynamicplanet)) (accessed on 29 June 2018)) model, which contains 12 plates in total (Figure 2). Figure 1: Accumulative frequency-size distribution of the earthquake dataset acquired from the ISC with a time range from 1904 to 2014. Plate boundaries are the border areas between two plates. There are 28 boundaries in this study (Figure 2). Because the purpose of this paper is to study the energy transfer relationship between plate border areas based on statistical physics methods, earthquakes are divided into 28 regions according to adjoining plate boundaries (Table 1). The earthquake energy release is related to the moment magnitude [53,54]. Therefore, the energy released by an earthquake with a moment magnitude (\(M_{\rm w}\), an evaluation method of earthquake magnitude) was calculated by the following equations. Due to the inconsistency and heterogeneity of earthquake occurrence, the energy release of an earthquake is processed into energy release at annual intervals. Following the above procedure, all energy release at plate boundaries was transformed into natural logs to help induce stationarity (Figure 3).