## 3 Results and Discussion
### Earthquake Displacement
#### 3.2.1 Deformation of Tohoku-Oki Earthquake  
The Mw9.0 Tohoku-Oki earthquake occurred on 11 March 2011, at 05:46:24 UTC in the east of the Oshika Peninsula of Tohoku is located at 38.10\({}^{\circ}\)N, 142.60\({}^{\circ}\)E, with a 30 km depth of epicenter. It is one of the best-recorded earthquakes in history since Japan built one of the densest GPS networks in the world. It is also the fourth-largest earthquake in the world since 1900. Table 1 lists the information of the selected stations and the distance between the epicenter and each station calculated by 1 Hz GPS data using GAMIT/TRACK and the proposed SF-PPP method. The distribution of the epicenter and the selected stations are presented in Figure 2. According to the works in [2], 32 GPS stations and station 0848 (825.2 km far away from the epicenter) are utilized as the rover station and base station, respectively. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Site** & **Distance (km)** & **Site** & **Distance (km)** & **Site** & **Distance (km)** & **Site** & **Distance (km)** \\ \hline
0906 & 191.9 & 0201 & 173.0 & 0156 & 284.1 & 0026 & 358.5 \\
0167 & 160.8 & 0547 & 184.4 & 0543 & 244.8 & 0921 & 333.3 \\
0172 & 126.3 & 0910 & 168.6 & 0553 & 240.5 & 0030 & 320.5 \\
0918 & 122.1 & 0029 & 165.4 & 0926 & 233.9 & 0925 & 272.0 \\
0549 & 126.6 & 0174 & 172.7 & 0190 & 223.6 & 0191 & 264.5 \\
0550 & 98.8 & 0548 & 161.0 & 0554 & 219.2 & 0932 & 264.1 \\
0037 & 146.1 & 0934 & 193.5 & 0033 & 212.1 & 0231 & 295.5 \\
0919 & 145.4 & 0180 & 189.7 & 0199 & 221.3 & 0049 & 271.2 \\ \hline \end{tabular}
\end{table} 
Table 1: Epicentral distance of the selected GPS stations. As the earthquake occurred at 05:46:24 UTC, the dynamic displacements from 05:40:21 to 05:55:20 UTC were adopted to reflect the whole process. The results of eight rover stations were adopted as examples to illustrate the performance of the two methods. Meanwhile, since there was a Common Mode Error (CME) in all stations' sequences [51], it covered the weak or transient signals that had a visible influence on extracting the deformation characteristic of each station in the area network. Works from [PERSON] et al. [52] suggest that CME might be engendered by satellite orbit biases, ocean loading tidal correction residuals, atmospheric tides (\(S_{1}\) and \(S_{2}\) tidal wave), etc., and it may be affected by the implementation path of the reference frame. In addition, while the earthquake impact range is wide, or the reference station is near to the rover station, the disturbance of the earthquake on the reference station also will be superposed on each observation station under relative positioning mode. This circumstance is named the coseismic interference of the reference station and will present itself as CME [2]. Figures 3 and 4 show the coseismic displacements of the GPS stations. Those stations move towards the southeast in the horizontal component. Both the GAMIT/TRACK and SF-PPP solutions can present accurately the displacement trend. However, the magnitude of the displacement, especially in the east, of the GAMIT/TRACK solutions is slightly (i.e., about 36.8 cm for 0172) different from the SF-PPP method. The reason is that the intensity scale of the Tohoku-Oki earthquake is strong enough, and the range of influence is  
Figure 2: Distribution of the selected GPS stations and the location of the 2011 Tohoku-Oki earthquake epicenter; the green point represents the reference station. wide. It leads to large fluctuations in the reference station 0848 and results in displacement superposition. Moreover, the time series of GAMIT/TRACK in the east direction has an obvious CME. The regular method is eliminating the influence by using PCA spatial filtering. Nevertheless, as an absolute positioning method, the SF-PPP method can prevent the sequences from the influence of CME, which makes SF-PPP a potential low-cost technique in earthquake deformation inversion.