## 3 Real GNSS Position Time Series Analysis  
The 25 GNSS stations located in Yunnan Province were selected for our study and their location is shown in Figure 1. Since the observations of most stations started in 2011, the time span in this investigation was from 2011 to 2017. Together with the position time series, formal errors were also provided in the GNSS data products of the China earthquake administration, which can be downloaded from the website, [[ftp://ftp.cgps.ac.cn/products/position](ftp://ftp.cgps.ac.cn/products/position)]([ftp://ftp.cgps.ac.cn/products/position](ftp://ftp.cgps.ac.cn/products/position)). Formal errors were different for the observations of each station at each epoch ([PERSON] et al., 2015). Weighted Least Squares was applied to model the linear term, annual signal, semi-annual signal ([PERSON] et al., 2015) and correct the offsets in the time series. What remained was the residual time series to be analyzed. Position time series with formal errors larger than 10, 10 and 20 mm, respectively, for North, East and Up components were discarded. Outliers were eliminated by interquartile range (IQR) statistics ([PERSON] et al., 2015) and once outliers were found in one component, the other two components were also removed. The standard deviations of unit weight derived from Equation (5) are shown in gray bars for all stations in Figure 2. We can see from Figure 2 that the standard deviations of Up components were significantly larger than the other two components. Moreover, for the same coordinate component, the standard deviations of unit weight were different for different stations and the mean values for North, East and Up components were 1.56 mm, 1.96 mm and 5.50 mm, respectively. This illustrates that it is unreasonable that unit weight adopted for each station at each epoch be used in forming covariance in PCA. Additionally, the standard deviation of weight factors is shown in blue in Figure 2. The mean standard deviation of the weight factor was 0.13, 0.17 and 0.14 for North, East and Up, respectively. We can see that the weight factor in East had the largest variation among the three components, while North ranked the least. Figure 1: Location of the selected 25 GNSS stations in YunNan Province. Figure 2: Standard deviation of unit weight (gray bar) and weight factor (blue line) for each station. The eigenvectors showed that the spatial responses of only the first PC were consistent; therefore, the responses derived from PCA and IPCA are depicted in Figure 3. We can see that the spatial responses derived from IPCA were different to those from PCA, for the three components. The mean responses from PCA and IPCA were 73.69% and 74.63% for North, 55.17% and 54.28% for East, and 69.96% and 68.16% for Up. Their maximum relative differences were 4.30% (North) and 6.13% (Up) at XIAG station, and 6.25% (East) at YNLA station. The mean relative differences were 1.28%, 1.46% and 1.84% for North, East and Up, respectively. The first PC derived from IPCA and the difference between PCA and IPCA are shown in Figure 4, with blue and green colors, respectively. We can see that differences did exist and the mean absolute differences were 0.11 mm, 0.22 mm and 0.45 mm, respectively, for North, East and Up components. Figure 4: First PC from IPCA and the difference between PCA and IPCA for three components. Figure 3: Spatial response of Principal Component Analysis (PCA) and Improved Principal Component Analysis (IPCA) for three components. Analysis of CME showed that it consisted of white and flicker noise and that the flicker noise was dominant, as shown in Table 1. Moreover, the proportion of flicker noise in CME derived from IPCA was slightly larger than that derived from PCA.