# Surface Subsidence Monitoring in Kunming City with Time-Series InSAR and GNSS
## 4 Results and Discussion
### Comparative Analysis of Vertical Deformation Informationining  
In order to better study the accurate relative deformation in Kunming city area, it is necessary to transfer the velocity under the ITRF2014 framework to the background of the Eurasian plate. In order to analyze the vertical velocity field under the overall no-net rotation datum of the CORS reference station. 5 reference points are taken as the stable reference datum. Based on the measured velocity of the CORS station under the ITRF2014 framework. The ordinary least squares is used to estimate the Euler vector of the whole site relative to ITRF2014 frame, and then the measured velocity and the Euler vector model can be inversely calculated. Since there are only 8 stations used, in order to better reflect the deformation effect, this paper adopts the Kriging method to interpolate the velocity  
Figure 9: Deformation rate in the mining area and time series cumulative settlement diagram of P5. field in Kunming city area. This method is an unbiased and optimal interpolation method for the interpolation of discrete points with uneven space. According to the distribution of 8 CORS stations in this paper, 10 m \(\times\) 10 m grid division is carried out in the range of 102\({}^{\circ}\) E-103\({}^{\circ}\) E, 24\({}^{\circ}\) N-25\({}^{\circ}\) N, and the velocity field in the vertical direction was interpolated. As shown in Figure 10, the error ellipse represents 95% confidence. The vertical velocity field obtained by CORS station is compared with the deformation rate of InSAR in the same time period, and the results are shown in Table 1.  
According to the comparison results of deformation rates between InSAR and CORS, the vertical motion trend of Dianchi Lake rising in the west and falling in the east is generally reflected. As shown in Figure 10, the area around Xinjie town in the east of Dianchi Lake presents a downward trend, with the maximum settlement velocity reaching about 40 mm/year, while the area in the west presents an upward trend, with a rising velocity of 2-17 mm/year. The settlement trends obtained by two different monitoring methods are consistent. The average annual subsidence rate of site XIAH and QINL are high, reaching \(-45.57\) mm/year and \(-40.53\) mm/year, respectively, while the CHG0 site is stable and the average annual subsidence rate is low, reaching 0.58 mm/year. The Root Mean Square Error (\(RMSE\)) is taken as the evaluation index, see Formula (7). The \(RMSE\) of ANNI, BJIE, CHGO and other 5 stations are respectively 0.78 mm, 0.63 mm, 6.20 mm, 0.41 mm, 3.50 mm, 1.83 mm, 0.34 mm and 1.56 mm. Through calculation, the residuals of the two stations are all within 10 mm and the maximum is 7.04 mm, the minimum is 1.65 \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Station** & **CORS/(mm/Year)** & **InSAR/(mm/Year)** & **RMSE/mm** \\ \hline ANNI & 5.99 & 3.50 & 0.78 \\ BJIE & \(-10.10\) & \(-12.34\) & 0.63 \\ CHG0 & 0.58 & 7.62 & 6.20 \\ JINN & \(-31.76\) & \(-33.57\) & 0.41 \\ KMCH & 2.49 & 7.78 & 3.50 \\ QINL & \(-40.53\) & \(-44.36\) & 1.83 \\ TJIE & \(-16.28\) & \(-17.93\) & 0.34 \\ XIAH & \(-45.57\) & \(-49.10\) & 1.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of annual average deformation rates between InSAR and CORS data. Figure 10: Vertical velocity field after interpolation. mm. It shows that SBAS-InSAR method is suitable for monitoring surface subsidence and has certain reliability. \[RMSE=\sqrt{\frac{1}{m}\sum_{i=1}^{m}(\Delta H_{i}-\Delta h_{i})^{2}} \tag{7}\]  
In the formula, \(\Delta h_{i}\) is the settlement value of CORS of data point \(i\). \(\Delta H_{i}\) is the settlement value of the \(i\) point corresponding to the CORS position on the SAR image. m is the number of SAR data points corresponding to CORS points. Generally, stable sites are selected for the construction of CORS station. In order to more accurately analyze the cumulative deformation of InSAR time series.