## 3 Data and Methodology
### Methodology  
#### 3.2.1 Time Series InSAR Analysis with SBAS  
SBAS-InSAR is a time-series InSAR technology based on D-InSAR that overcomes the problems of spatiotemporal decorrelation and atmospheric interference [49]. The SBAS-InSAR technology was proposed by [PERSON] et al. in 2002 [27]. It is a time-series method based on multi-master images used to obtain the deformation rate of the study area using the SVD method of a matrix.  
Assuming that \(N+1\) SAR images were acquired for the same region at regular times (\(t_{0},\dots,t_{N}\)), M differential interferograms can be generated. The inequality of \(M\) is defined as follows:  
\[\frac{N+1}{2}\leq M\leq\frac{N(N+1)}{2} \tag{1}\]  
For the differential interferogram j generated from the images acquired at \(t_{A}\) and \(t_{B}\) (\(t_{A}<t_{B}\)), the phase of any point \((x,r)\) is as follows:  
\[\delta\phi_{j}(x,r)=\phi(t_{B},x,r)-\phi(t_{A},x,r)\approx\triangle\phi_{disp }+\triangle\phi_{topo}+\triangle\phi_{orb}+\triangle\phi_{atm}+\triangle\phi_{ noise} \tag{2}\]  
where \(\phi(t_{B},x,r)\) and \(\phi(t_{A},x,r)\) are the phase of two images at the point \((x,r)\); \(\triangle\phi_{disp}\) is the phase formed by the cumulative deformation of the line of sight (LOS) at \(t_{B}\) and \(t_{A}\) relative to \(t_{0}\); and the phase errors caused by topography, orbit, atmosphere, and noise are represented by \(\triangle\phi_{topo},\triangle\phi_{orb},\triangle\phi_{atm},\triangle\phi_{ noise}\)[50; 51].  
The Environment for Visualizing Images (ENVI) software and its subordinate module SARscape were employed to process SAR images from the research area. Six steps were used: generation of the connection graph, interferometric processing, refinement and reflattening, first inversion, second inversion, and geocoding. The processing flowchart is shown in Figure 3.  
Figure 3: Flowchart of SBAS-InSAR processing. Note: GCP—ground control points.  
According to the geological conditions of the study area, the spatial baseline and temporal baseline were set at 2% and 180 d, respectively. After three-dimensional (3D) unwrapping, 109 interferometric pairs were generated with a maximum spatial baseline of 116.3 m and a minimum of 59 m. As shown in Figure 4, the 14 February 2019 image (yellow point) was selected by the software as the super master image. Then, the Goldstein filter and 3D unwrapping method were used for interferometric processing, and the unwrapping threshold was set to 0.2. After that, 12 interferometric pairs with poor coherence were deleted, and 97 interferometric pairs were used in subsequent time-series analysis. In the non-deformation region, an appropriate amount of ground control points was uniformly selected for refinement and re-flattening, and the control points were screened to ensure that there were sufficient control points and deviation was within 2.5. In the first inversion, we selected the linear model to estimate the surface deformation rate and residual topography. Ground control points were introduced in the second inversion to eliminate atmospheric phase interference and obtain a more accurate time-series displacement. Finally, geocoding was performed to obtain the average deformation velocity and displacement of the study area in the direction of the radar LOS.