## 3 Methodology of Processing
### SBAS-InSAR Algorithm
Matrix A is an approximate correlation matrix. If all the data belong to a baseline set, then \(L=1\), \(M\geq N\), where A is an N-order matrix. When \(M=N\), the system of equations had a unique solution. When \(M>N\), the system of equations is overdetermined. The least squares method could be used to solve the estimated value of \(\varphi(x,r)\):  
\[\varphi(x,r)=\Big{(}A^{T}A\Big{)}^{-1}A^{T}\delta\varphi(x,r) \tag{4}\]  
Usually, the data set was scattered in several subsets, \(L>1\), where \(A^{T}A\) was a singular matrix, and the rank of \(A\) is \(N-L+1\). The equations have an infinite number of solutions. In order to obtain a unique solution, SBAS-InSAR uses a Singular Value Decomposition (SVD) method to jointly solve multiple baseline sets, and find the least squares solution in the least norm sense to obtain the cumulative deformation result. The SARscape 5.2.1(Sarmap Company, Caslano, Switzerland) plugin was used, which was based on ENVI 5.3 software (Exelis Visual Information Solutions Company, Broomfield, America), and the detailed workflow of InSAR processing was given in the following parts:  
The first step was to graphically output the generated interferograms. When the SAR images are entered alongside the spatial and temporal baseline threshold, the maximum logarithm that can be obtained was \((N\times(N-1))/2\), and the tool would automatically select the best combination for pairing. In this study, a 50% spatial baseline of the critical baseline and time baseline was set to 365 days. These pairs were interfering and then used for SBAS inversion (Figure 2). The program automatically selected a super master image, which was used as the reference image throughout the process, and all the pairs were registered to the super master image [17]. The second step was to interfere with all the paired interference image pairs, including coherence generation, de-leveling, filtering, and phase unwrapping. All the data pairs were registered to the super-master image. What is important in this step was to obtain a satisfactory interferogram by adjusting the parameters and coefficients. Thus, the interferogram showed part of the low coherence area, and after the first screening, we chose to increase the intensity of the filter strength. The Goldstein filtering method is a commonly filtering method. In this study, the processing tools of the interference processing module were used to process some representative image pairs to debug the satisfactory processing parameters. After the second screening, the phase unwrapped graph was checked to determine if the coherence threshold needs to be adjusted until a satisfactory result was obtained. Finally, the unwrapping method this paper used was Delaunay Minimum Cost Flow (MCF), which was a good way to connect a set of high-coherence pixels and other isolated high-coherence regions, thus this method was recommended to minimize the impact of phase transitions. The third step was to remove the constant phase and phase transitions that still exist in the unwrapped phase diagram, resulting in a re-leveling result. In SARscape, there were two optimization methods on the flattening parameter panel: orbit optimization and residual phase optimization. This paper used an orbital optimization method that utilized an orbital polynomial model to correct the orbital parameters of the secondary image to eliminate the ramp phase. The next step was to estimate the deformation rate and residual topography, and reduce the atmospheric phase as much as possible by filtering. Atmospheric filtering played a role in the smoothing of the time series. The removal of the atmosphere was achieved by low-pass filtering and high-pass filtering. Finally, the deformation results in the time series were obtained. The software not only calculated the deformation rate of the Line-Of-Sight (LOS) direction, but also the vertical direction. This study used the deformation results in the vertical direction for analysis [17]. Finally, the deformation results in the time series were obtained.