## 3 Methodology of Processing  
### SBAS-InSAR Algorithm  
InSAR combines synthetic aperture radar technology with interferometric technology. Synthetic Aperture Radar (SAR) is an active microwave remote sensing that is used to record the scattering intensity information and phase information of the ground object. The former reflects the surface properties (water content, roughness, feature type, et al. ), while the latter contains distance information between the sensor and the target. The basic principle of interference is the complex conjugate multiplication of SAR images in the same area to extract the topographic or deformation information of the target. The modes of radar interference include orbital interferometry, cross-track interferometry, and repeated orbital interferometry. This paper used repeated rail interference, and the interference phase expression is as follows:  
\[\varphi_{int}=\varphi_{flat}+\varphi_{topo}+\varphi_{def}+\varphi_{atmo}+\varphi_ {noise} \tag{1}\]  
In the equation, \(\varphi_{flat}\) represents flat phase; \(\varphi_{topo}\) represents the topographic phase, which can be used to recover topographic information; \(\varphi_{def}\) represents the phase caused by ground deformation between \(t_{A}\) (start time) and \(t_{B}\) (end time); \(\varphi_{atmo}\) represents the temporal atmospheric phase at different SAR acquisition \(t_{A}\) and \(t_{B}\); \(\varphi_{noise}\) represents the phase caused by observation noise (including the temporal decorrelation, orbital errors, and thermal noise). In this paper, SBAS-InSAR technology by [PERSON] [45] was applied to calculate the ground deformation of Sentinel-1 SAR images in the research area, which greatly optimized the problems of decoherence and atmospheric effects caused by the excessive spatial baseline of D-InSAR technology, thus increasing the frequency of time sampling. The SBAS-InSAR method used an interferogram generated by SAR pairs with a short temporal-spatial baseline to improve coherence and reduce phase noise by the multi-view processing of differential interferograms to extract high-coherence pixels. This method inherited the advantages of the conventional D-InSAR method and could obtain the evolution of long-term slow surface deformation, which improved the time resolution of deformation monitoring. Thus, this method was selected as the main method to calculate the ground deformation of Sentinel-1 SAR images in the research area. The essential principles of SBAS-InSAR technology were as follows:  
Suppose there are \(N+1\) repeated orbital SAR images in time series \(t_{0}\), \(t_{1}\),..., \(t_{n}\). By setting the time and space baseline thresholds, we can get \(L\) small baseline sets. Within each set, the baseline of the interference pair is small, while the base of the interference pair is large between each set. Therefore, there are a total of \(M\) differential interferograms, where \((N+1)/2\leq M\leq N\) (\(N+1\))/2. Suppose that the differential interference phase (\(t_{k}\), \(x\), \(r\)) at any time (\(t_{k}\)) and the initial time (\(t_{0}\)) on any pixel (\(x\),\(r\)) is unknown, and the differential interferograms \(\delta\varphi_{k}\) (\(x\),\(r\)) (\(k=1\),..., \(M\)) is the observation. For any differential interferogram, there is:  
\[\delta\varphi_{k}(x,r)=\varphi(t_{i},x,r)-\varphi\Big{(}t_{j},x,r\Big{)}=4,\ \lambda(d(t_{i},x,r)-d(t_{i},x,r)) \tag{2}\]  
where \(d(t_{i}x,r)\) and \(d(t_{j}x,r)\) are the cumulative deformation variables relative to the start time, respectively. There are \(M\) differential interferograms; therefore, M equations can be obtained according to Equation (2), and the equations are represented by a matrix:  
\[\delta\varphi(x,r)=A\varphi(x,r) \tag{3}\]  
where \(A\) is an \(M\times N\) matrix consisting of -1, 0, and 1 elements; for example, Formula (1) in the matrix corresponds to line k, the value of the first element is 1, while the value of the last element is \(-1\), and the other values are 0; \(\delta\varphi(x,r)\) and \(\varphi(x,r)\) are \(N\)-order vectors.