## 2 Materials and Methods
### Research Methodology  
The PS-InSAR technique (Figure 4) selects stable points with high reflectivity in the image as PS (Persistent Scatterer) points after long time series screening. The phase information that affects the coherence of SAR images, such as terrain, atmosphere, and flatlands, is separated based on the phase information of the selected points, producing phase information that reflects significant terrain changes. The selection of permanent scatterer points uses the ratio of the standard deviation of amplitude to the mean value, the magnitude of this value determines the stability of PS points, and the points with high amplitude deviation values are experimentally selected as valid data. The value of Amplitude deviation value for identifying the selected PS points is calculated use Equation (1). \[D_{\varphi(\text{i},j)}=\frac{std[\varphi(i,j)]}{mean[\varphi(i,j)]}\leq Th, \tag{1}\]  
where \(D_{\varphi(\text{i},j)}\) is the ratio of the standard deviation of the amplitude and the mean value of each pixel \((i,j)\) in the image; \(Th\) represents the set threshold value. If \(D_{\varphi(\text{i},j)}\leq Th\), the pixel meets the coherence requirement, the pixel is selected as the permanent scatterer point. Figure 3: (**a**) Canal second-order leveling points location map; (**b**) Model chart of high fill; (**c**) Live aerial image. 1�  
The PS point phase can be expressed by Equation (2) when image alignment and interference operations are performed on master and slave images during SAR image data processing, which contains the residual elevation phase, topographic phase, noise phase, etc. \[\varphi_{\text{int}}=\varphi_{flat}+\varphi_{def}+\varphi_{topo}+\varphi_{atm}+ \varphi_{noise}, \tag{2}\]  
where \(\varphi_{flat}\) is the flat earth phase; \(\varphi_{def}\) is the surface deformation phase in the \(LOS\) (Line of Sight) direction; \(\varphi_{topo}\) is the introduced DEM phase difference; \(\varphi_{atm}\) is the atmospheric phase difference; \(\varphi_{noise}\) is the image noise phase difference. Among them, the flat earth phase, surface deformation phase, and residual terrain phase can be expressed by Equations (3)-(5), respectively. \[\varphi_{flat}=\frac{4\pi}{\lambda R\tan\theta}B_{\perp}\Delta R, \tag{3}\]  
\[\varphi_{def}=\frac{4\pi}{\lambda}T\Delta v, \tag{4}\]  
Figure 4: Flow chart of PS-InSAR. \[\varphi_{topo}=\frac{4\pi}{\lambda R\sin\theta}B_{\perp}\Delta h, \tag{5}\]  
where \(\lambda\), \(\theta\), and \(R\) are the radar wavelength, incidence angle, and slope distance, respectively; \(B_{\perp}\) is the spatial baseline; \(T\) is the time baseline; \(\Delta v\) is the \(LOS\) directional deformation rate increments; \(\Delta h\) is the elevation correction increments. The interferometric phase model established above plays a major role in the linear deformation rate and elevation error, and there is spatial correlation between adjacent PS points, and the neighborhood difference model established according to two adjacent PS points is shown as Equation (6). \[\Delta\varphi_{diff}=\frac{4\pi}{\lambda}T\Delta v+\frac{4\pi}{\lambda R\sin \theta}B_{\perp}\Delta h+\Delta w, \tag{6}\]  
where \(\Delta v\) is the deformation increment; \(\Delta h\) is the phase elevation error increment; \(\Delta w\) is the residual phase. The residual phase includes atmospheric, noise, and nonlinear phases. The atmospheric phase and noise phase of the selected PS points in the same location and the same space tend to be close to zero, which can be neglected in the process of interference processing. If \(\Delta w\) is neglected, the distribution of PS points can be connected into a mesh according to the distribution of PS points, and the deformation increment and elevation increment can be solved by Equation (6) to obtain the deformation rate field of the region of interest.