## 3 Methodology  
### Permanent Scatterer Interferometry (PSI) Data Processing  
Since the D-InSAR technology is susceptible to atmospheric phase delays and incoherence [30; 31], [PERSON] presented a time-series InSAR technique based on permanent scatterer interferometry (PSI) and extended it to a nonlinear deformation mode [32; 33]. PSI is a technique for obtaining surface deformation information through long-time stable reflection points (i.e., PS points, such as artificial buildings, exposed rock, and sand) [34; 35; 36]. By unwrapping the PS network, the interference of the atmosphere on the deformation phase can be greatly reduced, and the residual atmosphere and noise phases can also be removed or weakened by space-time filtering, so we can retrieve high precision surface deformation. For the phase value of any pixel \((\mathrm{x},\mathrm{y})\) in a differential interferogram \((\mathrm{T_{i}})\), we assume that the deformation is made up of linear and nonlinear parts that are consistent in urban environments [37; 38]:  
\[ \begin{array}{ll}\Phi_{\mathrm{i}}(\mathrm{x},\mathrm{y},\mathrm{T_{i}})=&- \frac{4\pi}{\lambda\cdot\mathrm{R}\cdot\sin\theta}\mathrm{B_{i}^{\perp}}\cdot \varepsilon(\mathrm{x},\mathrm{y})-\frac{4\pi}{\lambda}\cdot\mathrm{T_{i}} \cdot\mathrm{v}(\mathrm{x},\mathrm{y})\\ &-\mathrm{a}\cdot\frac{4\pi}{\lambda}\cdot\sin(2\pi\cdot\mathrm{T_{i}})+\varphi _{\mathrm{i}}^{\mathrm{res}}(\mathrm{x},\mathrm{y},\mathrm{T_{i}})\end{array}  \tag{1}\]  
where  
\[\varphi_{\mathrm{i}}^{\mathrm{res}}(\mathrm{x},\mathrm{y},\mathrm{T_{i}})= \varphi_{\mathrm{i}}^{\mathrm{nl}}(\mathrm{x},\mathrm{y},\mathrm{T_{i}})+ \varphi_{\mathrm{i}}^{\mathrm{a}}(\mathrm{x},\mathrm{y},\mathrm{T_{i}})+ \varphi_{\mathrm{i}}^{\mathrm{n}}(\mathrm{x},\mathrm{y},\mathrm{T_{i}}) \tag{2}\]  
Here, \(\mathrm{B_{i}^{\perp}}\), \(\mathrm{T_{i}}\) are the spatial perpendicular baseline and time interval of the interference pair, respectively; \(\lambda,\ \mathrm{R},\ \theta\) represent wavelength, slant distance, and local incident angle of the target point, respectively; \(\mathrm{v}(\mathrm{x},\mathrm{y}),\ \varepsilon(\mathrm{x},\mathrm{y})\) are the linear deformation rate in line of sight and height error of pixel \((\mathrm{x},\mathrm{y})\), and a is the amplitude of seasonal deformation; and \(\varphi_{\mathrm{i}}^{\mathrm{res}}(\mathrm{x},\mathrm{y},\mathrm{T_{i}})\) is a complex of the residual deformation phase, the atmospheric delay phase, and the noise phase. After constructing the network of PSs according to the regulation, the phase increment value between each arc can be obtained by using the difference method, which can be expressed as follows:  
\[ \begin{array}{ll}\Delta\Phi_{\mathrm{i}}(\mathrm{x_{p}},\mathrm{y_{p}}; \mathrm{x_{q}},\mathrm{y_{q}},\mathrm{T_{i}})&=-\frac{4\pi}{\lambda\cdot \mathrm{R}\cdot\sin\overline{\theta}}\cdot\overline{\mathrm{B_{i}^{\perp}}} \cdot\Delta\varepsilon(\mathrm{x_{p}},\mathrm{y_{p}};\mathrm{x_{q}},\mathrm{y_ {q}})-\frac{4\pi}{\lambda}\cdot\mathrm{T_{i}}\cdot\Delta\mathrm{v}(\mathrm{x_{ p}},\mathrm{y_{p}};\mathrm{x_{q}},\mathrm{y_{q}})\\ &-\Delta\mathrm{a}(\mathrm{x_{p}},\mathrm{y_{p}};\mathrm{x_{q}},\mathrm{y_{q}}) \cdot\frac{4\pi}{\lambda}\cdot\sin(2\pi\cdot\mathrm{T_{i}})\\ &+\Delta\varphi_{\mathrm{i}}^{\mathrm{res}}(\mathrm{x_{p}},\mathrm{y_{p}}; \mathrm{x_{q}},\mathrm{y_{q}},\mathrm{T_{i}})\end{array}  \tag{3}\]  
where \(\overline{\mathrm{B_{i}^{\perp}}},\ \overline{\mathrm{R}},\ \overline{\theta}\) are the average values of the corresponding parameters of the adjacent PS points \(\mathrm{p}\) and \(\mathrm{q},\ \Delta\varepsilon,\ \Delta\mathrm{v},\ \Delta\mathrm{a}\) are the height error increment, the linear deformation rate increment, and the seasonal deformation amplitude increment, respectively; \(\Delta\varphi_{\mathrm{i}}^{\mathrm{res}}\) shows the increment of the corresponding residual phase.