## 2 Methods
### Principles Involved in the Method  
#### 2.2.1 Phase Gradient Stacking and Fusion  
The phase gradient can be obtained without phase unwrapping, allowing us to acquire the true gradient value, as demonstrated by [PERSON] [31], who used the phase gradient to calculate the deformation gradient. Moreover, since the phase gradients of many interferograms do not influence each other, they can compensate for the incoherence present in some regions caused by temporal and spatial baselines. By stacking the phase gradients, we consistently obtain effective results for the entire region, enabling us to observe regions in low coherence. Here, the central difference method is used to calculate the phase gradient. The center pixel has eight neighboring pixels, so using the central difference method only needs to calculate the phase gradient in four directions (phase gradients in opposite directions are negative to each other). Taking the center pixel (i,j) as an example, the phase gradients in the four directions are calculated as follows:  
\[ \begin{cases}\Delta\varphi_{0}(i,j)=\varphi_{i,j+1}-\varphi_{i,j-1}\\ \Delta\varphi_{45}(i,j)=\varphi_{i-1j+1}-\varphi_{i+1j-1}\\ \Delta\varphi_{90}(i,j)=\varphi_{i-1j}-\varphi_{i+1j}\\ \Delta\varphi_{135}(i,j)=\varphi_{i-1j,-1}-\varphi_{i+1j+1}\end{cases}  \tag{1}\]  
\(\Delta\varphi_{\text{k}}\) represents the phase gradient in a particular direction of the central pixel. We define the range phase gradient as \(\Delta\varphi_{0}\), the upper right corner phase gradient as \(\Delta\varphi_{45}\), the orientation direction as \(\Delta\varphi_{90}\), and the upper left corner phase gradient as \(\Delta\varphi_{135}\). Since the wrapped differential interferogram has values in the range \((-\pi,\pi]\), the phase gradient calculation results lie within the range \((-2\pi,\,2\pi]\). However, results in the range \((-2\pi,\,-\pi]\) and \((\pi,2\pi]\) occur due to phase jumps. To obtain the true gradient value within \((-\pi,\pi]\), we wrapped the phase gradient as follows:  
\[\Delta\varphi^{\prime}= \begin{cases}\Delta\varphi+2\pi,&\Delta\varphi<-\pi\\ \Delta\varphi,&-\pi\leq\Delta\varphi\leq\pi\\ \Delta\varphi-2\pi,&\Delta\varphi>\pi\end{cases}  \tag{2}\]  
\(\Delta\varphi^{\prime}\) is the phase gradient of the difference interferogram. At each pixel point (i,j), phase gradients in four directions can be obtained: \(\Delta\varphi 0\) (i,j), \(\Delta\varphi 45\) (i,j), \(\Delta\varphi 90\) (i,j), and \(\Delta\varphi 135\) (i,j). Here, the phase gradient is calculated using differential interferograms in the SAR coordinate system, with the \(0^{\circ}\) direction indicating the ranging direction and the \(90^{\circ}\) direction indicating the azimuthal direction. In the final phase gradient result, there are inevitable random phase gradients caused by random noise points and local micro gradients caused by the atmosphere, etc. Here, we adopt two strategies to solve this problem. First, we mask the low coherence region based on coherence, because the low coherence region is often noisy so it is difficult to obtain effective information; secondly, we stack and sum the phase gradients of interferograms constructed by short baseline sets, which can weaken some atmospheric effects on large spatial scales. However, due to the differences in temporal and spatial baselines, the gradient results obtained by the differential interferogram of different temporal baselines are also different. Therefore, the method for different temporal baselines is used here, and the temporal baselines are used as a weighting factor to stack the phase gradients of different temporal baselines.