## 3 Methodology
### Interferogram and Phase Unwrapping  
First, we converted raw SAR data (ALOS, ALOS-2, Sentinel-1) to SLC format and used DEM data to register the slave image with the master image. Then we selected the optimal interferometric pair by calculating the temporal and spatial baselines of the primary and secondary images. After optimal interference pair selection, the next step is to generate interferograms. In the interferogram, each point has a phase value, which contains much important information. Let us assume point P in the master and slave image. Each SAR image contains phase and amplitude information. For point P, the phase can be modeled as:  
\[\phi(P)=\varphi\ +\frac{4\pi}{\lambda}\text{r}+\alpha+\text{n} \tag{1}\]  
where \(\varphi\) is the original phase controlled by target scatter attributes, such as roughness and moisture, \(\lambda\) is the wavelength of the SAR sensor, r is the distance between the sensor and the  
Figure 2: Flowchart of the processing approach.  
target, \(\alpha\) is the atmospheric phase, and n represents the noise phase. In the interferogram, for point P, the phase can be modeled as:  
\[\Delta\phi(P)=\Delta\varphi\ +\frac{4\pi}{\lambda}\Delta\pi+\Delta\alpha+\Delta\
u \tag{2}\]  
where \(\Delta\varphi\) is the phase difference generated by the change in the target's properties, \(\frac{4\pi}{\lambda}\Delta\pi\) is the distance difference between the two observations to point P, \(\Delta\alpha\) is the different atmospheric phase, and \(\Delta\
u\) is the noise phase.  
Through Equation (2), the interferogram can be generated from two registered SAR images. The range of the interferogram is \(-\pi\) to \(\pi\). After generating the interferogram, the next step is phase unwrapping. Phase unwrapping is the process of estimating the whole phase difference between a reference pixel and other pixels. The phase unwrapping algorithm calculates the phase difference between adjacent pixels and then integrates these phase differences, which is equivalent to calculating the number of color fringes starting from the reference pixel. For most unwrapping algorithms, minimizing the residual weighting function between the estimated unwrapping phase difference and the original phase difference is used. In this study, we used a minimum cost flow (MCF) unwrapping algorithm. The phase unwrapping algorithm target is to minimize Equation (3):  
\[\sum_{\mathrm{ij}}w^{\mathrm{(x)}}_{\mathrm{ij}}\Big{|}\Delta\phi^{\mathrm{(x) }}_{\mathrm{ij}}-\Delta\psi^{\mathrm{(x)}}_{\mathrm{ij}}\Big{|}+\sum_{ \mathrm{ij}}w^{\mathrm{(y)}}_{\mathrm{ij}}\Big{|}\Delta\phi^{\mathrm{(y)}}_ {\mathrm{ij}}-\Delta\psi^{\mathrm{(y)}}_{\mathrm{ij}}\Big{|} \tag{3}\]  
\(\Delta\psi^{\mathrm{(y)}}\) is the unwrapping phase difference in the y direction and \(\Delta\psi^{\mathrm{(x)}}\) is the wrapping phase difference in the x direction.  
We used ISCE software ([[https://github.com/isce-framework/isce2](https://github.com/isce-framework/isce2)]([https://github.com/isce-framework/isce2](https://github.com/isce-framework/isce2)), accessed on 20 March 2022) for this p_processing. To increase the signal-to-noise ratio, during processing, we set 14:4, 16:8 and 3:9 multilook in the azimuth and range direction for ALOS, ALOS-2 and Sentinel-1 interferograms, respectively. After the multilook processing, the spatial resolution (azimuth pixel resolution \(\times\) range pixel resolution) of ALOS, ALOS-2 and Sentinel-1 was 50 m \(\times\) 10 m, 5 m \(\times\) 35 m and 23 m \(\times\) 3 m, respectively. To accelerate the processing rate, we set 15 threads based on an Intel(R) Xeon(R) Gold 6129 CPU with 16 CPU cores for parallel processing.