## 3 Method
### SBAS-InSAR Technique  
The basic principle of SBAS-InSAR is as follows. First, based on N + 1 registered SAR images, M differential interferograms are generated by setting appropriate combinations of the temporal and spatial baseline threshold [28; 29; 30; 31; 32]. Then, phase unwrapping is performed to obtain absolute phase values. For the differential interferogram(i) generated from two SAR images acquired at different times, \(t_{A}\) and \(t_{B}\), the interferometric phase at any point can be expressed as  
\[\triangle\phi_{i}=\phi_{t_{B}}-\phi_{t_{A}}\approx-\frac{4\pi}{\lambda}(d_{t_{ B}}-d_{t_{A}})+\triangle\phi_{i}^{topo}+\triangle\phi_{i}^{attn}+ \triangle\phi_{i}^{noise} \tag{1}\]  
In the formula, \(i\in\left(1,\ldots,M\right),\text{ and }d_{t_{B}}\) and \(d_{t_{A}}\) are the radar line-of-sight cumulative surface deformations at the two acquisition times, respectively. After removing the topographic phase (\(\triangle\phi_{i}^{topo}\)), atmospheric delay phase (\(\triangle\phi_{i}^{attn}\)), and noise phase from the differential interferogram (\(\triangle\phi_{i}^{noise}\)), only the surface deformation phase remains in the equation. To ensure the obtained time series of surface deformations has physical meaning, the deformation phase is typically rewritten as the product of the average deformation rate between the two acquisition times and the time interval. Based on M unwrapped differential interferograms, this can be further expressed in matrix form:  
\[A\cdot\
u+\varepsilon=\triangle\phi \tag{2}\]  
In the formula, \(A\) represents a coefficient matrix of dimension M \(\times\) N; \(\varepsilon\) denotes the error term. When all interferograms belong to the same subset, the least squares method can be used to solve Formula (2), thereby obtaining the surface deformation rate. On this basis, numerical integration of the solved deformation rate over various time periods can yield the time series deformation.  
Figure 4: Research flow chart. Based on the collected fundamental data of the study area, a comprehensive landslide hazard identification method and interpretation marker were established. Initial potential landslide sites were identified using integrated techniques, verified via Google Earth, and subsequently analyzed through typical area analysis and spatial analysis.  
When interferograms are located in different subsets, the coefficient matrix \(A\) becomes rank-deficient. In such cases, the Singular Value Decomposition (SVD) method is employed to compute the generalized inverse of \(A\), enabling the estimation of the minimum-norm solution for surface deformation rates.  
SVD is preferred over QR factorization because it provides a full spectral decomposition \(A=\mathbf{U}\cdot\sum\mathbf{V}^{\mathrm{T}}\), where the diagonal matrix \(\sum\) contains singular values that reflect the intrinsic dimensional structure and allow identification of rank deficiencies. This makes SVD particularly effective for stabilizing solutions in ill-posed or underdetermined systems.  
In contrast, QR factorization decomposes \(A\) into an orthogonal and upper-triangular matrix (\(A=\mathbf{Q}\cdot\mathbf{R}\)), which does not reveal singular value distribution and is therefore less suited for analyzing and compensating for rank deficiency in SBAS-InSAR time series inversion.  
The SBAS-InSAR technique has two unique advantages in landslide deformation monitoring: (1) it generates redundant differential interferograms, which can effectively eliminate the influence of errors such as atmospheric delay effects and gross errors and (2) it can increase the temporal sampling rate of deformation time series, providing high spatial density monitoring results of landslide deformation. However, it also has the following shortcomings: a large number of redundant differential interferograms can increase the computational burden and the precision of the interferometric phase in low-coherence areas is relatively low [32; 33].