In our study, SBAS-InSAR and PS-InSAR algorithms are applied to monitor the landslide in the Kunming transmission line corridor and the technical route is represented in Fig. 2. First, POD and DEM data were applied to preprocess SAR images. Next, the time-series deformation and deformation rates are obtained using SBAS-InSAR and PS-InSAR. Combined with the relevant information of the research region (such as precipitation, geology, etc.), we made a sequential deformation analysis of the landslide area. Finally, the main influencing factors leading to the landslide were obtained.

## 3.1. Basic principles of SBAS-InSAR

First of all, by setting certain temporal and spatial baseline thresholds, image pairs with strong coherence are obtained. Then, differential interference is performed on the interference pairs with successful pairing. Next, the interference pairs with low coherence or poor interference results are removed and the unwrapping results of the remaining interference pairs are subject to orbital refining and re-flattening. Then, the residual phase of the previous results is separated, and a small baseline linear model is applied to calculating the deformation and elevation of all image pairs. Finally, the deformation results are projected into a geographic coordinate system (Berardino et al., 2002; Hu et al., 2014).

Supposing a set of *N* radar images covering the study region, *M* interferograms are generated by setting a baseline threshold. *M* satisfies the inequality which is shown as below (Lundgren et al., 2001; Dong et al., 2014):

$$\frac{N}{2}\le M\le \frac{N\left(N-1\right)}{2}$$

1

Assuming the *j**th* interferogram is generated from two SAR images obtained at times *t**A* and *t**B* (*t**B* > *t**A*) with the flat-earth and topographic phases removed, the interferometric phase can be defined as (Costantini, Rosen, 1999):

$${\Delta }{\phi }_{j}\left(x,y\right)={\phi }\left({t}_{B},x,y\right)-\phi \left({t}_{A},x,y\right)$$

$$\approx \frac{4\pi }{\lambda }[d\left({t}_{B},x,y\right)-d({t}_{A},x,y\left)\right]$$

2

Where \(\phi \left({t}_{B},x,y\right)\) and \(\phi ({t}_{A},x,y)\) represent the phases of SAR images at *t**B* and *t**A* respectively. *λ* represents the central wavelength. \(d\left({t}_{B},x,y\right)\) and \(d({t}_{A},x,y)\) are the cumulative deformation in the LOS direction at times *t**B* and *t**A* relative to time *t**0*, respectively. The vector phase of interferograms is indicated in the form of a matrix as follows:

$$G\phi =\varDelta \phi$$

3

Where *G* denotes an *M×N* coefficient matrix. \({\phi }^{T}=[\phi \left({t}_{1}\right),\dots , \phi ({t}_{N}\left)\right]\) represents the vector of unknown phases relevant to high-coherence pixels. \({\Delta }{\phi }^{T}=[{\Delta }\phi \left({t}_{1}\right), \dots ,\varDelta \phi ({t}_{M}\left)\right]\) denotes the vector of unwrapped phases related to differential interferograms.

By transforming Eq. (3) into Eq. (4), the deformation rates of high-coherence pixels is calculated.

Where *S* is an *M×N* coefficient matrix. *V**T* is defined as:

$${V}^{T}=[{V}_{1}=\frac{{\phi }_{1}}{{t}_{1}-{t}_{0}},\dots ,{V}_{N}=\frac{{\phi }_{N}-{\phi }_{N-1}}{{t}_{N}-{t}_{N-1}}]$$

5

The estimated deformation rate can be obtained by the Least Square (LS) or Singular Value Decomposition (SVD) algorithm (Casu et al., 2006).

## 3.2. PS theory

The amplitude and amplitude dispersion index threshold are utilized to screen the PS points ( Ferretti et al., 2000). In this method, the pixels with a higher amplitude are chosen based on the amplitude domain dispersion index and set as the PS candidate points. Next, through the high coherence characteristics of PS stable scattering, combined with the image of amplitude dispersion index and coherence coefficient index, more accurate PS points can be obtained. (Ferretti et al., 2000). The phase of a PS point in the *i**th* differential interferogram and *x**th* pixel is indicated as (Fornaro et al., 2008):

$$\varDelta {\phi }_{int,x,i}=W\{{\phi }_{def,x,i}+{\phi }_{topo,x,i}+{\phi }_{atm,x,i}+{\phi }_{noise,x,i}\}$$

6

Where \({\phi }_{def,x,i}\) is the deformation phase generated in the LOS direction; \({\phi }_{topo,x,i}\) indicates the residual phase after DEM is introduced in the differential interference step. \({\phi }_{atm,x,i}\) and \({\phi }_{noise,x,i}\) represent the atmospheric delay phase and noise phase, respectively. According to Eq. (6), the SAR images are filtered adaptively to eliminate the phases that affect the decorrelation. The phase stability of the remaining pixels can be tested by using Eq. (7).

$${\gamma }_{x}=\frac{1}{N}\left|\sum _{i=1}^{N}\text{e}\text{x}\text{p}\left\{j\right({\phi }_{int, x,i}-{\phi }_{s,x,i}-\varDelta {\phi }_{h,x,i}\left)\right\}\right|$$

7

Where *j* denotes the complex unit; \({\phi }_{int, x,i}\) is the unwrapped observation phase; \({\phi }_{s,x,i}\) is the elevation-related component; \(\varDelta {\phi }_{h,x,i}\) represents the terrain-related component and *N* indicates the number of interferograms. With this standard, the candidate PS points are selected first and then unwrapped according to the coherence coefficient of the coherence map, to extract the stable PS points (Sousa et al., 2010).