## 3 Data and Methods
### Methods
#### 3.2.2 Multidimensional Small Baseline Subset (MSBAS) Technique  
The MSBAS technique is an extension of the SBAS technique, which can simultaneously process both ascending and descending D-InSAR interferograms and produce 2-D deformation time series  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Satellite**} & \multirow{2}{*}{\begin{tabular}{c} **Orbit** \\ **Direction** \\ \end{tabular} } & \multirow{2}{*}{**Path/Track**} & \multirow{2}{*}{**Frame**} & \multicolumn{2}{c}{**Scene**} & \multicolumn{2}{c}{**Time**} & \multirow{2}{*}{\
\begin{tabular}{c} **Incidence** \\ **Angle** \\ \end{tabular} } \\  & & & & & & \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Sentinel-1A/B \\ (C-Band) \\ \end{tabular} } & \multirow{2}{*}{Ascending} & 98 & 118 & 56 & 2017/04–2019/03 & 33.75 \\  & & 69 & 118 & 66 & 2017/03–2019/05 & 33.73 \\ \cline{1-1} \cline{2-6}  & \multirow{4}{*}{Descending} & 3 & 470 & 50 & 2017/04–2019/03 & 34.08 \\ \cline{1-1}  & & 76 & 468 & 33 & 2016/10–2019/02 & 33.91 \\ \cline{1-1}  & & 76 & 472 & 54 & 2016/10–2017/04 & 33.95 \\ \cline{1-1} \cline{2-6} \cline{2-6} RADARSAT-2 (C-Band) & \multirow{2}{*}{Descending} & / & / & 12 & 2012/04–2016/06 & 26.23 \\ \cline{1-1} \cline{2-6} \cline{2-6} \cline{1-1} \cline{with dense temporal sampling and low noise, once SAR datasets cover the same region and have an overlap in the time domain [34; 35; 36; 37]. After removing topographic phase from every interferogram and unwrapping the phase, the MSBAS method is employed to estimate the vertical and the east-west deformation time series. As space-borne SAR satellites operate in a near-polar sun-synchronous orbit, the deformation in the north-south direction can be hardly retrieved. Therefore, the multidimensional time series model can be expressed in the following equation [34].  
\[\left(\begin{array}{c}-\frac{4\pi}{\lambda}\text{A}cosasin\theta\ \frac{4\pi}{ \lambda}\text{A}cos\theta\\ \beta I\end{array}\right)\left(\begin{array}{c}V_{E}\\ V_{U}\end{array}\right)=\left(\begin{array}{c}\Phi\\ 0\end{array}\right) \tag{1}\]  
where \(\lambda\), \(\alpha\) and \(\theta\) are the radar wavelength, the azimuth angle, and the incidence angle, respectively, A is a matrix constructed from the time interval between consecutive SAR acquisitions, \(\beta\) is a regularization parameter, which can be determined by using the L-curve method, and I is an identity matrix. \(V_{E}\) and \(V_{U}\) represent the east-west and vertical components (unit: m/a) of the ground deformation rate vector during each time interval, \(\Phi\) is the unwrapped interferometric phase (unit: radian) from both ascending and descending tracks. The unknown parameters \(V_{E}\) and \(V_{U}\) are estimated by solving the design matrix of Equation (1) via singular value decomposition (SVD) [20].  
Finally, the 2-D cumulative deformation time series at the \(i^{th}\) acquisition is reconstructed from the deformation rates in the following manner:  
\[d_{E}^{i}=\sum\
olimits_{i=1}^{n}V_{E}^{i}\Delta t_{i},\ d_{U}^{i}=\sum \
olimits_{i=1}^{n}V_{U}^{i}\Delta t_{i} \tag{2}\]  
where \(n=1,2,3\cdots,2(\sum_{k=1}^{K}N_{k}-1)\ d_{E}^{i}\) and \(d_{U}^{i}\) are the cumulative horizontal east-west and vertical deformations, respectively, \(N_{k}\) is the number of SAR acquisition dates from \(k^{th}\) SAR datasets, \(K\) is the number of different sensors, here \(K=2\).