## 3 Datasets and Methodology
### Methodology
#### 3.2.3 STL Model  
The model employs the Locally Estimated Scatterplot Smoothing (LOESS) approach to decompose complex time-series data into three components: trend, seasonal, and residual [26]. The decomposition is expressed as follows:  
\[Y_{t}^{k}=S_{t}^{k}+T_{t}^{k}+R_{t}^{k} \tag{9}\]  
where \(Y_{t}^{k}\) represents the original time-series data; \(S_{t}^{k}\) denotes the combined seasonal-trend component; \(T_{t}^{k}\) is the trend component; and \(R_{t}^{k}\) corresponds to the residual component. The model includes two iterative processes: an inner loop and an outer loop [27]. In the inner  
Figure 2: SBAS-InSAR flowchart.  
loop, the seasonal and trend components are updated sequentially; the outer loop adjusts robust weights for the next iteration [27].  
Assuming \(S_{t}^{k}\) and \(T_{t}^{k}\) represent the seasonal and trend components obtained after the \(kth\) iteration, the computation process for the \((k+1)\)th inner loop is as follows:  
(1) Detrending: Subtract the estimated trend from the original data to obtain the detrended series [26]: \(Y_{t}^{k}-T_{t}^{k}\).  
(2) Seasonal Smoothing: Divide the detrended series by the seasonal period P and apply LOESS smoothing to each subsequence. Extend the results to create a temporary seasonal series [28]:  
\[C_{t}^{(k+1)}=LOESS(Y_{t}^{k},d_{s},P_{s}) \tag{10}\]  
In the equation, \(d_{s}\) denotes the smoothing bandwidth for the seasonal component, and \(p_{s}\) represents the degree of the local polynomial used in the LOESS fitting.  
(3) Low pass filtering: The sequence \(C_{t}^{(k+1)}\) is subjected to two successive moving average (MA) filters of length \(n\), followed by an additional MA filter of length 3. This process extracts the low-frequency component, resulting in the output sequence \(L_{t}^{(k+1)}\)[29]:  
\[L_{t}^{(k+1)}=MA_{3}(\text{MA}_{n}(\text{MA}_{n}(C_{t}^{(k+1)}))) \tag{11}\]  
(4) Seasonal component extraction: Subtract the low-frequency sequence \(L_{t}^{(k+1)}\) from the temporary seasonal sequence \(C_{t}^{(k+1)}\), resulting in the updated seasonal component \(S_{t}^{(k+1)}\)[29]:  
\[S_{t}^{(k+1)}=C_{t}^{(k+1)}-L_{t}^{(k+1)} \tag{12}\]  
(5) Trend smoothing: Locally weighted regression (LOESS) is applied directly to the deseasonalized series to obtain the updated trend component \(T_{t}^{(k+1)}\)[29].  
The residual component is then calculated as  
\[R_{t}^{(k+1)}=Y_{t}-T_{t}^{(k+1)}-S_{t}^{(k+1)} \tag{13}\]  
where \(R_{t}^{(k+1)}\) denotes the residual component, \(Y_{t}^{k}\) represents the original time-series data, and \(T_{t}^{(k+1)}\) and \(S_{t}^{(k+1)}\) correspond to the trend and seasonal components estimated by the model, respectively [29].  
\[\rho_{t}=B(|R_{t}|/h) \tag{14}\]  
In the equation, \(B\) denotes:  
\[B=\left\{\begin{array}{l}{\left(1-u^{2}\right)^{2}},0\leq u\leq 1\\ 0,u\geq 1\end{array}\right. \tag{15}\]  
where \(\rho_{t}\) is the robustness weight at time t, and \(B\) is the bisquare weighting function used to adjust the weights based on the magnitude of the residuals. \(u=|R_{t}|/h\) represents the normalized residual, where \(h\) is a scaling parameter for normalization, typically determined based on a robust estimate of the residual distribution.