## 2 Materials and Methods
### StaMPS  
StaMPS, which was developed by considering previous PSI techniques, has been frequently used in the analysis of crustal movements [33; 47]. This method uses the spatial correlation of the interferometric phase to detect pixels with low phase changes in all terrain structures, with or without prominent objects such as buildings and bridges [48; 49]. The process consists of three main steps: interferogram generation, PS selection, and atmospheric filtration. First, appropriate sub-swath and bursts are selected in the SAR dataset, and precise orbit files are applied to them. Then, the master image is selected considering the time interval, vertical baseline, and least atmospheric effect, and all dependent images are recorded using the master image with the help of the S-1 Back Geocoding operator. After the coregistration process, interferograms are produced and prepared for StaMPS analysis \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sensor** & **Sentinel-1** & **Sentinel-1** \\ \hline Band & C & C \\ Wavelength & \textasci{}5.6 cm & \textasci{}5.6 cm \\ Track & 152 & 72 \\ Acquisition mode & Descending & Ascending \\ Imaging mode & IW & IW \\ Polarization & VV & VV \\ Time span & 4 May 2018–22 October 2022 & 10 May 2018–28 October 2022 \\ Number of images & 74 & 76 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Overview of Sentinel-1 dataset used in this study. by removing the topographic phase component. The entire processing block has been performed using SNAP and the freely available snap2 stamps scripts developed by [50]. The next steps of the processing block are performed in the StaMPS software, and in the first step, PS candidates are selected based on the amplitude distribution index. The amplitude distribution index is defined as the ratio of the standard deviation of each pixel to the average amplitude value and is calculated using Equation (1) [33; 51]:  
\[D_{A}=\frac{\sigma_{A}}{\mu_{A}} \tag{1}\]  
where \(D_{A}\) defines the amplitude dispersion value, and \(\sigma_{A}\) and \(\mu_{A}\) define the standard deviation and mean of the amplitude values [33]. The threshold value used is typically between 0.4 and 0.42 [52]. After determining the candidate pixels according to the amplitude distribution, the phase noise is estimated and removed for each candidate pixel using phase analysis. The residual phase of the \(x\)th pixel and the \(i\)th interferogram is given by Equation (2) [33]:  
\[\psi_{x,i}=W\{\phi_{D,x,i}+\phi_{A,x,i}+\Delta\phi_{S,x,i}+\Delta\phi_{\theta,x,i}+\phi_{N,x,i}\} \tag{2}\]  
where \(W\{\cdot\}\) defines the wrapping operator. Then, \(\phi_{D,x,i}\), \(\phi_{A,x,i}\), \(\Delta\phi_{S,x,i}\), \(\Delta\phi_{\theta,x,i}\), \(\phi_{N,x,i}\) represent the general terms for phase change due to movement of the pixel in the satellite LOS direction, phase change due to atmospheric delay between satellite passes, residual phase change due to satellite orbital error, phase change due to viewpoint, and phase noise, respectively [33; 52]. Then, candidate PS points are filtered according to the noise features estimated and extracted in the previous step so that PS points in the time series are determined based on the amplitude and phase analysis for each pixel in each interferogram. After filtering the PS points, the wrapped phase is corrected for spatially uncorrelated look angle (SCLA) error, and then the phase unwrapping step is performed. In the last step, SCLA errors mostly caused by digital elevation model (DEM) errors are predicted and removed, after this step atmospheric filtering is performed, and the LOS direction velocities for the region of interest are obtained. In this study, a total of 150 Sentinel-1A SAR images from the descending and ascending acquisition geometries acquired between May 2018 and October 2022 were obtained from ESA and used to detect the surface deformations caused by the Tendurek volcano. The master image selection from the SAR dataset was performed by considering temporal (<1000 days) and vertical baselines (<200 m) (Figure 2).