## 2 Materials and Methods
### InSAR Data and Processing  
The interferometric phase difference contains unwanted components introduced by factors such as topographic inaccuracies, atmospheric disturbances, and orbital errors. These components can obscure the accurate displacement signal, necessitating careful corrections. The total interferometric phase can be expressed in the linear approach [21]:  
\[\Delta\varnothing=\Delta\varnothing_{disp}+\Delta\varnothing_{topo}+\Delta \varnothing_{artifacts} \tag{1}\]  
where \(\Delta\varnothing_{disp}\) represents the phase component related to displacement in the Line of Sight (LOS) direction, which reflects ground subsidence. \(\Delta\varnothing_{topo}\) accounts for the phase contribution resulting from topography. \(\Delta\varnothing_{artifacts}\) encompasses errors and inaccuracies. Whilst the linear approach is commonly applied, it suffers from limitations in handling temporal inhomogeneity. This results in noisy estimations in time-series analysis that cannot be sufficiently reduced through standard techniques like self-similar multi-looking. A non-linear approach was adopted in this study to address this, enabling a more accurate extraction of temporal subsidence trends. The total interferometric phase in this approach can be expressed as follows [30]:  
\[\Gamma_{m,n}=(\gamma^{0}-\gamma^{\infty})\text{exp}\exp(-\frac{|\Delta t|}{ \tau}+\gamma^{\infty})\text{exp}(j\upsilon\frac{4\pi}{365\lambda}) \tag{2}\]  
where \(t\) is the temporal baseline between the two acquisitions, \(\lambda\) is the wavelength, \(\gamma^{0}\) and \(\gamma^{\infty}\) are the short-term decaying and long-term persistent coherence, \(\tau\) is the temporal decorrelation constant, and \(\upsilon\) is the ground velocity. Persistent Scatterer Interferometry (PSI), a type of interferometric SAR analysis, identifies stable points called permanent scatterers and analyses their behavior over time using a series of interferograms [31]. These interferograms are referenced to a single master SAR image, allowing for the precise tracking of surface subsidence at specific points. Unlike traditional methods, PSI focuses on individual scatterers instead of averaging over larger resolution cells, providing accurate measurements of changes at targeted locations [32]. The SAR images used for this analysis were acquired from Sentinel-1 satellites of the European Space Agency [33]. More theoretical background about the InSAR technique and PSI can be found in the literature [31; 34]. The InSAR Scientific Computing Environment 2.0 [35] automates critical tasks to prepare the SAR data for PSI analysis. The workflow begins by selecting the master image to optimize the temporal and perpendicular baselines relative to the slave images. This selection minimizes decorrelation and maximizes coherence across the interferometric network. Figure 5 illustrates the PSI network, where the center of the network represents the master image and the more minor points indicate the slave images. The connections (master-slave links) between the reference image and secondary images represent the interferograms used in the analysis. The colormap of these links visualizes  
Figure 4: Subsurface layer interpretation with references to drilling logs, SPT values, and the water table. Note typical SPT values for the filling layer—14–35, clay layer—4–8, and marl layer 44–50. the spatial coherence, with red indicating low coherence and blue representing high coherence. A threshold of 0.5 was applied to exclude links with insufficient temporal coherence, ensuring the quality and reliability of the interferograms. For topographic corrections, the SRTMGL1v003 Digital Terrain Model (DTM) was used [36]. This high-resolution dataset (30 m) was incorporated to correct for phase distortions caused by topographic variations, enabling accurate surface subsidence measurements. The processing stage utilized the pre-processed data to generate the PSI outputs, including time-series analyses and velocity maps.