## 2 Materials and Methods
### Dataset
#### 2.2.2 Multi-Temporal PS-InSAR  
SAR is an active sensor, and the sensor emits a signal, which the surface reflects, and the same sensor then detects again, as shown in Figure 6. Multi-Temporal InSAR (MT-InSAR), an advanced InSAR approach, measures displacement more accurately by examining the phase information from a stack of SAR data collected over the same region [39]. It can reduce errors in deformation estimations and address some of the limitations of conventional InSAR, such as uncorrelated phase disturbances [40]. Figure 4: Photo showing the position of the laser measurement sensors. The image is provided by the [PERSON]. Figure 5: Illustration showing the working principle of levelling on a diagnostic train. Figure 6: Displacement diagram of the railway in the line of sight and at multiple passes. In SAR interferometry, the target region is scanned using a constellation of satellites with identical instrumental and orbital properties or through a single satellite to obtain sequential acquisitions over time. The frequency of measurements is thus a function of the frequency of satellite passes. The electromagnetic spectrum's microwave region is where SAR satellites transmit their signals. The detected signal's phase and amplitude are represented in its data. Interferometry is based on the creation of interferograms and uses the phase differences between acquisitions, i.e., at various times, to estimate the movement of the ground surface, as seen in Figure 6[3; 41; 42]. As a result, deformations are found along the satellite's line of sight (LOS). The purpose of InSAR processing is to calculate the real displacement component, \(\Phi_{\text{Displ}}\), which is distinguished from other signal contributions as follows:  
\[\Phi_{\text{Displ}}=\Phi_{\text{Int}}-\Phi_{\text{RTE}}-\Phi_{\text{Atm}}-\Phi _{\text{Orb}}-\Phi_{\text{Noise}}-2\;\text{k}\pi, \tag{1}\]  
where \(\Phi_{\text{Int}}\) denotes the wrapped interferogram, \(\Phi_{\text{RTE}}\) represents the residual topographic error component, \(\Phi_{\text{Atm}}\) signifies the atmospheric component of each image, and \(\Phi_{\text{Orb}}\) denotes the orbital error component. Phase ambiguity is resolved through phase unwrapping techniques since \(\Phi_{\text{Noise}}\) accounts for phase noise and 2 k\(\pi\) regulates it [42]. To address these errors, noise and uncertainties encountered when trying to calculate the real displacement component, some auxiliary data and filters, which have been applied in SARPROZ(r), such as the Digital Elevation Model (DEM), precise orbit information from the image acquisition time, and, if available, weather information including precipitation and humidity information, are used. For example, DEM data are used to analyze the topographic effect. For this analysis, since Konya is predominantly a flat region, the 30 m-SRTM DEM (Shuttle Radar Topography Mission Digital Elevation Model) data are sufficient to eliminate the topographic error. In order to eliminate the orbital effect, sensitive orbit data are used, and finally, the atmospheric contribution can be estimated and eliminated by analyzing a sequence of images obtained at different time intervals [2; 42]. After eliminating the influences of topographic, atmospheric and residual noise, the remaining anomalies in phase can be attributed to subsidence occurring along the radar's LOS, as shown in Figure 6. It should be noted that multi-pass interferometry methods, such as PS-InSAR, allow for the identification and elimination of these artifacts [43]. PSs have consistent scattering properties throughout time and a dominant reflection inside each pixel cell. This reduces both temporal and geometric decorrelation. Furthermore, the signal interference can be assessed and eliminated utilizing a sequence of images obtained at various time intervals [44]. Utilizing a series of acquires, the accuracy of detecting dependent pixels can also be enhanced [45; 46].