## 2 Materials and Methods
### Principles of Slope Radar Monitoring  
S-SAR (Slope Synthetic Aperture Radar), a ground deformation monitoring system based on microwave remote sensing technology, achieves millimeter-level displacement measurement accuracy through the emission of electromagnetic waves and the reception of reflected signals from target areas (Figure 2). Integrating Synthetic Aperture Radar (SAR) imaging with Differential Interferometric Synthetic Aperture Radar (DInSAR) principles, this system demonstrates technical advantages including all-weather operation, non-contact measurement, and large-area continuous monitoring. It has become an essential monitoring solution for mine slopes and geological hazard prevention [18; 19; 20].  
During the operation of S-SAR, the radar continuously emits Frequency-Modulated Continuous Wave (FMCW) signals characterized by linear frequency variation over time. The echo signals from targets at different distances exhibit frequency differences due to time delays. Through quadrature demodulation of the received scattered echoes, these frequency differences are converted into time differences, thereby achieving high range resolution \(R_{0}\). The calculation formula is as follows:  
\[R_{0}=\frac{c}{2B} \tag{4}\]  
where \(c\) is the electromagnetic wave propagation velocity, and \(B\) represents the signal bandwidth.  
Figure 1: Schematic diagram of Inverse Velocity Method.  
For azimuth resolution, when the radar antenna moves along the azimuth direction, the relative motion between the radar and targets at different azimuth positions generates Doppler frequency shifts. By recording and processing the echo signals from each target, the system distinguishes azimuth targets based on these Doppler frequency variations, thereby enhancing azimuth resolution. Ultimately, the fusion of range and azimuth information synthesizes a two-dimensional radar image. The azimuth resolution \(P_{0}\) is calculated as:  
\[P_{0}=\frac{\lambda}{2L} \tag{5}\]  
where \(\lambda\) is wavelength, and \(L\) denotes the synthetic aperture length of the radar.  
The deformation monitoring capability of S-SAR is based on differential interferometry. By performing coherent processing on the complex images acquired from two sequential measurements, the system extracts phase difference information. The phase difference is calculated using the following formula [21]:  
\[\Delta\phi=\frac{4\pi}{\lambda}R+\phi_{\text{atm1}}+\phi_{top1}+\phi_{noise1} \tag{6}\]  
where \(\Delta\phi\) is the Interferometric phase difference; \(R\) is the Line-of-sight (LOS) displacement; \(\phi_{\text{atm1}}\) is the Atmospheric delay phase; \(\phi_{top1}\) is the Topographic phase; and \(\phi_{noise1}\) is the Noise phase.  
The topographic phase is eliminated through differential interferometric processing, while atmospheric phase correction is applied to mitigate the effects of atmospheric delay. Finally, LOS deformation inversion is performed. For slope monitoring scenarios, the deformation gradient is typically assumed to vary linearly within the pixel range. The least squares method is employed to unwrap discrete phase data, combined with precision calibration parameters, to achieve millimeter-level deformation monitoring accuracy. The deformation magnitude is calculated as follows:  
\[R=\frac{\lambda}{4\pi}\cdot\Delta\phi \tag{7}\]  
The specific technical parameters of S-SAR are shown in Table 1.  
Figure 2: Image of the slope radar.