# Analysis of Mining Waste Dump Site Stability Based on Multiple Remote Sensing Technologies
## 3 Methodology  
### Small Baseline Subset Analysis  
Current TS-InSAR approaches are generally categorized into two groups. The first group uses interferograms generated in reference to a common master, e.g., the traditional PSI approach. The second group uses only good interferograms generated from all possible image pairs, e.g., the SBAS approach. Since the vegetation in mining areas has been seriously damaged, most of the area is composed of fragmented rock, gravel, sand and silt. The traditional PSI algorithm developed for urban areas does not work very well in the study area [5; 6]. Besides, at least 20 SAR images are necessary in order to get a robust time series analysis result using traditional PSI. On the other hand, the small baseline subset method makes full use of the interferograms and, with small spatial and temporal baselines, can overcome the limitations of decorrelation with a reduced amount of SAR images [7; 8; 9]. Compared with the original SBAS method which only operates with isolated subsets of interferograms, the modified SBAS approach in the Stanford method for persistent scatterers (StaMPS) software can ensure temporal continuity by connecting separated subsets of interferograms with larger baselines [12; 13]. It has been widely applied in the displacement monitoring of natural scenes with limited amounts of data [48]. Due to the above mentioned reasons, the modified SBAS approach in StaMPS developed for displacement monitoring of rural areas was well suited to this study [12]. The SBAS approach in StaMPS first generated interferograms with given thresholds on spatial and temporal baselines. It then connected separate subsets with larger baselines to ensure temporal continuity [12]. In the StaMPS SBAS, slow decorrelating filtered phase (SDFP) pixels were selected by carrying out amplitude dispersion and phase characteristics analysis. Then, the spatially correlated phase contribution was estimated and removed with bandpass filtering in the frequency domain. The spatially uncorrelated look angle error was then removed according to its correlation with the perpendicular baseline. After removing these two phase terms, a three dimensional phase unwrapping  
Figure 3: Spatial and temporal baselines used for TS-InSAR analysis based on small baseline subset (SBAS) analysis. The asterisks indicate the synthetic aperture radar (SAR) images and blue lines represent the interferograms. was carried out. The unwrapped phase of each pixel could then be divided into components based on surface displacement, topographic error, atmospheric disturbance, orbital error and noise. By applying iterative filtering in spatial-temporal domains, these different components could be successfully separated. Afterwards, time series deformation in the line-of sight (LOS) direction could be extracted using singular value decomposition (SVD) [12]. Due to the intrinsic, side-looking geometry of SAR satellites, the estimated displacement in LOS is just a projection of the real displacement. On the other hand, the deformation along the slope direction was measured by total station instruments. In order to assess the accuracy of the SBAS results, the deformation in LOS direction needed to be translated to the slope direction. For landslides, the simple assumption that the displacement was parallel to the slope surface was made [17; 37; 38; 39]. Since the COSMO-SkyMed images were collected in descending orbit, and the sensor worked in a right side-looking direction. We will take Point A in Figure 4 as an example; the displacement along the slope direction can be split into vertical and horizontal components, as shown in the following equation:  
\[ \begin{array}{l}d_{A_{\Delta},v}=d_{A}\cdot\sin(\beta)\\ d_{A_{\Delta},h}=d_{A}\cdot\cos(\beta)\end{array}  \tag{1}\]  
where \(d_{A}\) is the displacement of Point A parallel to the slope direction, \(\beta\) is the gradient of the slope, and \(d_{A_{\Delta},v}\) and \(d_{A_{\Delta},h}\) are the vertical and horizontal components of \(d_{A}\) respectively.