# Ground Displacement in East Azerbaijan Province, Iran, Revealed by L-band and C-band InSAR Analyses
## 3 Methods
### SBAS Analysis
So, the maximum temporal gap for a potential SBAS pair is assumed to be 365 days, and the spatial (normal) baseline eligible for an SBAS pair is up to 45% of the critical baseline shown in Equation (1). Although more SAR images are preferred for SBAS analysis, 15 images is marginally enough [48]. Figure 4 shows that the criteria applied for SBAS network creation have enough integrity to minimize the errors, as the pairs are continuously connected to each other. The algorithm is adopted to retrieve the highest coherence values, on the one hand, and keep the integrity of the SBAS network for the pairs with coherence higher than 0.8, on the other hand. Therefore, interferograms with a coherence value lower than 0.8 are withdrawn. The minimum and maximum normal baselines are 24 and 352 m, respectively. The selected pairs must be co-registered to one of the images. Image co-registration is a process where 2 or more SAR images have the same geometric nature and corresponding pixels should represent the same objects that might be integrated. This is an essential step for SBAS time series analysis to make sure that pixel values for a certain object are correctly resampled and able to create the same voxel of the objects. We co-register the images to a super master image that is located in a fair position (both temporally and spatially) to the other images. Figure 4: (**a**) Arrangement of interferometric synthetic aperture radar (InSAR) pairs and corresponding mean coherence values for each pair. (**b**) InSAR links of PALSAR-2 (black diamonds) and Sentinel-1 (purple circles). Super master image for small baseline subset (SBAS) analysis of PALSAR-2 data indicated by red diamond. In Figure 4a, the super master image is indicated by a small red diamond in the middle of the network that is used to generate 8 interferograms. Moreover, it can satisfy the major temporal and spatial limitations of time series analysis as it is located in fair position with respect to the other images (Figure 4b). Overall, 86 pairs were analyzed, and their average coherence values are shown in Figure 4a. Generally, short pairs have higher mean coherence values and long pairs have lower mean coherence values: most of the pairs have an average coherence value between 0.5 and 0.8. The 1 arc-second Shuttle Radar Topography Mission (SRTM) DEM (30 m resolution) along with 50 ground control points (GCPs) were used for removal of topographic and atmospheric phases. The mean coherence map of all pairs, the topography map, and interferograms are criteria used for the selection of GCPs in highly coherent areas with smooth topography, far from the subsiding areas. The method described above is efficient when geodetic measurements are limited or not available. Once the displacement map in LOS is generated and reprojected in a geographic/geodetic coordinate system, in order to compare the results of PALSAR-2 with other datasets, such as Sentinel-1, the LOS values can be transformed into vertical values. The transformation of coordinates is done by assuming a stable (motionless) area in the results, selected based on high coherence values, away from the subsiding areas. For a three-dimensional displacement map, both ascending and descending datasets of PALSAR-2 are necessary. Since our PALSAR-2 dataset was limited only for the ascending dataset, the retrieval of vertical values could be done under several assumptions. The SAR imaging system is not highly sensitive to north-south movements due to its pole-to-pole movements. We assume that displacements in the N-S and E-W directions are negligible and only the vertical displacement can be inferred, as follows:  
\[V_{v}=\frac{V_{LOS}+\ V_{EW}sin\theta cos\alpha}{cos\theta} \tag{5}\]  
where \(V_{v}\) is the vertical displacement rate, \(V_{LOS}\) is the LOS deformation rate, \(V_{EW}\) is the east-west displacement rate, \(\alpha\) is the azimuthal angle of the LOS, and \(\theta\) is the incidence angle of the satellite.