# Monitoring of Ground Movement and Groundwater Changes in London Using InSAR and GRACE
## 3 Materials and Methods
### Subsidence from PSInSAR  
The Interferometry Synthetic Aperture Radar (InSAR) provides the possibility to map the movement of the Earth surface with high accuracy. SAR data pairs with good coherence are required for informative interferogram generation. InSAR calculates the phase difference between various SAR acquisitions taken from the same orbital track. Persistent Scatterer InSAR (PSInSAR) differs from conventional interferometry as it only uses pixels that show stability in phase for several interferograms. These stable pixels can be termed as Persistent Scatterers (PSs) or permanent scatterers [38]. The PSInSAR time series analysis allows us to do the following:  
1. Allow better selection of coherent pixels;
2. Atmosphere/orbit errors can be reduced by filtering in space and time;
3. Make DEM (Digital Elevation Model) error estimation possible;
4. Make the most reliable phase unwrapping possible (3D);
5. Make sub-pixel resolution possible.  
The inclination of ENVISAT-ASAR satellite ground tracks at the SAR scene centre was 14\({}^{\circ}\) in the south-north axis at the latitude of London, and the incidence angle of the employed sensor modes was  
Figure 2: Methodology used for the research. (* SRTM DEM—Shuttle Radar Topography Mission Digital Elevation Model, ** TWS—Terrestrial Water Storage, *** LSM—Land surface Model).  
23\({}^{\circ}\) measured from the vertical direction. This means that the employed LOS could estimate purely vertical motions as approximately 92% of their actual amount, E-W motions as approximately 38% and N-S as only approximately 9% [39].  
The PSInSAR analysis in ENVI Sarscape [40] is a semi-automated process and involves multiple steps. The first step is to select a master image, with reference to which all other slave images are co-registered. The master image is selected based on the minimum mean baseline of the stack, which means that the image should have an ideal temporal and spatial position with respect to the other ones. This simplifies data co-registration and provides higher coherence, as small baselines are less sensitive to volume de-correlation [41].  
To select the reference point, the PS algorithm in SARscape follows one of the two following principles: (a) If the area is larger than a given surface threshold, the whole image is divided in more subsets (considering an overlap) and each one will be processed separately with an own reference point, otherwise too many parameters should be estimated and the atmosphere estimation would become less accurate. So, in the final step, all single areas will be mosaicked. (b) On the other hand, if the area is smaller than this surface threshold, one reference point is sufficient, and the image will not be divided. This surface threshold is called \"Area for Single Reference Point (sqkm)\". In our case this value was 25 km\({}^{2}\) and the first principle was followed. In total there were 63 ground control points.  
After co-registration, interferograms were generated for each slave image using the same master image. Then interferogram flattening was performed using a reference DEM SRTM V4. The better the reference DEM accuracy (or resolution) the better the result in terms of topography removal. Then first step inversion was performed to derive the coherence, displacement velocity and residual topography, which were used to flatten the complex interferograms. Then the second inversion step was performed to address the atmospheric phase components of the linear model products coming from the first inversion. Then, finally, the PS products were geocoded to display the velocity maps in both raster and vector formats.