# Spatio-Temporal Distribution of Ground Deformation Due to 2018 Lombok Earthquake Series
## 2 Materials and Methods
Each datum would be separated by its orbit to be replaced with an absolute orbit, i.e., the orbit of the satellite position when the satellite senses the surface of the earth. The images with the correct orbital information were then transferred to the Back Geocoding process. Image resampling would be carried out using the Digital Elevation Model (DEM) which transformed the DEM coordinate system into an Earth-Centered Rotating (ECR) based Cartesian coordinate system. The resampling method was based on DEM and radar image resolution. Since the Sentinel-1 image has medium resolution and the DEM was derived from SRTM with WGS84 Geoid, it supported bilinear interpolation as a resampling method. The process of applying the satellite orbit and Back Geocoding which had geometric orientation was still insufficient for Sentinel-1 interferometric processing [4; 6]. In order to increase the accuracy, Enhanced Spectral Diversity (ESD) was applied to estimate constant azimuth shifts between radar images by minimizing the phase discontinuity throughout the burst. Interferometry was formed by multiplying the amplitude of the master image and the slave image when the phase difference of each image was displayed. The interferometric phase was generated from SAR image pixels which depended only on the difference between the flight path and the cell resolution in interferometry. In interferometric processing, elevation or deformation was estimated by eliminating other sources of errors. The flat-earth phase had to be removed from interferogram because it was produced by the curvature of the surface reference. This process could be done through the subtracted flat-earth phase, so that the topographic variations did not appear [3]. It was also intended to obtain accurate topographic or deformation information. The flat-earth phase was estimated using orbital information from metadata and subtracted from interferogram. The results obtained had coherent values (0.0 to 1.0/no useful information to perfect interferogram without noise). The minimum coherence value given by the European Space Agency (ESA) for the formation of the Digital Surface Height Model was 0.20. In order to be able to continue the process of estimating deformation using DInSAR required an image coregistration with a coherence value greater than 0.20. In this study, we mask out the coherence \(\leq\) 0.5 in order to have a good quality interferogram. Low coherence presented in the interferograms could be caused by complex speckle noise from dense vegetation cover [46; 47; 48] and high rate of deformation [49; 50; 51]. The interferogram was produced from unified burst arrays. It needed an improvement in the form of merging all bursts into a complete interferogram through the TOPSAR Deburst process to identify range and azimuth. Each line in the direction of the sub-swath with the same time label would be merged with the adjacent sub-swaths. The interferogram could then be flattened by removing the topographic phase. DEM SRTM was used as a topographic model to perform the Topographic Phase Removal process. This step was implemented for deformation phase computation because eliminating topographic phase would remove the elevation value from the image pair interferogram and would leave only the deformation phase. The DEM SRTM acted only as topographic phase simulator, then it was removed from the interferogram of the processed image pairs. In order to reduce noise in the fringes and to produce good deformation, the result from the previous step had to be filtered using Goldstein Phase Filtering by maintaining the fringes at the edges. The first process that occurs was an adaptive filter that was carried out before the frequency estimation was used to increase the accuracy of the estimation. Furthermore, to maintain the fringes characteristic, the estimated fringes frequency in each filtering patch was removed from the original noise phase [5; 6]. Then the residual phase is refined using a Goldstein filter.