# Spatial Distribution and Monitoring of Land Subsidence Using Sentinel-1 SAR Data in Java, Indonesia
## 2 Data and Methodology
### Data Coverage and Processing  
The data used in this study are Sentinel-1 data spanning from 2017 to 2022. Java Island is traversed by five descending Sentinel-1 tracks. However, the last track, which covers the east end of the island, has been excluded because the number of available images is only 54 images, which is relatively low compared to more than 150 images retrieved from other tracks. In total, we used 650 tracks to produce deformation maps in this study. To generate subsidence maps in Java Island from SAR data, small-baseline criteria have been used to form interferograms and estimate the cumulative subsidence relative to a primary date [22]. The LS rate is then calculated using a linear model from the estimated cumulative subsidence. Interferogram pairs are constructed using the Delaunay Triangulation Network to reduce the number of interferograms used in time-series inversion while still preserving the design matrix rank. The temporal and perpendicular baselines thresholds are still applied to ensure that only small-baseline interferograms are generated; in this case, the thresholds are 180 days and 200 m, respectively. It should be noted that the perpendicular baseline of Sentinel-1 interferograms become longer after 2022 due to the tubing effect [23]. In total, 1818 interferograms have been generated using this method. This is much lower compared  
Figure 1: The physiography of Java (from [17]). to more than 10,000 interferograms generated using only temporal and perpendicular baseline thresholds (less than 185 days and 200 m, respectively, in this case). Digital Elevation Model Nasional (DEMNAS) or Indonesia's Digital Elevation Model (DEM) with a spatial resolution of 0.27 arcsecond (8 m) of spatial resolution and an average accuracy of 5 m [24; 25] has been utilized to model topographic effects. To unwrap the interferograms, Minimum Cost Flow has been used followed by an iterative model based on [26]. To reduce tropospheric effects, the Generic Atmospheric Correction Online Service (GACOS) model has been applied to all generated interferograms [27; 28]. The reference points for each track are placed in alignment with non-deformed GNSS Continuous Operating Reference Stations (CORSs) on Java Island managed by Badan Informasi Geospasial (BIG; Indonesian Geospatial Information Agency). The corresponding CORSs are the BAKO, CSUM, CPBL, and CMAG stations for track 047, 149, 076, and 003, respectively (see Figure 2). Interferogram Corrections  
The first step of data filtering on the interferogram is to ensure that only qualified coherence pixels are used for further processing. Only pixels with a coherence higher than 0.3 are used for LS rate estimation. Generally, low coherence is caused by heavy vegetation and watered land such as ponds, rice fields, and lakes. Fish farming, which is usually located in coastal areas, causes a large part of the regions to have low coherence. Dense forests that are usually located in the volcanic or mountainous areas also have severely low coherence. All coherence interferogram pixels contain several phase contributions [29] and can be written as the following phase combination:  
\[\phi_{ifg}=\phi_{defo}+\phi_{atm}+\phi_{orbit}+\phi_{DEM}+\phi_{noise} \tag{1}\]  
Figure 2: Rate of LS in Java. This map shows the annual subsidence rates measured in mm/year. The red dots indicate the CORS position used for validation; the black boxes represent the data track of InSAR, with (**a**) track 047, (**b**) track 149, (**c**) track 076, and (**d**) track 003; the black triangles show the reference points that are used for each track. where \(\phi_{ifg}\) is the interferogram phase, \(\phi_{atm}\) is the atmospheric phase contribution, \(\phi_{orbit}\) is the phase contribution from orbital error, \(\phi_{DEM}\) is the phase contribution from DEM error, and \(\phi_{noise}\) is other uncorrelated noise phase contribution. Here, all phase contributions, except deformation, are considered as errors.