# Entity Embeddings in Remote Sensing: Application to Deformation Monitoring for Infrastructure
## 2 Data and Software  
SAR is an active sensor, in that the signal emitted from the satellite reflects off the surface and is then re-detected by the same satellite. SAR satellites operate at wavelengths within the microwave part of the electromagnetic spectrum. Their data consist of the amplitude and phase component of the detected signal. Several processing schemes are feasible, and interferometry is based on the generation of interferograms, involving the use of the phase difference between acquisitions (i.e., at different times) to estimate the movement of the ground surface [33]. Because the difference in phase is used, the movement can be detected at high precision as a fraction of the wavelength of the signal. The available InSAR approaches can be categorised broadly as follows: (a) Persistent Scatter (PS) interferometry [34], (b) Short-Baseline Subsets (SBASs) and their variations [35], and (c) hybrid approaches combining both PS and SBAS elements, such as StaMPS [36] and SqueeSAR [37]. PS-InSAR processing aims to detect strong and stable signals from dominant reflectors such as man-made structures and sharp-edged objects. On the other hand, SBASs are designed to detect the cumulative contribution of smaller, distributed scatterers of radar signals in non-urban areas, such as agricultural fields, forests, and diverse land covers. For more-comprehensive reviews of these techniques, readers can refer to, e.g., [38; 39]. \"Sentinel-1\" is a SAR satellite from the European Space Agency's Copernicus program. It operates in the C-band, which has a wavelength of approximately 5.5 cm. Sentinel-1 data have an intermediate spatial resolution of 5 m by 20 m and a temporal resolution of a 12-day revisit depending on the location on Earth [40]. In this study, intermittent SBAS data were used on 2.5 years of the Sentinel-1 descending stack [41]. Deformations are detected in the Line-Of-Sight (LOS) of the satellite. To decompose LOS deformation signals into their horizontal and vertical components of motion, data from two geometries are required. This is not the case for Cadia, where only one orbit (descending) is available from Sentinel-1 at the time of failure. Figure 1a plots the spatial distribution of the average satellite LOS velocity measurements obtained from this stack over Cadia TSF. A clear subsidence (red) is visible along the inner rim of both the failed north and stable south TSFs. Figure 1b is a zoom-in of the north TSF failure zone. The InSAR data span a total of 68 dates, from 2015-12-02 to 2018-02-25 (YYYY-MM-DD). The last InSAR data were captured 12 days before the north TSF failure on the 9 th of March 2018. The across-dam temporal behaviour of the Cadia TSFs is illustrated in Figure 2a,b for the failed north TSF and stable south TSF, respectively, where \"downstream\" indicates towards the toe of the dam. There were significantly higher de  
Figure 1: Spatial view of the InSAR data over Cadia TSFs. (**a**) Illustration of InSAR velocity measurements averaged over the whole SAR data stack (from 2015-12-02 to 2018-02-25). Basemap image copyright © ESA Sentinel-2 data. ISBAS InSAR data © Terra Motion. (**b**) Zoom-in of the failed area. Basemap image copyright © 2021 Maxar Technologies © CNES/Airbus © Google Earth. the upstream compared to the downstream parts of the TSFs due to the underlying thicker tailings [19]. Depending on the type of InSAR processing, a variety of attributes may describe the ground deformation measurements. The dependent variable, deformation, is predicted using the other attributes: the date, the geographical coordinates (latitude and longitude), and the coherence of the measurements. Coherence serves as an indicator of the quality of InSAR data, where higher coherence corresponds to greater accuracy in the deformation signals. Moreover, it is possible to extract additional attributes such as the velocity or acceleration from InSAR data.