# Entity Embeddings in Remote Sensing: Application to Deformation Monitoring for Infrastructure
## 1 Introduction  
Mining is at the core of our global energy transition. An estimated three billion tons of metals will be required to produce the renewable energy technologies [1, 2]. To put this in the context of the challenge posed to the extractive industries, this number is small compared to the amount of material that will need to be taken out of the ground. For example, over 98% of the material in copper mining is waste. Therefore, the often forgotten consequence of our metal-hungry future is the handling of the enormous amount of resulting mine waste. Usually, mine waste is stored behind large earthen dams, known as \"Tailings Storage Facilities\" (TSFs). Due to mining being one of the oldest industries, over 30,000 TSFs are estimated to exist worldwide, a quarter of which are abandoned and not monitored at all [3]. Even relatively well-monitored TSFs can sometimes fail, resulting in socio-environmental tragedies such as the Brumadinho failure in 2019 [4] and, most recently, the Jagersfonteinfailure in 2022 [5]. Unfortunately, the number of catastrophic TSF failures is increasing [6]. Therefore, there is a critical need for a global monitoring capability for the TSFs of the world. A technology offering much promise towards this ambition is satellite Interferometric Synthetic Aperture Radar (InSAR). InSAR analysis enables the detection of millimetric-scale ground movements from satellite constellations hundreds of kilometres in space. The prospect for global monitoring with InSAR is imminent, as illustrated by the recent, bold initiative, the European Ground Motion Service [7; 8]. This initiative has extended ambitious nation-wide InSAR monitoring to the continental scale. Moreover, the applicability of advanced multi-temporal InSAR techniques [9] has been demonstrated for the monitoring of critical infrastructure such as bridges (e.g., [10; 11]), dams (e.g., [12]), underground construction activities (e.g., [13]), and ground de-watering (e.g., [14]). Although relatively sparse, several studies have explored the applicability of InSAR for the monitoring of TSFs. A key research question has been whether precursory indications of structural failure are detectable from InSAR preceding TSF failures, such as the Brumadinho (e.g., [15]) and Cadia failures [16; 17; 18; 19]. Most studies have explored this question from the perspective of analysing the robustness and limitations of particular custom post-processing of the raw SAR data into InSAR. For example, [PERSON] et al. (2021) [15] was able to detect deformation trends that were inconsistent with expected ground consolidation settlements of Brumadinho TSF. Although potentially anomalous measurements were also detected by [20], those authors concluded that the statistical significance of these anomalies is insufficient (due to the high signal-to-noise ratio) to reliably trigger an early-warning alert. Nevertheless, there is a general consensus on the feasibility of detecting anomalous deformation from InSAR preceding the Cadia TSF failure [16; 17; 18]. [PERSON] et al. (2021) [18] demonstrated that the signal is discernible regardless of the raw SAR data type and resolution, from both medium- (Sentinel-1) and high-resolution commercial (Radarsat-2) data. [PERSON] et al. (2019) [17] proposed an \"inverse velocity method\" for the estimation of the failure date using InSAR for a variety of slope instabilities, including the Cadia TSF failure. Their proposed technique has been adopted by a variety of InSAR-TSF-monitoring studies for both Cadia [16] and Brumadinho [15]. In those studies, anomalous measurements were identified both qualitatively and visually, i.e., whether any obvious clusters of high subsidence measurements occurred near the failure area. However, the location of the failure surface is not known without the benefit of hindsight analysis. Therefore, there is a need for a robust approach to identifying anomalous InSAR deformation behaviour as they develop over time.