## 4 Applications of InSAR in Landslide Monitoring
### Recent Advances in Landslide Monitoring with InSAR
#### 4.2.3 Integration of InSAR for Landslide Failure Time Prediction  
Landslide prediction is vital for both researchers and practitioners in the fields of risk management, early warning, and prevention. Landslide prediction typically encompasses several aspects, such as displacement [71; 72], failure time [73; 74], potential affected areas [75; 76], and susceptibility mapping [77; 78]. Among these, landslide susceptibility mapping, which focuses on spatial prediction and delineating regions prone to landslides, will be discussed in Section 5. This section mainly focuses on failure time prediction, which typically relies on time-series monitoring of landslides. Predicting failure time is especially critical for guiding the determinations of the appropriate timing for interventions and prioritizing response efforts. Based on creep theory, landslides are typically categorized into three stages: initial deformation, uniform deformation, and accelerated deformation [79]. Failure time prediction primarily focuses on the analysis of the tertiary stage. The most widely used model for this purpose is perhaps the Fukuzono model, also known as the inverse velocity model (INV), which establishes a quantitative relationship between velocity and acceleration during the final stage before failure [80]. Over the years, this model has been refined and widely applied in failure time prediction [81; 82; 83; 84; 85]. A key requirement for such prediction is the acquisition of accurate velocity-time data. Previous studies have mainly relied on in situ sensors' monitoring, which face challenges in installation in remote areas and economic burdens. As introduced in Section 1, the advent of InSAR has significantly transformed landslide research. In failure time prediction, several scholars have explored using InSAR-derived displacement data to estimate failure time. [PERSON] et al. were among the first to apply InSAR monitoring to failure time prediction [86]. They selected 56 landslides worldwide and successfully forecasted the failure dates for 4 of them, achieving a precision of less than five days. Another early successful case was the study by [PERSON] et al. on the Moxian landslide, where they successfully estimated the failure date based on Sentinel-1 data and the INV, closely matching the actual failure event [87]. Additionally, [PERSON] et al. used InSAR to predict the failure time three weeks in advance [73]. While this result might be influenced by the relatively long acceleration period and favorable observation conditions in the study area, it strongly demonstrated the feasibility of using InSAR for failure time prediction. [PERSON] et al. applied the INV and its modified version to accurately predict temporal windows of slope failure in the Himalayan region, further illustrating the applicability and practicality of InSAR-based predictions in remote, mountainous regions [88]. While there are other similar successful cases [76; 89], most of these studies prefer to rely on the INV and its modifications. In fact, many other failure time prediction methods, such as the slope gradient method and the velocity over acceleration method, have also been shown to be effective for failure time estimation [90; 91; 92; 74]. However, there is limited insight into their application in failure time prediction using InSAR-derived displacement data. Furthermore, deterministic methods often fail to account for uncertainties, leading to potentially unreliable predictions. While probabilistic analysis methods are well-established and widely used in conventional landslide monitoring, their application in InSAR-based failure time prediction remains relatively unexplored. Recognizing this gap, [PERSON] et al. were the first to integrate InSAR measurements with the INV and sequential Bayesian updating for probabilistic analysis, quantifying uncertainties and providing a more robust and reliable failure time prediction [93]. Despite this progress, the potential of applying probabilistic analysis in such scenarios remains insufficiently explored.