## 4 Applications of InSAR in Landslide Monitoring
### Recent Advances in Landslide Monitoring with InSAR
#### 4.2.2 Expanding Dimensions: 3D Monitoring with InSAR  
InSAR measurements are typically taken along the line of sight (LOS) direction (Figure 8a). LOS observations only capture the component of movement along the radar's line of sight, depicting the vector sum of vertical, north-south, and east-west, which may not fully capture the deformation characteristics of landslides. For example, horizontal movements parallel to the radar path or vertical displacements perpendicular to the LOS cannot be fully captured, leading to potential misinterpretation of the actual deformation. Moreover, the complexity of landslide dynamics, including rotational and translational movements, cannot be comprehensively resolved through single LOS observations alone. To overcome the limitations of single LOS measurement, advancements in 3D landslide deformation monitoring have been made (Figure 8b). In fact, three significantly different geometric observations are required for the measurement of landslide three-dimensional (3D) deformation, which can then be used to calculate the 3D deformation information using Formula (2). \[ \begin{bmatrix}LOS_{1}\\ LOS_{2}\\ LOS_{3}\end{bmatrix} = \begin{bmatrix}-\cos\alpha_{1}\sin\theta_{1}\sin\alpha_{1} \sin\theta_{1}\cos\theta_{1}\\ -\cos\alpha_{2}\sin\theta_{2}\sin\alpha_{2}\sin\theta_{2}\cos\theta_{2}\\ -\cos\alpha_{3}\sin\theta_{3}\sin\alpha_{3}\sin\theta_{3}\cos\theta_{3}\end{bmatrix} \begin{bmatrix}D_{e}\\ D_{n}\\ D_{o}\end{bmatrix}  \tag{2}\]  
where \(D_{e}\), \(D_{n}\), \(D_{o}\) indicate the deformation along the east, north, and vertical directions, respectively. \(LOS_{1}\), \(LOS_{2}\), and \(LOS_{3}\) are the LOS deformation measured by SAR satellites. \(\alpha_{1}\), \(\alpha_{2}\), and \(\alpha_{3}\) are the heading angle of SAR satellites. \(\theta_{1}\), \(\theta_{2}\), and \(\theta_{3}\) are the incidence angle of SAR images. However, the current spaceborne SAR platforms mainly operate in near-polar orbits, with typically two types of observations, i.e., ascending and descending orbits, resulting in only two significantly different geometric observations, especially for non-polar regions. Consequently, methods for landslide 3D deformation monitoring using spaceborne InSAR can be broadly categorized into two types. The first type involves incorporating other techniques, such as pixel offset tracking (POT), to aid in 3D measurements, as demonstrated by [PERSON] et al. [67], who reconstructed the 3D displacement field of the Hooskanaden landslide based on POT. Nevertheless, this type of method is more suitable for large-scale monitoring, as the deformation measurement accuracy derived from POT is relatively low. Second, it is also possible to reduce the reliance on diverse geometric observations under specific assumptions, or based on prior information, such as reasonably ignoring north-south deformation according to the landslide location or assuming a translational sliding pattern to neglect vertical deformation. Based on the selected articles, the majority of studies have adopted this approach to achieve 3D deformation monitoring of landslides. For instance, [PERSON] et al. [68] conducted an analysis of the vertical and east-west deformation in the Woda landslide area using Sentinel-1A ascending and descending datasets, which is insensitive to north-south displacement due to the flight direction characteristics of Sentinel-1A. [PERSON] et al. [69] measured the east-west and vertical deformation rates of the Zongling landslides using both ALOS/PALSAR-2 ascending datasets and Sentinel-1A ascending and descending datasets. [PERSON] et al. [70] employed a surface-parallel flow model to measure the 3D deformation of the Jiaju landslide. It is worth noting that although multi-orbit InSAR has become the mainstream approach for landslide 3D deformation monitoring, for slope-scale research in steep, rugged  
Figure 8: **(a)** Line of sight (LOS) measurement with InSAR. **(b)** Multi-orbit InSAR for 3D landslide deformation monitoring.