# Generation of Complete SAR Geometric Distortion Maps Based on DEM and Neighbor Gradient Algorithm
## 1 Introduction  
It is acknowledged that geometric distortion is an inherent error of synthetic aperture radar (SAR) images because of side-looking geometry and topographic relief. SAR geometric distortion (SGD) can be divided into various types, i.e., foreshortening, layover, and shadow. Furthermore, in the object space, the layover and shadow regions can be divided into active and passive subregions [1]. The presence of SGD has many negative effects on SAR images, especially those acquired over the mountainous areas. For instance, the SAR signal is useless in areas affected by layover and shadow [2], which makes phase unwrapping immensely difficult. This is the main reason the application of interferometric SAR (InSAR) techniques has been hampered in mountainous areas [3; 4]. In addition, those distortions are bound to result in imprecise classifications of land use [5], inconsistencies in the digital elevation model (DEM) [6; 7], and underestimation for deformation areas [8]. Since the SGD is the inherent error of the SAR image, many researchers prefer distortion simulation to distortion correction. This is of great importance since with simulated distortions, we can calculate the best imaging geometry without the SAR image, which provides us with a chance to select the most suitable SAR data for the interested area. During the last two decades, several approaches have been developed to simulate the SGD. [PERSON] and [PERSON] [1] proposed a layover and shadow map (LSM) algorithm to simulate the layover and shadow, including active as well as passive ones. However, many parameters, such as height, imaging time measured in arc length along the flight path, and nadir distance, are required in the method, leading to many uncertainties in the generation of the layover/shadow. [PERSON] [9] presented a simple algorithm based on the surface slope that can be applied very rapidly to indicate those areas only corresponding to active shadow and layover. [PERSON] and colleagues [10; 11] integrated the synthesized effects of local topography into the R-index algorithm. Although the R-index can successfully identify the areas of foreshortening, it only accounts for the effects of active layover and cannot identify areas of passive layover and shadow (either active or passive). [PERSON] et al. [12] presented a GIS-based imitated InSAR procedure by using the \"one-observer\" method to predict areas where layover and shadow will occur. However, this method requires a very large DEM that would reduce the accuracy of the layover-shadow simulation. [PERSON] et al. [13] combined the LSM and R-index algorithms to generate foreshortening, layover (both active and passive), and shadow (both active and passive). However, this method does not correct the boundaries among the distortions as a result of ignoring the spatial relationship with passive distortion, which will yield inaccurate simulation results. In 2006, [PERSON] and [PERSON] [14] proposed a method for simulating the foreshortening and active layover/shadow (hereafter referred to as F-ALS). The F-ALS method identifies the ranges of aspect and slope which determine the foreshortening and active layover/shadow by analyzing the visibility conditions of unstable hillsides with different orientations [15]. Nevertheless, there is an obvious limitation to the F-ALS method in that it is incapable of deriving passive distortion, since the transition zone between passive distortion and non-distortion cannot be confirmed. This leads to incorrect coverage of the simulated distortion and makes it difficult to predict the distribution of persistent scatters. It is worth noting that passive layover can be employed to calculate the height of a building by creating a template based on the building's outline [16]. Looting can also be investigated by exploiting the relationship between the range of the passive layover and shadow. However, the relationship cannot be exhaustive of all possible combinations that can be found in real-world situations [17].