## 1 Introduction  
Sub-pixel correlation (SPC) is an important technique for surface deformation monitoring. It calculates the pixel offsets across two optical images [1]. While initially used for the acquisition of glacier flow velocity fields [2], this technique gradually became used for the monitoring of other surface deformations. As optical satellite data availability and diversity have expanded, SPC has evolved from obtaining deformation information based on a single image pair to analyzing the surface deformation time series using multi-images [3; 4; 5]. Nowadays, the SPC technique has been widely used in the monitoring of dune migration [6; 7], earthquakes [8; 9; 10; 11], glacial movement [12; 13], landslides [14; 15; 16], and so on. However, the offset fields obtained by SPC have many error sources, such as spatial-temporal decorrelated noise, long wavelength orbit error, satellite attitude jitter distortions, stripe artifacts, and topographic shadow artifacts [17; 18]. These errors limit the deformation monitoring accuracy, subsequently affecting deformation signal extraction and characterization. Therefore, studying the causes and correction methods of these errors in the SPC-derived offset fields is of great significance for the application and development of optical images. When addressing the removal of stripe errors in single remote sensing images, researchers typically rely on grayscale analysis to correct these errors. These studies often employ edge-detection and line-tracing techniques to identify and eliminate stripe errors [19; 20; 21]. These methods are highly automated, rapid, and efficient. However, their applicability in the offset field is limited. In surface deformation monitoring, it is crucial to consider the deformation characteristics of the study area. For instance, manually masking deformation regions is necessary to prevent the loss of deformation information. Errors in the offset fields acquired by SPC are usually related to the satellite imaging principle, range, and conditions. It is essential to investigate the systematic error composition and correction methods for different satellites. SPOT imagery's stripe error in the offset field can be effectively removed using the mean subtraction method [22]. The stripe artifacts of Landsat 8, produced during the push-broom imaging process, can be removed by limiting the spatial baseline and radiant energy [17]. PlanetScope imagery, which faces discontinuities in deformation values between frames due to frame imaging, can effectively resolve this issue using an approach based on polynomial surface fitting [23]. Considering the imaging principle of Sentinel-2, the optimized \"Mean elimination method\" can effectively mitigate satellite attitude jitter distortions [18]. Therefore, the error sources and correction methods differ among optical images acquired by various satellites. RapidEye satellites were successfully launched by Germany in August 2008 and were in orbit for 11 years until March 2020, accumulating a large amount of archived data for surface deformation monitoring. Boasting high temporary and spatial resolutions, these images offer multi-spectral information [24; 25] and hold promising applications in earth observations. Based on abundant spectral information, RapidEye data have been widely used in crop growth monitoring [26; 27], feature identification and classification [28; 29], and feature information extraction [30; 31]. In geo-disaster research, RapidEye imagery, owing to its high temporal and spatial resolution, is widely used for landslide identification and inventory [32; 33; 34; 35; 36]. Furthermore, utilizing the SPC technique, RapidEye imagery can extract large-scale surface deformation information, making it an essential data source for the quantitative analysis of geo-disasters, such as earthquakes, glacier movements, and large-scale landslides.