Refining regional gravity anomalies and vertical deflections of high-degree earth gravity model from residual terrains based on the spatial domain method

Abstract The Earth's gravity field is a fundamental physical field for research and analysis in Earth sciences. However, the limited degree of expansion in the gravity field model introduces truncation errors, which hinder the accurate representation of high-frequency information in Earth's gravity field model. To address this issue, this study refined the gravity field model in the spatial domain by constructing a residual terrain model. This study refined the XGM2019e-2159 gravity field model for the study area in Colorado, USA (108°W–104°W, 37°N–41°N). First, the residual terrain model (RTM) was constructed using the high-resolution terrain model SRTMV4.1 and the reference topography model Earth2014. Subsequently, the residual terrain model was discretized into regular grid prisms. Based on Newton's law of universal gravitation, the disturbance potential of each prism within a specified range at the computation point is calculated using the rectangular prism method in the spatial domain. Next, the disturbance potential is used to compute the RTM gravity anomalies and RTM vertical deflections. The results were verified using ground measured gravity anomaly data NGS99 and vertical deflection data GSVS17. The results show that, after RTM correction, the root mean square (RMS) of the difference between modeled and measured gravity anomalies decreased from 19.71 mGal to 13.80 mGal, and the effect of residual terrain correction improves as terrain undulation increases. The RMS of the North–South and East–West component differences between modeled and measured vertical deflections was 1.44″ and 1.82″ before correction, and decreased to 0.89″ and 0.93″ after RTM correction. Finally, a power spectral density analysis of the XGM2019e-2159 gravity anomaly and vertical deflection models before and after RTM correction showed a significant increase in short-wavelength energy after correction. These results indicate that RTM correction effectively compensated for truncation errors in the XGM2019e-2159 gravity anomaly and vertical deflection models, significantly improving data quality. Graphical Abstract