Research On The Refinement Method Of Local Earth Gravity Field Mode

Studying and determining the detailed structure of Earth’s gravity field and its temporal variations is one of the fundamental tasks in geodesy,with significant scientific importance for national fundamental surveying and mapping and the research and application of Earth sciences.After discussing the basic characteristics of the spectral and spatial domains of spherical radial basis functions in detail,this paper optimized the spectral bandwidth and horizontal position of the center of the spherical radial basis functions and compared the modeling effects of point mass kernel and Abel-Poisson kernel spherical radial basis functions.Furthermore,by using the regularized functional matching tracking algorithm,this paper attempted to approximate the local gravitational potential by combining spherical harmonic functions and Abel-Poisson kernel spherical radial basis functions.The main research content and conclusions of this paper are as follows:(1)To address the issue of the inability to achieve data adaptivity for the center horizontal position of spherical radial basis functions determined by the Reuter grid,an optimization design of the center horizontal position of spherical radial basis functions was carried out using a K-means method based on ISODATA.The numerical results in the Auvergne experimental area showed that the STD of residual gravity anomaly on the control points was reduced from 1.363 m Gal to1.291 m Gal,indicating a good optimization effect.(2)When modeling local gravity fields using remove-restore technique,the height anomaly obtained by using point mass kernel or Abel-Poisson kernel spherical radial basis functions analytical formulas are susceptible to long wavelength errors,and using shallow depths is not conducive to obtaining highprecision gravity anomalies.To address this issue,this paper optimized the spectral bandwidth of spherical radial basis functions using the turning point method.The numerical results show that the method does not significantly improve the accuracy of gravity anomaly solutions,but it does significantly improve the accuracy of height anomaly solutions.(3)This paper compares the modeling results of point mass kernel and AbelPoisson kernel spherical radial basis functions.According to the numerical results of the Auvergne data set,the modeling accuracy of the two kernel functions for gravity anomalies is similar,while the modeling results of Abel-Poisson kernel spherical radial basis functions for height anomalies are slightly better than those of point mass kernel.(4)The combination of two types of basis functions by the regularized functional matching tracking algorithm was used to approximate the local potential of gravitation.The numerical results show that the functional matching pursuit algorithm can utilize the characteristics of different types of basis functions and achieve adaptive selection of the basis functions.