Quasi-Geoid Refinement Based On Modified Stokes And Hotine Formulas In Jilin Province

The geoid is a gravity equipotential surface that coincides with mean sea level and extends into the interior of the continents.It reflects information about the internal material structure and density distribution of the Earth,and plays an important role in geodesy,geophysics,earth science and other fields.As the starting surface for China’s elevation datum,a high-precision quasi-geoid combined with Global Navigation Satellite System(GNSS)can replace traditional elevation surveying methods,accelerating the construction of digital China and providing enormous economic,social,and scientific benefits.The calculation of the geoid is the solution to the boundary-value problem of the Earth,and it involves determining the shape of the Earth and its external gravity field based on ground gravity observations data.The Hotine and Stokes formulas,which solve the second and third boundary-value problems of the Earth,are applied to model the geoid.Using Hotine and Stokes formulas with modified kernel functions combined with the earth gravity field model can effectively alleviate the impact of missing gravity signals in distant areas and reduce truncation errors.In this study,XGM2019 e,EIGEN-6C4,and SGG-UGM-2 gravity field models were used as reference models,and freeair gravity data were used as integration sources.Stokes and Hotine formulas with deterministic(WG,VK)and stochastic(biased,unbiased,optimal)modifications were used to compute the quasi-geoid of Jilin Province.The selection of parameters is crucial in geoid modeling.This study analyzed the effects of different parameters(fixed parameters,modification limits,integration radius,and terrestrial gravity error variance)on the global root mean square error(RMSE)of the geoid modeling using various modification methods and selected appropriate parameters based on the trend of the global root mean square error.This paper evaluated the accuracy of the quasi-geoid calculation results based on the expected global root mean square error and highprecision GPS/leveling data checks from both theoretical and practical perspectives.Considering that terrain is one of the factors affecting the precision of geoid modeling,we divided Jilin Province into plain and mountainous regions according to differences in terrain and evaluated the accuracy separately.The parameter analysis results show that,in the low-degree part,the coefficient errors of the EIGEN-6C4 model are significantly larger than those of the XGM2019 e and SGG-UGM-2 models,resulting in its relatively larger global root mean square error.The error variance of the modification limits and terrestrial gravity data has a significant impact on the global RMSE,reaching the level of centimeters,and the integration radius has a relatively small impact on it.The expected global RMSE calculation shows that,theoretically,the SGG-UGM-2 model has the highest modeling accuracy,followed by XGM2019 e,and the EIGEN-6C4 model has the lowest modeling accuracy.There is no significant difference in modeling the global RMSE using Stokes and Hotine formulas.Stochastic modification is better than deterministic modification,and unbiased and optimal modifications perform the best.Adopting GPS/leveling data test to evaluate the accuracy of the quasi-geoid,there is a significant improvement compared with the original model.The corresponding highest accuracies of the original models XGM2019 e,EIGEN-6C4,and SGG-UGM-2 in Jilin Province are 5.37,5.79,and 6.07 cm,respectively,and after refinement,the highest accuracies are 3.08,3.06,and 2.91 cm,respectively.The precision test results of the partition show that the accuracy of each model is significantly better in the plain area than in the mountainous area.The highest accuracies in the plain area and the mountainous area are 2.05 cm and 3.53 cm,respectively.Among them,the original model SGG-UGM-2 has the worst accuracy in the mountainous area,but after refinement,its geoid model performs the best in the mountainous area.Based on different reference gravity field models,deterministic and stochastic modifications perform inconsistently in different study areas.There is no substantial difference in accuracy between Stokes and Hotine formulas in both plain and mountainous areas.The reference gravity field model and the kernel function modification method have a significant impact on the modeling accuracy of the geoid,and in practical calculations,it is necessary to select different combinations of reference models and kernel function modification methods.