Refining Regional Geoid Based On The Spherical Cap Harmonic Method

In this paper,we analysis the problem to approach regional geoid with high precision and high resolution by using the spherical cap harmonic theory based on the potential theory.The article first introduces the basic theory of refinement region(quasi)geoid.Some refinement methods and fitting methods are summarized.Then we discuss the problem of Gravity field theory used to calculate the geoid.Based on the EGM2008 model,the application of refinement regional quasi geoid is analyzed.Based on the theory of Gravity field theory,the theory of spherical cap harmonics is analyzed.The data calculated by the EGM2008 model as the observed value,the error approximation experiment of four different regional geoid is carried out by using the spherical cap harmonics method and the applicability of the spherical cap harmonics method are summarized.Finally,the spherical cap harmonic model is adjusted based on the method of spherical cap mapping and the adjusted method is used to approximate the high precision and high resolution geoid.The main research contents of this paper are as follows:(1)The basic theory and method of refining the regional(similar)geoid are summarized,the flow chart of some methods are also summarized,and several fitting methods are analyzed.(2)Calculation of geoid theory is studied based on gravity field model.Based on the EGM2008 model and the downloaded high-resolution grid data,Jiangxi geoid and Jiangxi geoid height fluctuation in longitude(latitude)direction were calculated,The structure of regional geoid in Jiangxi Province is analyzed.The formula for calculating the spatial resolution of centimeter level geoid is derived.It is calculated that the centimeter level resolution of the geoid is 7 ?.(3)In order to calculate the regional geoid theory for the spherical cap harmonic method,the advantages of the spherical harmonic method are demonstrated.Taking the regional geoid calculated by EGM2008 as the observation value,four regional approximation numerical experiments with spherical cap harmonicwere carried out.The article summarizes the applicability of the spherical cap harmonic method.(4)Based on the idea of spherical cap mapping,the ASHA technique is used to improve the spherical cap harmonic model,and the integer-degree associated Legendre functions is used to replace the non-integral orderassociated.Legendre functions to overcome the order of the spherical cap harmonic model.The geoid of the corresponding spherical cap was calculated using EGM2008 as the observed value.Through the approximation experiments of three order in four radius area of spherical cap,the adjusted spherical cap harmonic method can be used to calculate the high precision and high resolution regional geoid.