Constructing Municipal Quasi-Geoid Model By Virtual Spherical Harmonic Method

As an important part of modern elevation datum,quasi-geoid model is an important hinge to realize the integration of plane and elevation survey.With the rapid development of digital cities,the construction of city-level high-precision quasi-geoid model is the most important.At present,the commonly used methods for constructing quasi-geoid model include geometric method,gravity method and composition method.Firstly,the high-order gravity field model is used to obtain the quasi-geoid in the region based on "removal and recovery" method,and then the quasi-geoid model in the region can be obtained by fitting with GNSS leveling data.So the choice of fitting method determines the precision of quasi-geoid model.In this paper,the virtual spherical harmonic method is introduced,the basic theory of the virtual spherical harmonic method is expounded,and the feasibility and superiority of the virtual spherical harmonic method in the construction of city-level quasi-geoid model are illustrated through theoretical analysis and numerical experiments.The main research contents of this paper are as follows:(1)The basic theory of regional quasi-geoid model is summarized,and various methods and theories of regional quasi-geoid are summarized.The experimental results show that the fifth degree polynomial fitting effect is the best.(2)Based on the basic theory of geoid determination by potential model,the expansion of perturbation potential on spherical harmonic function is deduced.The EGM2008 gravity field model is used to carry out numerical experiment of truncation error.The experimental results show that if centimeter level geoid is to be determined,the calculation order of model must reach more than 2000 order.Therefore,a high order gravity field model is needed to reduce the influence of model truncation error on calculation accuracy.Therefore,the EGM2008 gravity field model is used again to verify that the convergence of disturbance potential in latitude of China meets the requirement of centimeter level geoid calculation.At present,there are four common ultrahigh order gravity field models,namely EGM2008,EIGEN-6C4,XGM2019 e and SGG-UGM-2.Through numerical experiments,it is determined that e IGEN-6C4 gravity field model will be used in subsequent experiments.(3)By describing the basic theory of spherical cap harmonic method and analyzing the limitations of spherical cap harmonic method,the virtual spherical cap harmonic method is introduced.That is to use the idea of spherical crown harmonic mapping to transform the original spherical crown coordinate system into the new coordinate system,on the premise of ensuring the accuracy,the non-integral Legendre function can be replaced by the integral Legendre function for calculation.Taking Ningbo city as an example,the feasibility of virtual spherical harmonic method in constructing city-level quasi-geoid model is verified,and the superiority of virtual spherical harmonic method is highlighted by comparing with spherical crown harmonic method and fifth degree polynomial fitting method.(4)Taking Zhejiang Province and Chongqing city as examples,the applicability of virtual spherical harmonic method in constructing city-level quasi-geoid is verified from two aspects of urban scope and urban topography.In the process of experiment,it is found that the model accuracy is directly proportional to the model order,so when the virtual spherical harmonic method is used to approach the municipal geoid,enough data points should be obtained to participate in the calculation,and the accuracy can be improved by increasing the model order.