Research On Determining The Global Earth Gravity Model From Satellite Gravity Gradients

This dissertation mainly performs research in the theory, methods and applied computation models of determining global gravity model from observations of satellite gravity gradients. The central ideas and new standpoints are lists as follows:(1) With theories pertinent to satellite gradiometry, the principles of satellite gradiometry are dissertated in detail. Besides, the different expressions of satellite gravity gradients tensor in several curvilinear coordinate systems and the transformation methods between any two of them are given.(2) The establishment of the observation equations both in orbit plane and spherical are based on the spherical harmonic and orbital element expressions of the earth potential, gravitation vector and gravitation tensor, which also makes great contributions to generalized spherical harmonics and non-singular formulae of correlated integrals. Then, the harmonic analysis and spherical harmonic synthesis formulae are obtained, and simulations are made.(3) Generalized torus harmonic analysis is established based on the satellite gravity gradient tensor. With the support of gravity gradient data, the mapping relations from sphere to torus and that between Fourier analysis and harmonic analysis on sphere are emphasized. The torus harmonic analysis is modified, thus the generalized torus harmonic analysis which could deal with the gravitational vector and gradient tensor is obtained.(4) The point mass harmonic analysis which is put forward and established based on satellite gravity gradient tensor improves the theory of point mass model. Through the special differential coefficient operation relation between the calculated point and the fluxional points in spheric polar coordinate system, global point mass model is established based on satellite gravitation gradient tensor components. The way of partitioned recurrence matrices which is put forward to divide huge linear equations solves the bottleneck problem in the stability solution of global point mass model. And then the least square solution is attained. The applied formula of point mass harmonic analysis is obtained with the spherical harmonic expressions of point mass. Besides, spectrum-based point mass harmonic analysis is also discussed.(5)Line mass harmonic analysis, which could effectively overcome the disadvantages of spectrum-based point mass harmonic analysis and point mass harmonic analysis, is brought forward.(6)Further research is made to modify the complex LSC harmonic analysis based on gravity gradient tensor. Complete covariance of gravity gradient tensors and that of tensors and gravity potential coefficients are presented. With the observational data of gravity gradient which are in grid form with the same longitude interval, covariance of gravitational potential and disturbed gravity gradient has partitioned Toeplitz recurrence structure, and then FFT is used to reduce its degree. With the support of complex collocation, the vector and tensor LSC harmonic analysis which is based on gravity gradient tensor is further discussed.(7)The theory on the determination of the gravity model based on gravity gradient tensor invariant is established, which could overcome the bias caused by satellite attitude errors effectively. Furthermore, observational equations and the solutions of invariants both in sphere approximation and considering J2 item are discussed in detail. Finally, simulation experiments of space-wise such as generalized torus harmonic analysis are made to validate the efficiency and feasibility of gradient tensor invariants.