Research Of Methods Of Spherical Harmonic Analysis Of The Earth's Gravity Field

As a necessary procedure in modeling the Earth's gravity field based on all kinds of observation data,the harmonic analysis on a sphere or ellipsoidal surface is also a necessary technique that needs further researching.In this paper, torus harmonic analysis method of the Earth's gravity field is researched. The new system of self-consistent harmonic analysis of the Earth's gravity field is built up in which the Legendre function as well as their derivatives are obtained. The main work is listed as follows:1. Algorithms of the generalized spherical harmonics and their fixed integral are researched. A lot of computing methods of the fully normalized associated Legendre function are detailedly discussed. Advantages and disadvantages of these methods are compared in three aspects: numerical efficiency, numerical precision and arithmetic overflow. Algorithmic formulae of generalized spherical harmonics and their fixed integrals, which are used in harmonic analysis and synthesis, are deduced. A set of improved algorithms used for harmonic analysis of very high degree and order are put forward, which solves the problem on arithmetic overflow.2. This paper studies and establishes torus harmonic analysis method of recovering the Earth's gravity field with all kinds of gravity observation data. With the application of the mapping relationship from a sphere to a torus and the method of B-Spline interpolation, this paper obtains a relation of Fourier analysis and harmonic analysis on the torus, and realizes the self-consistent harmonic analysis of the Earth's gravity field.3. The between-every-other-order recursive methodology of the fixed integrals concerning spherical harmonics which appears in harmonic analysis and synthsis are formulated. The realization of efficient and stable computation of the fixed integrals makes it become true that we can transform the Fourier spectrum to spherical spectrum of different functionals of the disturbing gravity field.4. The author develops a set of computing software about harmonic synthesis and harmonic analysis based on the methods this thesis puts forward. It is proved that the recovery of the Earth's gravity field with higher accuracy and faster speed is possible using the torus harmonic analysis by the simulations, which also verifies the validity and practicability of the method presented in the paper.