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本文从地磁场的高斯(球谐)分析是“三维问题”出发,研究了高斯分析由于测点离散化而产生的一系列理论问题。包括:1.离散球谐函数的正交性;2.高斯分析在测点离散条件下的误差分析,给出了估计高斯系数误差的基本关系式,并由此分析了影响待求高斯系数误差的各种因素;3.测点离散条件下高斯系数的独立性,指出测点的分布和权重选取不满足离散球谐函数正交关系将影响高斯分析的“三维意义”。
In this paper, Gaussian (spherical harmonic) analysis of geomagnetic field is a “three-dimensional problem”, and a series of theoretical problems arising from the discretization of Gaussian analysis are studied. Including: 1. The orthogonality of the discrete spherical harmonic function; 2. The error analysis of the Gaussian analysis under the condition of the discrete points, gives the basic formula to estimate the Gaussian coefficient error, and then analyzes the influence of Gaussian coefficient error ; 3. The independence of Gaussian coefficient under the condition of discrete points of measurement points, pointing out that “the three-dimensional significance” of Gaussian analysis will be influenced by the distribution of measurement points and the failure of weight selection to satisfy the orthogonal relationship of discrete spherical harmonics.