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Starting from the fact that Gaussian (spherical harmonic) analysis of geomagnetic field is a ’three-dimensional problem’, some theoretical problems of Gaussian analysis arising from the discretization observational points are studied in this paper. Firstly, the orthogonality of discrete harmonic functions is discussed. Secondly, the basic relationship for estimating the errors of Gaussian coefficients to be determined in Gaussian analysis of discrete observational points is obtained by using perturbation method, and from this relationship the various factors influencing the errors of Gaussian coefficients to be determined and their relationship are studied. Finally, the investigation of the independence of Gaussian coefficients in discrete Gaussian analysis points out that if the distribution of observational points and the choice of weights make the orthogonality relations not satisfied, ’three-dimensional significance’ of Gaussian analysis will be impaired.
Starting from the fact that Gaussian (spherical harmonic) analysis of geomagnetic field is a ’three-dimensional problem’, some theoretical problems from the discretization observational points are studied in this paper. First, the orthogonality of discrete harmonic functions is discussed. Secondly, the basic relationship for estimating the errors of Gaussian coefficients to be determined in Gaussian analysis of discrete observational points is obtained by using perturbation method, and from this relationship the various factors influencing the errors of Gaussian coefficients to be determined and their relationship Finally, the investigation of the independence of Gaussian coefficients in discrete Gaussian analysis points out that if the distribution of observational points and the choice of weights make the orthogonality relations not satisfied, ’three-dimensional significance’ of Gaussian analysis will be impaired .