In this paper, we use the spherical harmonic coefficients published in Parkinson's book (1983) to calculate the correction coefficients η1 and η2, which are needed in the application of the modified Z/H method.
The Walsh transform of spherical harmonic expansion and fast algorithm is presented. The differences between the Walsh transform and the Walsh-Fourier transform, and the Fourier transform are discussed. The results of the Walsh transform and the Fourier transform made by the geopotential coefficients of the Earth's gravity field model OSU81 are analysed.
And the spherical field and the circular field of displacement field are expressed by complex vector spherical harmonic functions, which provide the study of various kinetic effects with theoretical supports.
Spherical harmonic series have many of the same wonderful properties as Fourier series, but have lacked one important thing: a numerically stable fast transform analogous to the Fast Fourier Transform (FFT).
Without a fast transform, evaluating (or expanding in) spherical harmonic series on the computer is slow-for large computations probibitively slow.
Recently, fast and reliable algorithms for the evaluation of spherical harmonic expansions have been developed.
In this paper, a new numerical method, the coupling method of spherical harmonic function spectral and finite elements, for a unsteady transport equation is discussed, and the error analysis of this scheme is proved.
Spherical harmonic series solution of fields excited by vertical electric dipole in earth-ionosphere cavity