At present,there are still some difficulties in the theoretical derivation and numerical calculation of the Green's function of the spherical layered earth.First,the Green's function in the form of infinite Legendre series is derived by the spherical layered electromagnetic theory,and the recursive algorithm of the weight function of Legendre series is proposed.On this basis,the complex image method for solving spherical layered Green's function is presented,which transforms the summation of infinite series of Green's function into the superposition of complex image potential function.Moreover,the upper error limit of the algorithm is derived,and the accuracy of the method is verified by examples.In order to solve the numerical singularity and the extremely slow convergence of the earth-scale spherical layered Green's function,a solution based on multiple precision algorithm is proposed,which further proves the advantages of the complex image method in computing speed and accuracy.The method in this paper solves the theoretical and computational problems of spherical layered Green's function,and can be used as an effective solution to the spherical layered Green's function at the earth scale.
关键词
球形分层大地/格林函数/复镜像法/多精度算法/误差上限计算公式
Key words
spherical layered earth/Green's function/complex image method/multiple precision algorithm/upper bound of error formula
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