基于球面边值问题的点质量调和分析方法

Point mass harmonic analysis method based on spherical boundary value problem

对全球扰动点质量模型而言,可以假定虚拟扰动质点系位于地球内部同一Bjerhamar球面上,同时把边值界面视为球面.本文针对这一假设下所形成的线性方程组的系数阵,运用快速傅里叶变换的方法,得到了点质量模型解算中利用分块循环矩阵分解大型线性方程组的新方法.全球30′×30′扰动点质量模型259200阶方程组的解算分解为720个360阶方程组的解算,解决了点质量模型构建中大型线性方程组的稳定解算问题.推导了全球点质量模型与球谐位系数模型的转换关系,得到了一种基于球面边值问题的点质量调和分析方法.数值模拟试验表明,在适当选取点质量埋深度的情况下,本文的点质量调和分析方法较传统的调和分析方法精度更高.

The global disturbing point mass model is based on the assumption that the virtual disturbing point mass are located on the same Bjerhamar sphere inside the earth and at the same time the boundary is a sphere surface. From the assumption linear equations has to be solved for the point masses. The paper is aimed at the solution of point masses by decomposing huge linear equations in terms of blocked circular matrix using the Fast Fourier Transform method. For global 30′×30′ point masses, the solution was completed by decomposing a 259200-order linear equations into 720 360-order equations. The method solves the stability problem that occurs in the solution of huge linear equations for point mass modeling. The conversion from global point-mass model to spherical harmonic coefficient was made and a point mass harmonic analysis method based on spherical boundary value problem was derived. Numerical simulation proves that the proposed method is more accurate than conventional harmonic analysis method.