广义球谐函数定积分计算方法的改进

Inprovements on the Computation of Fixed Integral of Generalized Spherical Harmonics

运用球谐函数定积分的基本递推公式,推导了在重力场球谐综合与球谐分析中出现的广义球谐函数定积分的计算公式;给出了其适用于超高阶次的改良型递推公式。数值试验表明,该改良公式具有较高的计算精度和计算速度,解决了超高阶次广义球谐函数定积分计算的溢出问题,拓展了这类定积分的计算公式。他们的数值实现为利用位模型计算高分辨率扰动重力场元格网平均值、重力场球谐综合分析等奠定了基础。

This paper deduces some formulae about the fixed integral of generalized spherical harmonics, using basic recursive formula on integral of spherical harmonics, which often exist in the synthesis and analysis on spherical harmonics, and some modified formulae are presented. According to numeric tests, the underflow problems on the computing for fixed integral of generalized spherical harmonics are solved by the modified formulae and at the same time, these formulae improve the computing accuracy. The numerical realization of the kind of fixed integral is the numerical basis of high-resolution gridding mean value computation of different functionals of the disturbing gravity field using the Earth's gravity field model and spherical harmonic analysis and synthesis methods of the gravity field.