全张量重力梯度数据的谱表示方法

在文献「１」的基础上，进一步研究全张量重力梯度数据的全局和局部分量的广义球谐谱表示和轨道根数据表示，并给出了广义球谐函数与球谐函数这间的关系，从理论上得到了全张量重力梯度数据的描述方法和由全张量重力梯度网格数据恢复全球重力位谱系数的基本公式，本文对全张量重力梯度数据的谱表示和谱分析所做的工作，对由重力梯度张量的部分分量恢复全球重力位普系数有一定的参考价值。

Spectral Representation of the Full Gravity Tensor

This paper mainly focuses on the generalized spherical harmonic series representation of satellite gradiometry and on the generalized spherical harmonic analysis of satellite gradiometry. Using the form of generalized spherical harmonics, the combination of several components of satellite gradiometry can be represented as in series of generalized spherical harmonics, which are several subsets of larger group of orthogonal functions,i.e. the D functions. If the observations are preprocessed by averaging to form a constant radius, equiangular grid, we can easy obtain good formulae for high degree and order global spherical harmonic analysis from D functions as eigenfunctions. We conclude if we view upon the data set as being a set of observations distributed in some way in three dimensional space, a regular, global of observations in geocentric Cartesian system or in local geocentric spherical coordinate system is more convenient for recovery of spherical harmonic coefficients, and if we consider the data set as a time series, the observations given in subsequent points along a satellite orbit, the observations in geocentric Cartesian system or in orbital coordinate system is more convenient for computation of spherical harmonic coefficients.