论确定全球大地水准面的斯托克斯方法

On Stokes' Approach for Determining Global Geoid

确定全球大地水准面最常用的方法是斯托克斯方法。然而,除了人们熟知的缺陷之外,斯托克斯方法还存在人们没有意识到的理论困难:当大地水准面位于参考椭球(WGS-84椭球)内部时,在大地水准面上及其与参考椭球面界定的区域中扰动位没有定义,当然在这部分区域也不调和。为了解决这一困难,可以选取一个包含在大地水准面内部的由4个基本参数唯一确定其外部正常重力位的参考椭球(简称内部椭球),其中心与WGS-84椭球的中心重合,其中的两个基本参数,旋转角速度和地心引力常数,与WGS-84椭球面的相同,另外两个参数,半长轴和扁率,如此选取,使得内部椭球产生的新的正常重力位在WGS-84椭球面上与大地水准面上的重力位W0相等。这样,传统的斯托克斯方法中存在的理论困难不复存在。

Stokes＇ approach is one of the most frequently used approaches for determining the global geoid. However, besides the well-known drawbacks, there still exist theoretical difficulties： in case that the geoid is below the surface of a reference ellipsoid, the disturbing potential function is not defined and neither harmonic in the whole region outside thegeoid. To take away these difficulties, we choose an inner ellipsoid enclosed by thegeoid, with four fundamental parameters, with its center coinciding with that of the ellipsoid, and two of which, the geocentric constant and rotation rate, coincide with the corresponding parameters of the ellipsoid, and the other two parameters, semi-major axis and flattening, are chosen in such a way that the new normal gravity potential generated by the inner ellipsoid has the constant W0 on the surface of the ellipsoid, where W0 is the geopotential constant on the geoid. By this new formulation, the disturbing potential function is harmonic in the whole region outside the geoid, and the difficulties existing in the conventional Stokes＇ aooroach vanish.