A new method for computing the ellipsoidal correction for Stokes's formula
A new method for computing the ellipsoidal correction for Stokes's formula
复制标题
斯托克斯公式椭球校正计算的新方法
DOI：
10.1007/s001900050280
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发表时间：
2000
影响因子：
4.4
通讯作者：
M. Sideris
中科院分区：
文献类型：
--
作者：
Z. L. Fei;M. Sideris
本文将Stokes公式从球面边界面推广到椭球面边界面。由Stokes公式求得的球面大地水准面高N0和椭球改正N1组成的椭球大地水准面高解，使相对大地水准面高误差从O（e2）减小到O（e4），在实际应用中可以忽略不计。椭球改正N1表示为关于球面大地水准面高度N0的积分与N0和前三个地球位系数的简单解析函数之和。积分中的核函数在原点处具有与原始斯托克斯函数相同的奇异度。通过与其他解的比较，证明了该解比Molodensky等人的解更有效。和莫里茨的解，并且当在已经评估了球面大地水准面高度N0的区域中进行椭球校正N1的评估时，它也比Martinec和Grafarend的解更有效。
Abstract. This paper generalizes the Stokes formula from the spherical boundary surface to the ellipsoidal boundary surface. The resulting solution (ellipsoidal geoidal height), consisting of two parts, i.e. the spherical geoidal height N0 evaluated from Stokes's formula and the ellipsoidal correction N1, makes the relative geoidal height error decrease from O(e2) to O(e4), which can be neglected for most practical purposes. The ellipsoidal correction N1 is expressed as a sum of an integral about the spherical geoidal height N0 and a simple analytical function of N0 and the first three geopotential coefficients. The kernel function in the integral has the same degree of singularity at the origin as the original Stokes function. A brief comparison among this and other solutions shows that this solution is more effective than the solutions of Molodensky et al. and Moritz and, when the evaluation of the ellipsoidal correction N1 is done in an area where the spherical geoidal height N0 has already been evaluated, it is also more effective than the solution of Martinec and Grafarend.