斯托克司函数逼近及截断误差估计

本文对高度异常及垂线偏差的截断误差进行了估计,导出了高阶截断系数的近似表达式。这些截断系数是振幅逐渐衰减的正弦函数,而且其振幅与斯托克司函数在界圆φ_0处的值密切相关。经分析认为,采用莫洛金斯基的最小平方逼近方法,将可使截断误差的数量级大为降低,值得在实际中采用。为了进一步提高截断系数的收敛速度,建议在最小平方逼近的基础上,附加上界圆φ_0处的边界条件,这样将较单纯的逼近为优。为此提出两种实施的方法:利用拉格朗日的条件极值和利用样条函数逼近。

APPROXIMATION OF STOKES' FUNCTION AND ESTIMATION OF TRUNCATION ERROR

In this paper, the truncation errors of the height anomaly and vertical deflection are estimated, and the approximate expressions of the higher order truncation coefficients are derived. These truncation coefficients are sinusoidal functions with a gradually attenuated amplitude, which is closely correlated with the value of Stokes' function at the cap radius ψ0. It is considered through analysis that, the order of the truncation error may he greatly decreased by using the method of Molodensky's least squares approximation. So it is worth adopting in practice. In order to further raise the convergence velocity of the truncation coefficents, it is suggested that, adding the boundary conditions at the cap radius ψ0 on the basis of the least squares approximation, the result would he even better. In this connection we propose two methods for implementation: to use Lagrange's conditional extremum and the spline function approximation.