VK—Stokes核函数的性能分析

Performance Analysis of the VK- Stokes Kernel Function

为了获取高精度大地水准面、克服重力数据不能实现全球覆盖所带来的问题，常应用修正Stokes核函数。它能改善标准Stokes核函数特性，使其在较小积分范围内达到较高计算精度。本文基于地球重力场位系数模型EGM2008，分析了修正核函数（VK—Stokes）特性及其远区截断误差。计算分析表明：在近区0．2°积分半径内，VK—Stokes与标准Stokes和WG—Stokes核函数值接近；但随着积分半径增加，VK—Stokes较标准Stokes核函数收敛更快，且其远区截断误差数值也相对较小。由此可见，应用VK—Stokes核函数，既可实现在较小积分范围内提高计算能力，又能抑制其远区截断误差影响。

In order to get high accuracy of the geoid and to overcome the problem that the gravity data cannot cover the whole world, modified Stokes kernel function is often used to deal with the difficulty. It can improve Stokes kernel function char- acteristics and make it achieve high accuracy in the small integral range. The characteristics and the far - region truncation error of the VK - Stokes kernel function are analyzed in this paper based on the gravity potential coefficient of the model EGM2008. The results show that in the near- region of the integral radius 0.2° ,the VK- Stokes value is close to that of Stokes and WG - Stokes. But with the increasing of integral radius, VK - Stokes converges faster than Stokes and the truncation error of the VK - Stokes kernel function is relatively, small in the far - region. Thus it shows the VK - Stokes not only improves the ability of computation in the small integral range, but also controls the truncation error in the far- region.