中文摘要：

针对Stokes-Pizzetti积分用于外部扰动重力场计算中从空中趋近地面时存在着不连续和积分奇异的问题，对该式进行了改进。改进式引入地面计算点处的重力异常，得到一个从地面到空中统一适用的公式，并且中和了在地面计算点处的奇异性。类似地，改进了的Stokes公式在用于大地水准面计算时积分的奇异性同样起到了改善作用。

英文摘要：

The results of calculating exterior disturbing gravity field using Stokes-Pizzetti integral will be singular and discontinuous when the points are reaching the ground. For this problem, the improved formula is put forward in the paper. The gravity anomaly of the calculating points on the ground is introduced, a unified and continuous integral formula from the outside of the sphere to the surface is obtained. Meanwhile, the singular results of the cal- culating points on the ground are improved obviously. Similarly, when the geoid is calculated using the improved Stokes integral formula, the singular results are also irnprnwd.