确定外部扰动重力场的改进直接积分方法  

Improved Direct Integral Methods Calculating Exterior Disturbing Gravity Field

作　　者：刘长弘 吴晓平[2] 田家磊 赵东明[2] LIU Changhong WU Xiaoping TIAN Jialei ZHAO Dongming(68029 Troops, Lanzhou 730030, China Information Engineering University, Zhengzhou 450001, China)

机构地区：[1]68029部队 [2]信息工程大学

出　　处：《测绘科学技术学报》2016年第6期561-565,571,共6页Journal of Geomatics Science and Technology

基　　金：国家青年自然科学基金项目(41404020)

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。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.

关 键 词：重力场 Stokes-Pizzetti积分 POISSON积分 扰动引力 奇异积分 eigen-6c2模型 

分 类 号：P223[天文地球—大地测量学与测量工程]