基于Stokes公式的扰动重力梯度张量无奇异计算模型  

A Non-singular Model for Computing the Gradient Tensor of Disturbing Gravity Based on Stokes Formula

作　　者：黄佳喜 张胜军 李厚朴[2] HUANG Jiaxi;ZHANG Shengjun;LI Houpu(92192 Troops,Ningbo 315122,China;Department of Navigation,Naval University of Engmeering,Wuhan 430033,China)

机构地区：[1]92192部队,浙江宁波315122 [2]海军工程大学导航工程系,湖北武汉430033

出　　处：《海洋测绘》2020年第1期19-23,共5页Hydrographic Surveying and Charting

基　　金：国家自然科学基金(41771487,41774021,41631072),湖北省杰出青年科学基金(2019CFA086)。

摘　　要：为有效解决Stokes积分奇异性问题,以扰动重力梯度张量的计算为例,采用双二次多项式插值和非奇异变换推导了解决计算点和临近格网点积分奇异的统一公式,分析了数据分辨率对中央区选取范围及积分奇异性的影响。选取某海域8°×8°。范围的重力异常数据进行数值实验,结果表明,该方法与传统去奇异方法在一些分量的差异可达数E,使用该方法更有助于提高计算精度。此外,针对不同分辨率的数据,合理选取中央区范围可有效避免计算结果产生舍入误差或奇异。In order to eliminate the singularity of Stokes integral,this paper presents an alternative method to compute the disturbing gravity gradient tensor.Unified formulas suitable for calculating point and nearing grid points with no singularity are derived by using biquadratic polynomial interpolation and non-singular transformation,and the innermost area effects caused by data resolution are also analyzed.Numerical tests based on gravity anomaly data at a sea area of 8°×8° show that the maximum differences between the proposed formulas and traditional methods respectively are several E in some components.The proposed formula is beneficial to improve the precision.In addition,with different data resolutions,a reasonable selection of the innermost area can effectively avoid rounding errors or singularities.

关 键 词：重力异常 扰动重力梯度张量 泰勒级数展开 双二次多项式 非奇异变换 

分 类 号：P223.6[天文地球—大地测量学与测量工程]