应用格林积分直接以地面边值确定外部扰动重力场

doi:10.11947/j.AGCS.2015.20140516

测绘学报 ›› 2015, Vol. 44 ›› Issue (11): 1189-1195.doi: 10.11947/j.AGCS.2015.20140516

应用格林积分直接以地面边值确定外部扰动重力场

田家磊, 吴晓平, 李姗姗

信息工程大学地理空间信息学院, 河南郑州 450001

收稿日期:2014-10-09 修回日期:2014-12-16 出版日期:2015-11-20 发布日期:2015-11-25
作者简介:田家磊(1988-),男,博士生,研究方向为物理大地测量。E-mail:tianjialei3037@163.com
基金资助:
国家863计划(2013AA122502);国家自然科学基金(41274029; 41304022)

A Direct Approach to Determine the External Disturbing Gravity Field by Applying Green Integral with the Ground Boundary Value

TIAN Jialei, WU Xiaoping, LI Shanshan

Institute of Geospatial Information, Information Engineering University, Zhengzhou 450001, ChinaAbstract

Received:2014-10-09 Revised:2014-12-16 Online:2015-11-20 Published:2015-11-25
Supported by:
The National High-tech Research and Development Program of China(863 Program)(No. 2013AA122502);The National Natural Science Foundation of China(Nos. 4127402941304022)

摘要/Abstract

摘要： 以地面为边界的Molodensky问题通常得到的是级数形式的解,高阶项体现了地面边值到某一光滑面上的改正,在应用中不仅遇到计算的复杂性、稳定性问题,也存在对数据密集要求的困难。本文从推求外部扰动重力场的应用出发,将格林公式用于数字地形面,在忽略水平分量的积分影响的情况下,得到以地面重力异常和高程异常差为边值确定外部扰动位的表达式,其核函数分别为距离倒数和Poisson核。该方法不需要对地面数据进行延拓处理,且核函数形式简洁,适于外部扰动重力场的随机计算。

关键词: 格林公式, 斯托克斯公式, 扰动重力, 重力异常, 边值问题

Abstract: By using the ground as the boundary, Molodensky problem usually gets the solution in form of series. Higher order terms reflect the correction between a smooth surface and the ground boundary. Application difficulties arise from not only computational complexity and stability maintenance, but also data-intensiveness. Therefore, in this paper, starting from the application of external gravity disturbance, Green formula is used on digital terrain surface. In the case of ignoring the influence of horizontal component of the integral, the expression formula of external disturbance potential determined by boundary value consisted of ground gravity anomalies and height anomaly difference are obtained, whose kernel function is reciprocal of distance and Poisson core respectively. With this method, there is no need of continuation of ground data. And kernel function is concise, and suitable for the stochastic computation of external disturbing gravity field.

Key words: Green formula, Stokes formula, disturbing gravity, gravity anomaly, boundary value problem

中图分类号:

P223

田家磊, 吴晓平, 李姗姗. 应用格林积分直接以地面边值确定外部扰动重力场[J]. 测绘学报, 2015, 44(11): 1189-1195.

TIAN Jialei, WU Xiaoping, LI Shanshan. A Direct Approach to Determine the External Disturbing Gravity Field by Applying Green Integral with the Ground Boundary Value[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(11): 1189-1195.

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应用格林积分直接以地面边值确定外部扰动重力场

A Direct Approach to Determine the External Disturbing Gravity Field by Applying Green Integral with the Ground Boundary Value

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