| 应用格林积分直接以地面边值确定外部扰动重力场 |
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| 引用本文： | 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. |
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| 作者姓名： | 田家磊 吴晓平 李姗姗 |
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| 作者单位： | 信息工程大学地理空间信息学院, 河南 郑州 450001 |
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| 基金项目： | 国家863计划，国家自然科学基金 |
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| 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。
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| 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 |
| 收稿时间： | 2014-10-09 |
| 修稿时间： | 2014-12-16 |
A Di rect Approach to Determine the External Disturbing Gravity Field by Applying Green Integral with the Ground Boundary Value |
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| TIAN Jialei,WU Xiaoping,LI Shanshan.A Di rect 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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| Authors: | TIAN Jialei WU Xiaoping LI Shanshan |
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| Institution: | Institute of Geospatial Information, Information Engineering University, Zhengzhou 450001, ChinaAbstract |
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| Abstract: | By using the ground as the boundary,Molodensky problem usual ly gets the solution in form of series.Higher order terms reflect the correction between a smooth surface and the ground boundary. Appl ication difficulties arise from not only computational complexity and stabi l ity maintenance,but also data-intensiveness.Therefore,in this paper,starting from the appl ication 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 anomal ies 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. |
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| Keywords: | Green formula Stokes formula disturbing gravity gravity anomaly boundary value problem |
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