| 随机Poisson方程Dirichlet大地边值问题的随机积分解 |
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| 引用本文： | 黄金水,朱灼文.随机Poisson方程Dirichlet大地边值问题的随机积分解[J].武汉大学学报(信息科学版),2005,30(10):900-904. |
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| 作者姓名： | 黄金水 朱灼文 |
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| 作者单位： | 武汉大学测绘学院,武汉市珞喻路129号,430079;武汉大学地球空间环境与大地测量教育部重点实验室,武汉市珞喻路129号,430079 |
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| 基金项目： | 国家教育部留学回国人员科研启动基金资助项目，中国科学院动力大地测量学重点实验室(L0401)，武汉大学地球空间环境与大地测量教育部重点实验室(14699903242330409) |
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| 摘 要： | 利用随机微分方程理论,给出了随机Poisson方程Dirichlet大地边值问题的随机积分解,讨论了随机与确定边值问题间的关联。对应视为随机过程的函数,若采用确定性边值问题求解,不确定性影响将被直接带入最终解中;若采用随机积分解,则类似Gauss白噪声的影响将被滤掉,这对进一步提高重力场的求解精度具有重要影响。
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| 关 键 词： | 重力场 边值问题 随机微分方程 随机积分 Poisson方程 Dirichlet问题 |
| 文章编号： | 1671-8860(2005)10-0900-05 |
| 收稿时间： | 2005-07-28 |
| 修稿时间： | 2005年7月28日 |
Stochastic Poisson Equation Dirichlet Boundary Value Problem in Physical Geodesy |
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| HUANG Jinshui,ZHU Zhuowen.Stochastic Poisson Equation Dirichlet Boundary Value Problem in Physical Geodesy[J].Geomatics and Information Science of Wuhan University,2005,30(10):900-904. |
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| Authors: | HUANG Jinshui ZHU Zhuowen |
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| Institution: | 1 School of Geodesy and Geomaties, Wuhan University, 129 Luoyu Road, Wuhan 430079, China;2 Laboratory of Geospace Environment and Geodesy, Wuhan University, 129 Luoyu Road, Wuhan 430079, China |
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| Abstract: | In this paper, the stochastic properties of gravity field is discussed and formulated. Stochastic properties of the gravity field are revealed dominantly following the appearance of various kinds of high accuracy gravimetric measurements. The higher the accuracy of the measurements the more the incompatibility among them. These combining with the measuring errors indicate that the gravity field should be viewed as a stochastic process, therefore the stochastic boundary value problem is proposed and formulated for the traditional topic. With the aid of the theory of stochastic differential equation, the stochastic integral solution of the stochastic Poisson equation Dirichlet boundary value problem is given, and the relation of stochastic solution with traditional solution of general Poisson equation Dirichlet boundary value problem is also discussed in detail. The results show that if the uncertain factors or random ingredients are leaving out, the stochastic GBVP becomes the traditional classical GBVP. |
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| Keywords: | gravity field boundary value problem stochastic differential equation stochastic integral poisson equation dirichlet problem |
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