随机Poisson方程Dirichlet大地边值问题的随机积分解

Stochastic Poisson Equation Dirichlet Boundary Value Problem in Physical Geodesy

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。

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.