Stochastic Poisson Equation Dirichlet Boundary Value Problem in Physical Geodesy

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.