Let S be the surface of the earth, S<sub>1</sub> its part occupied by land, S<sub>2</sub> its part by sea, andr means a distance of a variable point to the geocenter. As a new kind of geodeticb...Let S be the surface of the earth, S<sub>1</sub> its part occupied by land, S<sub>2</sub> its part by sea, andr means a distance of a variable point to the geocenter. As a new kind of geodeticboundary value problem （BVP）, the mixed BVP with respect to disturbing potential展开更多
A new solving method for Laplace equation with over-determined geodetic boundary conditions is pro- posed in the paper, with the help of minimizing some kinds of quadratic functional in calculus of variation. At first...A new solving method for Laplace equation with over-determined geodetic boundary conditions is pro- posed in the paper, with the help of minimizing some kinds of quadratic functional in calculus of variation. At first, the so-called variational solution for over-determined geodetic boundary value problem is defined in terms of principles in calculus of variation. Then theoretical properties related with the solution are derived, especially for its existence, uniqueness and optimal approximation. And then the computational method of the solution is discussed, and its expression is exhibited under the case that all boundaries are spheres. Finally an arithmetic example about EGM96 gravity field model is given, and the computational results show that the proposed method can efficiently raise accuracy to deal with gravity data. In all, the variational solution of over-determined geodetic boundary value problem can not only fit to deal with many kinds of gravity data in a united form, but also has strict mathematical basements.展开更多
How to determine the earth’s external gravity field with the accuracy of O(T2) by making use of GPS data and gravity values measured on the earth’s surface is dealt with in this paper. There are two main steps: to e...How to determine the earth’s external gravity field with the accuracy of O(T2) by making use of GPS data and gravity values measured on the earth’s surface is dealt with in this paper. There are two main steps: to extend these measured values on the earth’s surface onto the reference ellipsoid at first and then to seek for the integral solution of the external Neumann problem outside the ellipsoid. In addition, the corresponding judging criteria of accuracy to solve the GPS-gravity boundary value problem are established. The integral solution given in the paper not only contains all frequency-spectral information of the gravity field with the accuracy of O(T 2), but is also easily computed. In fact, the solution has great significance for both theory and prac- tice.展开更多
A higher step of study on the GOBVPs (geodetic overdetermined boundary value problems) is reached in this paper, which covers the proposal of new concept of pseudo-solutionon the GOBVPs, its strict definition of mathe...A higher step of study on the GOBVPs (geodetic overdetermined boundary value problems) is reached in this paper, which covers the proposal of new concept of pseudo-solutionon the GOBVPs, its strict definition of mathematics and solving principle. The so-called pseudosolution is a harmonical function having the property of optimum approximating the given boundary values in the sense of a relevant norm. Analytical expressions of the pseudo-solutions of two typical OBVPs for biboundary surfaces in physical geodesy, the problems S—D and S—N, are obtained, which is elegant and concise in form and convenient for practice, by using the derived formulas of norms of fractional exponential Sobolev's spaces in the case of spherical biboundary. The pseudo-solution is composed of two parts: the major is the solution of classical Stokes' problem, playing control role in field representation; the minor is correction term, serving the function of synergist and precision of the gravity field. Besides, a general case of the GOBVP is also dealt with.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘Let S be the surface of the earth, S<sub>1</sub> its part occupied by land, S<sub>2</sub> its part by sea, andr means a distance of a variable point to the geocenter. As a new kind of geodeticboundary value problem （BVP）, the mixed BVP with respect to disturbing potential
基金Supported by the National Natural Science Foundation of China (Grant No. 40374001)
文摘A new solving method for Laplace equation with over-determined geodetic boundary conditions is pro- posed in the paper, with the help of minimizing some kinds of quadratic functional in calculus of variation. At first, the so-called variational solution for over-determined geodetic boundary value problem is defined in terms of principles in calculus of variation. Then theoretical properties related with the solution are derived, especially for its existence, uniqueness and optimal approximation. And then the computational method of the solution is discussed, and its expression is exhibited under the case that all boundaries are spheres. Finally an arithmetic example about EGM96 gravity field model is given, and the computational results show that the proposed method can efficiently raise accuracy to deal with gravity data. In all, the variational solution of over-determined geodetic boundary value problem can not only fit to deal with many kinds of gravity data in a united form, but also has strict mathematical basements.
基金supported by Chinese Science Fund(Grant No.40374001).
文摘How to determine the earth’s external gravity field with the accuracy of O(T2) by making use of GPS data and gravity values measured on the earth’s surface is dealt with in this paper. There are two main steps: to extend these measured values on the earth’s surface onto the reference ellipsoid at first and then to seek for the integral solution of the external Neumann problem outside the ellipsoid. In addition, the corresponding judging criteria of accuracy to solve the GPS-gravity boundary value problem are established. The integral solution given in the paper not only contains all frequency-spectral information of the gravity field with the accuracy of O(T 2), but is also easily computed. In fact, the solution has great significance for both theory and prac- tice.
基金Project supported by the National Natural Science Foundation of China.
文摘A higher step of study on the GOBVPs (geodetic overdetermined boundary value problems) is reached in this paper, which covers the proposal of new concept of pseudo-solutionon the GOBVPs, its strict definition of mathematics and solving principle. The so-called pseudosolution is a harmonical function having the property of optimum approximating the given boundary values in the sense of a relevant norm. Analytical expressions of the pseudo-solutions of two typical OBVPs for biboundary surfaces in physical geodesy, the problems S—D and S—N, are obtained, which is elegant and concise in form and convenient for practice, by using the derived formulas of norms of fractional exponential Sobolev's spaces in the case of spherical biboundary. The pseudo-solution is composed of two parts: the major is the solution of classical Stokes' problem, playing control role in field representation; the minor is correction term, serving the function of synergist and precision of the gravity field. Besides, a general case of the GOBVP is also dealt with.
