共查询到10条相似文献，搜索用时 500 毫秒
1.
过去由于无法获得大地高数据,传统的第三大地边值问题采用重力异常作为边值条件。GNSS技术的发展为第二边值问题的研究带来了契机。研究比较成熟的第三边值理论无疑为第二边值问题提供了很好的参考和借鉴,对此开展将第三边值问题中计算似大地水准面的Molodensky理论方法应用于第二边值问题的研究。首先推导了Hotine算子与梯度算子的关系,然后给出了基于Molodensky理论求解第二边值问题的算法。实验结果表明,该算法与传统第三边值问题中Molodensky理论的边值解精度相当,说明基于Molodensky理论求解第二大地边值问题是完全可行的。 相似文献
2.
The goal of this paper is to present the finite element scheme for solving the Earth potential problems in 3D domains above
the Earth surface. To that goal we formulate the boundary-value problem (BVP) consisting of the Laplace equation outside the
Earth accompanied by the Neumann as well as the Dirichlet boundary conditions (BC). The 3D computational domain consists of
the bottom boundary in the form of a spherical approximation or real triangulation of the Earth’s surface on which surface
gravity disturbances are given. We introduce additional upper (spherical) and side (planar and conical) boundaries where the
Dirichlet BC is given. Solution of such elliptic BVP is understood in a weak sense, it always exists and is unique and can
be efficiently found by the finite element method (FEM). We briefly present derivation of FEM for such type of problems including
main discretization ideas. This method leads to a solution of the sparse symmetric linear systems which give the Earth’s potential
solution in every discrete node of the 3D computational domain. In this point our method differs from other numerical approaches,
e.g. boundary element method (BEM) where the potential is sought on a hypersurface only. We apply and test FEM in various
situations. First, we compare the FEM solution with the known exact solution in case of homogeneous sphere. Then, we solve
the geodetic BVP in continental scale using the DNSC08 data. We compare the results with the EGM2008 geopotential model. Finally,
we study the precision of our solution by the GPS/levelling test in Slovakia where we use terrestrial gravimetric measurements
as input data. All tests show qualitative and quantitative agreement with the given solutions. 相似文献
3.
混合边值问题的直接解算对于提高地球重力场模型的精度有着重要意义,本文主要讨论了量子力学中的维格纳3-i符号的计算方法以及利用3-i符号直接解算混合边值问题,模拟计算的结果表明,其解算精度是很高的。 相似文献
4.
就极空白对三类重力梯度边值问题球谐分析解的影响进行了定性探讨和定量分析,结果表明,基于球面边界的垂直-垂直重力梯度边值问题球谐分析解的零次项、垂直-水平重力梯度边值问题球谐分析解的一次项、水平-水平重力梯度边值问题球谐分析解的二次项受极空白问题的影响最为显著。 相似文献
5.
物理大地测量面临着越来越多的数据:高程异常、垂线偏差、重力异常、重力梯度等,因此出现了超定边值问题,本文采用求解偏微分方程最简单而又最常用的差分法,对这一问题进行了初步的研究。 相似文献
6.
Uniqueness and existence for the geodetic boundary value problem using the known surface of the earth 总被引：2，自引：0，他引：2
The geodetic boundary value problem using the known surface of the earth is defined and shown to have at most one solution.
Furthermore it is proved that the solution exists and that its harmonic part can be represented by the potential of a simple
layer under the sufficient condition that at the surface of the earth directions are known which lie differentially close
to the gradients of the gravity field. The advantages of this boundary value problem are outlined in comparison to the boundary
value problem formulated by Molodensky. 相似文献
7.
确定似大地水准面的Hotine-Helmert边值解算模型 总被引：1，自引：1，他引：0
空间大地测量技术的发展使大地高的观测成为可能,从而为第二大地边值问题的研究带来了新的机遇,本文对基于Helmert第二压缩法的第二边值问题(简称为Hotine-Helmert边值问题)展开研究。首先介绍了地形直接、间接影响的定义与算法,然后推导了Hotine-Helmert边值问题的解算模型。Hotine-Helmert边值理论无须计算地形压缩对重力的次要间接影响,因而较Stokes-Helmert边值理论更简单。此外,文中引入了一种低阶修正的Hotine截断核函数,该核函数较传统的截断核函数能有效地改善似大地水准面的解算精度。为了验证本文构建的Hotine-Helmert边值解算模型的有效性和实用性,本文将EIGEN-6C4模型的前360阶作为参考模型,利用Hotine-Helmert边值解算模型构建了我国中部地区6°×4°范围、1.5′×1.5′分辨率的重力似大地水准面,其精度达到±4.8 cm。 相似文献
8.
9.
Fernando Sansò 《Journal of Geodesy》1981,55(1):17-30
Summary The geodetic boundary value problem (g.b.v.p.) is a free boundary value problem for the Laplace operator: however, under suitable
change of coordinates, it can be transformed into a fixed boundary one. Thus a general coordinate choice problem arises: two
particular cases are more closely analyzed, namely the gravity space approach and the intrinsic coordinates (Marussi) approach. 相似文献
10.
Various formulations of the geodetic fixed and free boundary value problem are presented, depending upon the type of boundary data. For the free problem, boundary data of type astronomical latitude, astronomical longitude and a pair of the triplet potential, zero and first-order vertical gradient of gravity are presupposed. For the fixed problem, either the potential or gravity or the vertical gradient of gravity is assumed to be given on the boundary. The potential and its derivatives on the boundary surface are linearized with respect to a reference potential and a reference surface by Taylor expansion. The Eulerian and Lagrangean concepts of a perturbation theory of the nonlinear geodetic boundary value problem are reviewed. Finally the boundary value problems are solved by Hilbert space techniques leading to new generalized Stokes and Hotine functions. Reduced Stokes and Hotine functions are recommended for numerical reasons. For the case of a boundary surface representing the topography a base representation of the solution is achieved by solving an infinite dimensional system of equations. This system of equations is obtained by means of the product-sum-formula for scalar surface spherical harmonics with Wigner 3j-coefficients. 相似文献