共查询到17条相似文献，搜索用时 282 毫秒
1.
于锦海 《测绘科学技术学报》2003,20(1):7-9
研究了球界面下卫星测高问题的解法,利用有限逼近方法得到了下列结论:若陆地部分是球冠,则卫星测高问题的解可以转换成关于球谐级数位系数的线性方程组.同时证明了常用的Stokes问题、Dirichlet问题、Neumann问题可以看成卫星测高问题的特殊情况. 相似文献
2.
卫星测高问题的球谐级数解法 总被引：3，自引：0，他引：3
研究了球界面下卫星测高问题的解法，利用有限逼近方法得到了下列结论：若陆地部分是球冠，则卫星测高问题的解可以转换成关于球谐级数位系统的线性方程组。同时证明了常用的Stokes问题、Dirichlet问题、Neumann问题可以看成卫星测高问题的特殊情况。 相似文献
3.
李建成 《武汉大学学报(信息科学版)》2003,28(6):655-657
基于修改的Poisson积分 ,首先给出了球面扰动位向上延拓的积分表达式。在此基础上 ,由微分原理得出了球外部空间Neumann逆问题的解式 ,利用物理大地测量学的基本微分方程 ,导出了球外部空间的逆Stokes公式 ,并对这两类积分公式的核函数进行了讨论 相似文献
4.
Poisson重力边值问题 总被引：1，自引：0，他引：1
提出了Ｐｏｉｓｓｉｏｎ重力边值问题,即关于扰动位的Ｐｏｉｓｓｏｎ方程的Ｓｔｏｋｅｓ问题和Ｎｅｕｍａｎｎ问题。作为导引,先研究Ｐｏｉｓｓｏｎ方程的Ｄｉｒｉｃｈｌｅｔ问题,再分别引入一种辅助函数,将Ｓｔｏｋｅｓ问题和Ｎｅｕｍａｎｎ问题改化为Ｄｉｒｉｃｈｌｅｔ问题,从而立即得到它们的积分解,最终解式表现为两部分叠加,一部分仪与边界观测相关,另一部分对地形测量的响应,为研究地形测量对外部重力场和大地水准面 相似文献
5.
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。 相似文献
6.
重力场Dirichlet问题解的随机Poisson积分表示 总被引：1，自引：0，他引：1
在球近似下，顾及到庞大复杂的边界数据，借助重力场随机模型框架，直接给出了调和重力随机场Dirichlet问题解的随机积分表达式——随机Poisson积分式，并讨论了这个广义随机泛函与经典Poisson积分表达式的关系。 相似文献
7.
星载SAR水下地形和水深遥感的最佳雷达系统参数模拟 总被引：12，自引：1，他引：11
根据星载合成孔径雷达 (SAR)浅海水下地形和水深成像机理 ,建立了浅海水下地形和水深雷达后向散射截面仿真模型。该模型包括奈维 斯托克斯方程、谱作用量平衡方程和雷达后向散射模式。利用该模型仿真结果 ,探讨了不同波段 (P、L、C和X)、不同极化 (VV和HH)和不同入射角 (2 0°— 70°)的星载SAR测量浅海水下地形和水深的能力。研究结果表明 ,浅海水下地形和水深遥感的最佳波段为P波段 ,L波段次之 ,C波段比X波段要好一些。VV极化SAR的测量能力要强于HH极化。 2 0°— 40°是星载SAR测量浅海水下地形和水深的最佳入射角范围。 相似文献
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10.
地形对确定高精度局部大地水准面的影响 总被引：16，自引：0，他引：16
以计算香港大地水准面为例 ,着重研究了以下几点 :①DTM的分辨率对地形改正的影响 ;②质量柱体地形模型与质量线地形模型对计算地形改正的差异 ;③采用Helmert凝聚改正法 ,计算地形对大地水准面的间接影响 ;④比较经典Stokes Helmert方法与Sj¨oberg方法计算地形对大地水准面的影响 相似文献
11.
S. Ritter 《Journal of Geodesy》1998,72(2):101-106
The ellipsoidal Stokes problem is one of the basic boundary-value problems for the Laplace equation which arises in physical
geodesy. Up to now, geodecists have treated this and related problems with high-order series expansions of spherical and spheroidal
(ellipsoidal) harmonics. In view of increasing computational power and modern numerical techniques, boundary element methods
have become more and more popular in the last decade. This article demonstrates and investigates the nullfield method for
a class of Robin boundary-value problems. The ellipsoidal Stokes problem belongs to this class. An integral equation formulation
is achieved, and existence and uniqueness conditions are attained in view of the Fredholm alternative. Explicit expressions
for the eigenvalues and eigenfunctions for the boundary integral operator are provided.
Received: 22 October 1996 / Accepted: 4 August 1997 相似文献
12.
R. G. Bellaire 《Journal of Geodesy》1977,51(2):149-161
The boundary condition and solution of a Dirichlet problem on the upper half space are treated as random processes. It is
shown that the first-and second-order statistics of the solution to this problem are completely determined by the corresponding
statistics of the boundary condition. The mean of the solution is the mean of the process on the boundary. The correlation
function of the solution above the boundary is related to its value on the boundary by a Poisson integral formula.
formerly of The Analytic Sciences Corporation, Reading, Massachusetts 01867.
This research was supported in part by the Naval Weapons Laboratory, Dahlgren, Virginia, under Contract N00178-70-C-0200. 相似文献
13.
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
14.
Construction of Green's function to the external Dirichlet boundary-value problem for the Laplace equation on an ellipsoid of revolution 总被引：1，自引：0，他引：1
Green's function to the external Dirichlet boundary-value problem for the Laplace equation with data distributed on an ellipsoid
of revolution has been constructed in a closed form. The ellipsoidal Poisson kernel describing the effect of the ellipticity
of the boundary on the solution of the investigated boundary-value problem has been expressed as a finite sum of elementary
functions which describe analytically the behaviour of the ellipsoidal Poisson kernel at the singular point ψ = 0. We have
shown that the degree of singularity of the ellipsoidal Poisson kernel in the vicinity of its singular point is of the same
degree as that of the original spherical Poisson kernel.
Received: 4 June 1996 / Accepted: 7 April 1997 相似文献
15.
应用文献 [1 ]推导出的球谐系数与椭球谐系数的转换关系 ,给出了椭球界面下Neumann边值问题的积分解 相似文献
16.
球内Dirichlet问题解及其应用 总被引：4，自引：2，他引：2
本文基于球内调和函数的Ｄｉｒｉｃｈｌｅｔ问题的球谐解式,推导了球内调和空间的Ｐｏｉｓｓｏｎ积分,将其应用于航空重力测量数据的向下延拓时,积分边界面是空中面,边界值是空中重力异常或纯重力异常,推求地面重力异常可直接积分计算,而勿需像球外Ｐｏｉｓｓｏｎ积分那样迭代求解积分方程。 相似文献
17.
J. Li 《Journal of Geodesy》2005,79(1-3):64-70
Integral formulas are derived which can be used to convert the second-order radial gradient of the disturbing potential, as boundary values, into the disturbing potential, gravity anomaly and the deflection of the vertical. The derivations are based on the fundamental differential equation as the boundary condition in Stokes’s boundary-value problem and the modified Poisson integral formula in which the zero and first-degree spherical harmonics are excluded. The rigorous kernel functions, corresponding to the integral operators, are developed by the methods of integration. 相似文献