共查询到18条相似文献，搜索用时 109 毫秒
1.
借助以地心参考椭球面为边界面的第二大地边值问题的理论,基于Helmert空间的Neumann边值条件,给定Helmert扰动位的椭球解表达式,并详细推导第二类勒让德函数及其导数的递推关系、Helmert扰动位函数的椭球积分解以及类椭球Hotine积分核函数的实用计算公式,便于后续椭球域第二大地边值问题的实际研究。 相似文献
2.
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
3.
基于物理大地测量边值问题的解,利用一阶边界算子定义,推导重力异常Δg、单层密度μ、大地水准面高N,垂线偏差ε、扰动重力δg等扰动场元的解。利用球谐函数的正交特性,通过对核函数的算子运算,可以得到上述扰动场元的有关逆变换公式。相对经典物理大地测量公式应用的边界面条件,笔者将含有因子r的对应扰动场元反演关系的公式称为广义积分公式。针对常用的重力异常Δg、大地水准面高N,垂线偏差ε、扰动重力δg计算,重点分析它们之间的变换关系,给出利用某个选定扰动场元计算其他扰动场元的广义积分公式。同时,通过对积分边界面的讨论,分析经典公式与广义积分公式的差异和联系。最后,给出所有外部扰动场元与核函数映射的关系表。 相似文献
4.
大地水准面（数字高程基准）为国家高程基准的建立与维持提供了全新的思路。然而,受限于地形、重力数据等原因,高原地区高精度数字高程基准模型的建立一直是大地测量领域的难题。本文以格尔木地区为例,探讨了高原地区高精度数字高程基准模型的建立方法。首先,基于重力和地形数据,由第二类Helmert凝集法计算了格尔木重力似大地水准面。在计算中,考虑到高原地形对大地水准面模型的影响,采用了7.5″×7.5″分辨率和高精度的地形数据来恢复大地水准面短波部分的方法,以提高似大地水准面的精度。然后,利用球冠谐调和分析方法将GNSS水准与重力似大地水准面联合,建立了格尔木高精度数字高程基准模型。与实测的67个高精度GNSS水准资料比较,重力似大地水准面的外符合精度为3.0 cm,数字高程基准模型的内符合精度为2.0 cm。 相似文献
5.
高精度海岸带重力似大地水准面的若干问题讨论 总被引：1，自引：0，他引：1
针对海岸带多源重力数据和地形特点,通过理论分析和试算,对若干影响cm级似大地水准面确定的关键问题进行了剖析,得出了一些有益的结论。我国海岸带Molodensky一阶项对高程异常的贡献在10～30cm,需在Molodensky框架中精化重力似大地水准面;精细处理地形影响是提升多源重力场数据处理水平的重要途径;地球外空间不同高度、任意类型重力场参数的地形影响、地形补偿和地形Helmert凝聚算法可以统一;重力场数据处理中大地测量基准不一致的影响会随数据处理算法的不同而变化,在多源重力数据处理时此类影响易变得不可预测和控制;将地形Helmert凝聚理论引入Molodensky框架,可以解决以其他重力场参数(如扰动重力、垂线偏差等)为边界条件的似大地水准面精化问题。 相似文献
6.
基于重力场水平分量-垂线偏差对地形信息敏感的特点,根据边值理论由重力与地形数据确定格网垂线偏差模型,在此基础上,首先利用三维重力矢量-格网垂线偏差与格网重力异常,联合格网高程数据求得格网点间高程异常差,然后通过GPS/水准点的控制,构成紧密的几何条件,进行严密平差,从而获得高分辨率、高精度似大地水准面的数值模型。按照本文方法,利用我国6600多个GPS/水准点、1'×1'的格网垂线偏差、格网重力异常、格网高程数据,整体平差计算了我国陆海统一的似大地水准面模型,经GPS/水准点检核,全国似大地水准面的绝对精度达到了4 cm,相对精度优于7 cm。 相似文献
7.
本文针对海岸带多源重力数据和地形特点,通过理论分析和试算,对若干影响厘米级似大地水准面确定的关键问题进行了剖析,得出一些有益的结论。我国海岸带Molodensky一阶项对高程异常的贡献在10～30cm,需在Molodensky框架中精化重力似大地水准面;精细处理地形影响是提升多源重力场数据处理水平的重要途径;地球外空间不同高度、任意类型重力场参数的地形影响、地形补偿和地形Helmert凝聚算法可以统一;重力场数据处理中大地测量基准不一致的影响会随数据处理算法的不同而变化,在多源重力数据处理时此类影响易变得不可预测和控制;将地形Helmert凝聚理论引入Molodensky框架,可以解决以其他重力场参数（如扰动重力、垂线偏差等）为边界条件的似大地水准面精化问题。 相似文献
8.
利用测站点上的重力测量信息,根据Bruns公式研究了大地水准面高的变化特性,得出垂线偏差是大地水准面相对水准椭球面倾斜的线性改正,重力异常是大地水准面相对水准椭球面弯曲的线性改正,以及地形起伏效应构成大地水准面高的二阶变化等结论.在此基础上,提出了顾及测站点上重力场信息的大地水准面高的拟合方法,并分析了该方法相对于二次曲面函数拟合的优越性. 相似文献
9.
10.
11.
为解决世界各国高程基准差异的问题,提出联合卫星重力场模型、地面重力数据、GNSS大地高、局部高程基准的正高或正常高,按大地边值问题法确定局部高程基准重力位差的方法。首先推导了利用传统地面"有偏"重力异常确定高程基准重力位差的方法;接着利用改化Stokes核函数削弱"有偏"重力异常的影响,并联合卫星重力场模型和地面"有偏"重力数据,得到独立于任何局部高程基准的重力水准面,以此来确定局部高程基准重力位差;最后利用GNSS+水准数据和重力大地水准面确定了美国高程基准与全球高程基准W0的重力位差为-4.82±0.05 m2s-2。 相似文献
12.
E. W. Grafarend 《Journal of Geodesy》2001,75(7-8):363-390
In a comparison of the solution of the spherical horizontal and vertical boundary value problems of physical geodesy it is
aimed to construct downward continuation operators for vertical deflections (surface gradient of the incremental gravitational
potential) and for gravity disturbances (vertical derivative of the incremental gravitational potential) from points on the
Earth's topographic surface or of the three-dimensional (3-D) Euclidean space nearby down to the international reference sphere
(IRS). First the horizontal and vertical components of the gravity vector, namely spherical vertical deflections and spherical
gravity disturbances, are set up. Second, the horizontal and vertical boundary value problem in spherical gravity and geometry
space is considered. The incremental gravity vector is represented in terms of vector spherical harmonics. The solution of
horizontal spherical boundary problem in terms of the horizontal vector-valued Green function converts vertical deflections
given on the IRS to the incremental gravitational potential external in the 3-D Euclidean space. The horizontal Green functions
specialized to evaluation and source points on the IRS coincide with the Stokes kernel for vertical deflections. Third, the
vertical spherical boundary value problem is solved in terms of the vertical scalar-valued Green function. Fourth, the operators
for upward continuation of vertical deflections given on the IRS to vertical deflections in its external 3-D Euclidean space
are constructed. Fifth, the operators for upward continuation of incremental gravity given on the IRS to incremental gravity
to the external 3-D Euclidean space are generated. Finally, Meissl-type diagrams for upward continuation and regularized downward
continuation of horizontal and vertical gravity data, namely vertical deflection and incremental gravity, are produced.
Received: 10 May 2000 / Accepted: 26 February 2001 相似文献
13.
Geoid determination using one-step integration 总被引：1，自引：1，他引：0
P. Novák 《Journal of Geodesy》2003,77(3-4):193-206
A residual (high-frequency) gravimetric geoid is usually computed from geographically limited ground, sea and/or airborne gravimetric data. The mathematical model for its determination from ground gravity is based on the transformation of observed discrete values of gravity into gravity potential related to either the international ellipsoid or the geoid. The two reference surfaces are used depending on height information that accompanies ground gravity data: traditionally orthometric heights determined by geodetic levelling were used while GPS positioning nowadays allows for estimation of geodetic (ellipsoidal) heights. This transformation is usually performed in two steps: (1) observed values of gravity are downward continued to the ellipsoid or the geoid, and (2) gravity at the ellipsoid or the geoid is transformed into the corresponding potential. Each of these two steps represents the solution of one geodetic boundary-value problem of potential theory, namely the first and second or third problem. Thus two different geodetic boundary-value problems must be formulated and solved, which requires numerical evaluation of two surface integrals. In this contribution, a mathematical model in the form of a single Fredholm integral equation of the first kind is presented and numerically investigated. This model combines the solution of the first and second/third boundary-value problems and transforms ground gravity disturbances or anomalies into the harmonically downward continued disturbing potential at the ellipsoid or the geoid directly. Numerical tests show that the new approach offers an efficient and stable solution for the determination of the residual geoid from ground gravity data. 相似文献
14.
P. J. G. Teunissen 《Journal of Geodesy》1982,56(4):356-363
For computing the geodetic coordinates ϕ and γ on the ellipsoid one needs information of the gravity field, thus making it
possible to reduce the terrestrial observations to the reference surface. Neglect of gravity field data, such as deflections
of the vertical and geoid heights, results in misclosure effects, which can be described using the object of anholonomity. 相似文献
15.
A general scheme is given for the solution in a least-squares sense of the geodetic boundary value problem in a spherical,
constant-radius approximation, both uniquely and overdetermined, for a large class of observations. The only conditions are
that the relation of the observations to the disturbing potential is such that a diagonalization in the spectrum can be found
and that the error-covariance function of the observations is isotropic and homogeneous. Most types of observations used in
physical geodesy can be adjusted to fit into this approach. Examples are gravity anomalies, deflections of the vertical and
the second derivatives of the gravity potential.
Received: 3 November 1999 / Accepted: 25 September 2000 相似文献
16.
R. A. Hirvonen 《Journal of Geodesy》1962,36(1):69-71
Conclusion If we want to compute the height anomalies and the deflections of the vertical for a point where there are height differences
exceeding one kilometer in the neighborhood, a very dense net of gravity values must be observed, even when the topographic
corrections are used. In smoother regions, the simple Bouguer anomalies with a moderate spacing and with the estimation of
the mean heights give reliable results without further reductions. 相似文献
17.
E. Grafarend 《Journal of Geodesy》1973,47(3):237-260
Based on exterior calculus, the G. Frobenius integration theorem, holonomic and anholonomic Riemannian geometry, the typical
geodetic problems are summarized in a unified manner. The E. Cartan pseudotorsion of natural orthogonal coordinates causes
the misclosure of a closed three dimensional traverse. Natural coordinate differences are path dependent, anholonomic, nonintegrable,
nonunique, therefore. The geodetic pseudotorsion form depends only on the components of the A. Marussi tensor of gravity gradients.
A physically defined coordinate system can be found which is pseudotorsion free, whose coordinates are holonomic, integrable,
unique. The G. Frobenius transformation matrix is of rank three, explaining the number of three dimensions of an intrinsic
surface geometry. The matrix elements depend on either the second derivatives of the real gravity potential and the Euclidean
norm of its gravity vector or the second derivatives of the standard gravity potential, the Euclidean norm of its standard
gravity vector and the vertical deflections. Incomplete information of the earth's gravity field leads to the concept of boundary
value problems and satellite geodesy.
相似文献
18.
A new technique to determine geoid and orthometric heights from satellite positioning and geopotential numbers 总被引：1，自引：0，他引：1
L. E. Sjöberg 《Journal of Geodesy》2006,80(6):304-312
This paper takes advantage of space-technique-derived positions on the Earth’s surface and the known normal gravity field to determine the height anomaly from geopotential numbers. A new method is also presented to downward-continue the height anomaly to the geoid height. The orthometric height is determined as the difference between the geodetic (ellipsoidal) height derived by space-geodetic techniques and the geoid height. It is shown that, due to the very high correlation between the geodetic height and the computed geoid height, the error of the orthometric height determined by this method is usually much smaller than that provided by standard GPS/levelling. Also included is a practical formula to correct the Helmert orthometric height by adding two correction terms: a topographic roughness term and a correction term for lateral topographic mass–density variations. 相似文献