共查询到20条相似文献，搜索用时 31 毫秒
1.
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
2.
A formula for computing the gravity disturbance from the second radial derivative of the disturbing potential 总被引：6，自引：0，他引：6
J. Li 《Journal of Geodesy》2002,76(4):226-231
A formula for computing the gravity disturbance and gravity anomaly from the second radial derivative of the disturbing potential
is derived in detail using the basic differential equation with spherical approximation in physical geodesy and the modified
Poisson integral formula. The derived integral in the space domain, expressed by a spherical geometric quantity, is then converted
to a convolution form in the local planar rectangular coordinate system tangent to the geoid at the computing point, and the
corresponding spectral formulae of 1-D FFT and 2-D FFT are presented for numerical computation.
Received: 27 December 2000 / Accepted: 3 September 2001 相似文献
3.
Recurrence relations have been derived for truncation error coefficients of the extended Stokes' function and its partial
derivatives required in the computation of the disturbing gravity vector at any elevation above the earth's surface. The corresponding
formulae, the example of values of the truncation error coefficients for H=30.1 km and ψ0=30∘ and the estimations of truncation error are given in this article.
Received: 26 January 1996 / Accepted: 11 June 1997 相似文献
4.
四种改进积分法的低空扰动引力计算 总被引：1，自引：0，他引：1
针对Stokes积分方法计算扰动引力中计算点从空中趋近地面时存在积分奇异和不连续的问题,该文提出了去中央奇异点法、奇异点积分值修正法、中央格网加密算法和改进积分式法4种改进Stokes积分的计算公式,并进行了实验计算。计算结果表明:近地空间范围内,4种改进算法都能在一定程度上改进原始积分的奇异性问题;相同条件下,奇异点积分值修正法和改进积分式法计算精度最高,适宜于低空计算;改进积分式法通过理论推导,得到了从球外部到球面统一、连续且无奇异的改进Stokes积分公式,理论严谨。 相似文献
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ZHU Zhuowen HUANG Jinshui CAO Huasheng LUO Zhicai 《地球空间信息科学学报》2000,3(2):41-46
1 ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｖｅｎｔｉｏｎａｌｅｖａｌｕａｔｉｎｇｍｏｄｅｌｓｏｆｅｘｔｅｒｎａｌｇｒａｖｉ ｔａｔｉｏｎａｌｆｉｅｌｄｏｆｔｈｅｅａｒｔｈａｒｅｎｏｔｈｉｎｇｅｌｓｅｔｈａｎａｋｉｎｄｏｆｒｅａｌｉｚａｔｉｏｎｓｏｆｎｕｍｅｒｉｃａｌｓｏｌｕｔｉｏｎｓｔｏｇｅｏｄｅ ｔｉｃｂｏｕｎｄａｒｙｖａｌｕｅ ｐｒｏｂｌｅｍ .Ｉｎｔｈｅｓｅｎｓｅｏｆｌｉｎ ｅａｒｉｚａｔｉｏｎ ,ｇｅｏｄｅｔｉｃｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓａｒｅｒｅ ｄｕｃｅｄｔｏｅｘｔｅｒｎａｌｂｏｕｎｄ… 相似文献
8.
R. S. Mather 《Journal of Geodesy》1971,45(1):65-88
Summary The alternative harmonic representations of the disturbing potential, correct to the order of the flattening, are examined
and an example is given where the incorrect use of a spherical harmonic expansion can give rise to fallacious results. The
correct usage of the spherical harmonic expansion for the disturbing potential is given in the solution of the general surface
integral to define the indirect effect in the case of the non-regularised geoid. 相似文献
9.
For a special use a new modelling method of evaluating external disturbing potential is presented in this paper. Being different from classical methods in physical geodesy this method is grounded upon the theory of unified representation of gravitational field. The models created in this way are particularly satisfactory for a high-speed computation of gravitational field in low altitude because they take account of topographic effects and have their kernel functions with simple structure and weak singularity. 相似文献
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从最小二乘配置方法的基本原理出发,以我国某地区范围内1km分辨率的大地水准面高模型数据为例,根据实用公式计算了试验区大地水准面高的协方差值后,采用多项式函数模型和高斯函数模型分别拟合了该地区大地水准面高的局部协方差函数,并对试验区内18个检核点做了推估计算。根据推估值(Nfit)与实测值(NGPSL)的比较分析表明,虽然多项式协方差函数模型略优于高斯协方差函数模型,但它们都能以厘米级的精度拟合局部大地水准面,这表明了配置法用于精化厘米级大地水准面的有效性。 相似文献
12.
Summary Using a data set of 260 000 gravity anomalies it is shown that common characteristics for a local covariance function exist
in an area as large as Canada excluding the Rocky Mountains. After eliminating global features by referencing the data to
the GEM-10 satellite solution, the shape of the covariance function is remarkably consistent from one sample area to the next.
The determination of the essential parameters and the fitting of the covariance function are discussed in detail.
To test the reliability of the derived function, deflections of the vertical are estimated at about 230 stations where astrogeodetic
data are available. Results show that the standard error obtained from the discrepancies is about1″ for each component and that the error covariance matrix of least-squares collocation reflects this accuracy remarkably well. 相似文献
13.
R. Lehmann 《Journal of Geodesy》1997,71(9):533-540
Geodetic surface integrals play an important role in the numerical solution of geodetic boundary-value problems. In many
cases they can be evaluated using fast methods in the frequency domain (FFT). However, this is not possible in general, because
the domain of integration may be non-trivial (as is the surface of the Earth), the kernel function may not be of convolution
type, or the data distribution may be heterogeneous. Therefore, fast evaluation strategies are also required in the space
domain. They are more difficult to design because only one property is left where a more or less fast evaluation strategy
can be built upon: the potential type of the kernel function. Consequently, the idea is not to replace well-established frequency
domain techniques, but to supplement them. Our approach to this problem goes in two directions: (1) we use advanced cubature
methods where the integration nodes automatically densify in the vicinity of the evaluation points; (2) we use powerful computer
hardware, namely MIMD computers with distributed memory. This enables us to evaluate geodetic surface integrals of any practical
complexity in reasonable time and accuracy. This is shown in a numerical example.
Received: 7 May 1996 / Accepted:17 March 1997 相似文献
14.
Downward continuation and geoid determination based on band-limited airborne gravity data 总被引：4，自引：3，他引：4
The downward continuation of the harmonic disturbing gravity potential, derived at flight level from discrete observations
of airborne gravity by the spherical Hotine integral, to the geoid is discussed. The initial-boundary-value approach, based
on both the direct and inverse solution to Dirichlet's problem of potential theory, is used. Evaluation of the discretized
Fredholm integral equation of the first kind and its inverse is numerically tested using synthetic airborne gravity data.
Characteristics of the synthetic gravity data correspond to typical airborne data used for geoid determination today and in
the foreseeable future: discrete gravity observations at a mean flight height of 2 to 6 km above mean sea level with minimum
spatial resolution of 2.5 arcmin and a noise level of 1.5 mGal. Numerical results for both approaches are presented and discussed.
The direct approach can successfully be used for the downward continuation of airborne potential without any numerical instabilities
associated with the inverse approach. In addition to these two-step approaches, a one-step procedure is also discussed. This
procedure is based on a direct relationship between gravity disturbances at flight level and the disturbing gravity potential
at sea level. This procedure provided the best results in terms of accuracy, stability and numerical efficiency. As a general
result, numerically stable downward continuation of airborne gravity data can be seen as another advantage of airborne gravimetry
in the field of geoid determination.
Received: 6 June 2001 / Accepted: 3 January 2002 相似文献
15.
A data-driven approach to local gravity field modelling using spherical radial basis functions 总被引：3，自引：0，他引：3
We propose a methodology for local gravity field modelling from gravity data using spherical radial basis functions. The methodology
comprises two steps: in step 1, gravity data (gravity anomalies and/or gravity disturbances) are used to estimate the disturbing
potential using least-squares techniques. The latter is represented as a linear combination of spherical radial basis functions
(SRBFs). A data-adaptive strategy is used to select the optimal number, location, and depths of the SRBFs using generalized
cross validation. Variance component estimation is used to determine the optimal regularization parameter and to properly
weight the different data sets. In the second step, the gravimetric height anomalies are combined with observed differences
between global positioning system (GPS) ellipsoidal heights and normal heights. The data combination is written as the solution
of a Cauchy boundary-value problem for the Laplace equation. This allows removal of the non-uniqueness of the problem of local
gravity field modelling from terrestrial gravity data. At the same time, existing systematic distortions in the gravimetric
and geometric height anomalies are also absorbed into the combination. The approach is used to compute a height reference
surface for the Netherlands. The solution is compared with NLGEO2004, the official Dutch height reference surface, which has
been computed using the same data but a Stokes-based approach with kernel modification and a geometric six-parameter “corrector
surface” to fit the gravimetric solution to the GPS-levelling points. A direct comparison of both height reference surfaces
shows an RMS difference of 0.6 cm; the maximum difference is 2.1 cm. A test at independent GPS-levelling control points, confirms
that our solution is in no way inferior to NLGEO2004. 相似文献
16.
M. G. Sideris 《Journal of Geodesy》1996,70(8):470-479
Spectral methods have been a standard tool in physical geodesy applications over the past decade. Typically, they have been used for the efficient evaluation of convolution integrals, utilizing homogeneous, noise-free gridded data. This paper answers the following three questions:
- Can data errors be propagated into the results?
- Can heterogeneous data be used?
- Is error propagation possible with heterogeneous data?
17.
重力异常向上延拓全球积分模型在航空重力测量数据质量评估和向下延拓迭代计算等领域具有广泛的应用。为了消除积分核函数奇异性影响,需要对该模型进行基于积分恒等式的移去-恢复转换及全球积分域的分区改化处理。在此过程中,传统改化处理方法往往忽略了全球积分过渡到局域积分引起的积分恒等式偏差影响,从而导致不必要的计算模型误差,最终影响向上延拓计算结果的可靠性,甚至影响向下延拓迭代解算结果的稳定性。针对此问题,本文开展了重力异常向上延拓积分模型改化及向下延拓应用分析研究,依据实测数据保障条件和积分恒等式适用条件要求,导出了重力异常向上延拓积分模型的分步改化公式,提出了补偿传统改化模型缺陷的修正公式,并将最终的严密改化模型应用于重力异常向下延拓迭代解算。使用超高阶地球位模型EGM2008作为标准位场开展数值计算检验,分别对重力异常向上延拓分步改化模型的计算精度及在向下延拓迭代解算中的应用效果进行了检核评估,验证了采用严密改化模型的必要性和有效性。 相似文献
18.
J. F. Kirby 《Journal of Geodesy》2003,77(7-8):433-439
The geoid gradient over the Darling Fault in Western Australia is extremely high, rising by as much as 38 cm over only 2 km. This poses problems for gravimetric-only geoid models of the area, whose frequency content is limited by the spatial distribution of the gravity data. The gravimetric-only version of AUSGeoid98, for instance, is only able to resolve 46% of the gradient across the fault. Hence, the ability of GPS surveys to obtain accurate orthometric heights is reduced. It is described how further gravity data were collected over the Darling Fault, augmenting the existing gravity observations at key locations so as to obtain a more representative geoid gradient. As many of the gravity observations were collected at stations with a well-known GRS80 ellipsoidal height, the opportunity arose to compute a geoid model via both the Stokes and the Hotine approaches. A scheme was devised to convert free-air anomaly data to gravity disturbances using existing geoid models, followed by a Hotine integration to geoid heights. Interestingly, these results depended very weakly upon the choice of input geoid model. The extra gravity data did indeed improve the fit of the computed geoid to local GPS/Australian Height Datum (AHD) observations by 58% over the gravimetric-only AUSGeoid98. While the conventional Stokesian approach to geoid determination proved to be slightly better than the Hotine method, the latter still improved upon the gravimetric-only AUSGeoid98 solution, supporting the viability of conducting gravity surveys with GPS control for the purposes of geoid determination.
AcknowledgementsThe author would like to thank Will Featherstone, Ron Gower, Ron Hackney, Linda Morgan, Geoscience Australia, Scripps Oceanographic Institute and the three anonymous reviewers of this paper. This research was funded by the Australian Research Council. 相似文献
19.
New algorithms have been derived for computing terrain connections, all components of the attraction of the topography at
the topographic surface and the gradients of these attractions. These algorithms utilize fast Fourier transforms, but, in
contrast to methods currently in use, all divergences of the integrals are removed during the analysis. Sequential methods
employing a smooth intermediate reference surface have been developed to avoid the very large transforms necessary when making
computations at high resolution over a wide area.
A new method for the numerical solution of Molodensky's problem has been developed to mitigate the convergence difficulties
that occur at short wavelengths with methods based on a Taylor series expansion. A trial field on a level surface is continued
analytically to the topographic surface, and compared with that predicted from gravity observations. The difference is used
to compute a correction to the trial field and the process iterated. Special techniques are employed to speed convergence
and prevent oscillations.
Three different spectral methods for fitting a point-mass set to a gravity field given on a regular grid at constant elevation
are described. Two of the methods differ in the way that the spectrum of the point-mass set, which extends to infinite wave
number, is matched to that of the gravity field which is band-limited. The third method is essentially a space-domain technique
in which Fourier methods are used to solve a set of simultaneous equations. 相似文献
20.
J. Neumeyer F. Barthelmes O. Dierks F. Flechtner M. Harnisch G. Harnisch J. Hinderer Y. Imanishi C. Kroner B. Meurers S. Petrovic Ch. Reigber R. Schmidt P. Schwintzer H. -P. Sun H. Virtanen 《Journal of Geodesy》2006,79(10-11):573-585
Gravity recovery and climate experiment (GRACE)-derived temporal gravity variations can be resolved within the μgal (10?8 m/s 2) range, if we restrict the spatial resolution to a half-wavelength of about 1,500 km and the temporal resolution to 1 month. For independent validations, a comparison with ground gravity measurements is of fundamental interest. For this purpose, data from selected superconducting gravimeter (SG) stations forming the Global Geodynamics Project (GGP) network are used. For comparison, GRACE and SG data sets are reduced for the same known gravity effects due to Earth and ocean tides, pole tide and atmosphere. In contrast to GRACE, the SG also measures gravity changes due to load-induced height variations, whereas the satellite-derived models do not contain this effect. For a solid spherical harmonic decomposition of the gravity field, this load effect can be modelled using degree-dependent load Love numbers, and this effect is added to the satellite-derived models. After reduction of the known gravity effects from both data sets, the remaining part can mainly be assumed to represent mass changes in terrestrial water storage. Therefore, gravity variations derived from global hydrological models are applied to verify the SG and GRACE results. Conversely, the hydrology models can be checked by gravity variations determined from GRACE and SG observations. Such a comparison shows quite a good agreement between gravity variation derived from SG, GRACE and hydrology models, which lie within their estimated error limits for most of the studied SG locations. It is shown that the SG gravity variations (point measurements) are representative for a large area within the accuracy, if local gravity effects are removed. The individual discrepancies between SG, GRACE and hydrology models may give hints for further investigations of each data series. 相似文献