共查询到20条相似文献，搜索用时 603 毫秒
1.
The optimum expression for the gravitational potential of polyhedral bodies having a linearly varying density distribution 总被引：2，自引：0，他引：2
When topography is represented by a simple regular grid digital elevation model, the analytical rectangular prism approach
is often used for a precise gravity field modelling at the vicinity of the computation point. However, when the topographical
surface is represented more realistically, for instance by a triangular irregular network (TIN) model, the analytical integration
using arbitrary polyhedral bodies (the analytical line integral approach) can be implemented directly without additional data
pre-processing (gridding or interpolation). The analytical line integral approach can also facilitate 3-D density models created
for complex geometrical bodies. For the forward modelling of the gravitational field generated by the geological structures
with variable densities, the analytical integration can be carried out using polyhedral bodies with a varying density. The
optimal expression for the gravitational attraction vector generated by an arbitrary polyhedral body having a linearly varying
density is known. In this article, the corresponding optimal expression for the gravitational potential is derived by means
of line integrals after applying the Gauss divergence theorem. 相似文献
2.
A comparison of the tesseroid,prism and point-mass approaches for mass reductions in gravity field modelling 总被引：6，自引：3，他引：6
The calculation of topographic (and iso- static) reductions is one of the most time-consuming operations in gravity field
modelling. For this calculation, the topographic surface of the Earth is often divided with respect to geographical or map-grid
lines, and the topographic heights are averaged over the respective grid elements. The bodies bounded by surfaces of constant
(ellipsoidal) heights and geographical grid lines are denoted as tesseroids. Usually these ellipsoidal (or spherical) tesseroids
are replaced by “equivalent” vertical rectangular prisms of the same mass. This approximation is motivated by the fact that
the volume integrals for the calculation of the potential and its derivatives can be exactly solved for rectangular prisms,
but not for the tesseroids. In this paper, an approximate solution of the spherical tesseroid integrals is provided based
on series expansions including third-order terms. By choosing the geometrical centre of the tesseroid as the Taylor expansion
point, the number of non-vanishing series terms can be greatly reduced. The zero-order term is equivalent to the point-mass
formula. Test computations show the high numerical efficiency of the tesseroid method versus the prism approach, both regarding
computation time and accuracy. Since the approximation errors due to the truncation of the Taylor series decrease very quickly
with increasing distance of the tesseroid from the computation point, only the elements in the direct vicinity of the computation
point have to be separately evaluated, e.g. by the prism formulas. The results are also compared with the point-mass formula.
Further potential refinements of the tesseroid approach, such as considering ellipsoidal tesseroids, are indicated. 相似文献
3.
On the evaluation of the gravity effects of polyhedral bodies and a consistent treatment of related singularities 总被引：4，自引：2，他引：2
M. G. D’Urso 《Journal of Geodesy》2013,87(3):239-252
We show that the singularities which can affect the computation of the gravity effects (potential, gravity and tensor gradient fields) can be systematically addressed by invoking distribution theory and suitable formulas of differential calculus. Thus, differently from previous contributions on the subject, the use of a-posteriori corrections of the formulas derived in absence of singularities can be ruled out. The general approach presented in the paper is further specialized to the case of polyhedral bodies and detailed for a rectangular prism having a constant mass density. With reference to this last case, we derive novel expressions for the related gravitational field, as well as for its first and second derivative, at an observation point coincident with a prism vertex and show that they turn out to be more compact than the ones reported in the specialized literature. 相似文献
4.
基于Helmert第二压缩法进行边值解算时需要计算地形压缩对重力的直接影响和对（似）大地水准面的间接影响。计算近区直接、间接影响的传统积分算法仍是二重积分形式。该算法以网格中心点处的积分核作为网格积分核的平均值的计算模式在一定程度上引入了近似误差。另外,直接、间接影响的传统积分算法在中央区存在奇异性,需单独计算中央网格地形影响,因而增加了计算的复杂性。为此,本文推导了近区地形直接、间接影响的棱柱模型公式,一方面提高了地形影响的计算精度;另一方面中央区不存在奇异性,从而简化了计算过程。为避免棱柱模型存在的平面近似误差,可使用顾及地球曲率的棱柱模型算法计算地形影响。最后通过试验得出结论,在（似）大地水准面精度要求较高的应用中,应尽量使用顾及地球曲率的棱柱模型算法计算地形影响。 相似文献
5.
F. Wild-Pfeiffer 《Journal of Geodesy》2008,82(10):637-653
Topographic and isostatic mass anomalies affect the external gravity field of the Earth. Therefore, these effects also exist
in the gravity gradients observed, e.g., by the satellite gravity gradiometry mission GOCE (Gravity and Steady-State Ocean Circulation Experiment). The downward continuation of the gravitational signals is rather difficult because of the high-frequency behaviour
of the combined topographic and isostatic effects. Thus, it is preferable to smooth the gravity field by some topographic-isostatic
reduction. In this paper the focus is on the modelling of masses in the space domain, which can be subdivided into different
mass elements and evaluated with analytical, semi-analytical and numerical methods. Five alternative mass elements are reviewed
and discussed: the tesseroid, the point mass, the prism, the mass layer and the mass line. The formulae for the potential,
the attraction components and the Marussi tensor of second-order potential derivatives are provided. The formulae for different
mass elements and computation methods are checked by assuming a synthetic topography of constant height over a spherical cap
and the position of the computation point on the polar axis. For this special situation an exact analytical solution for the
tesseroid exists and a comparison between the analytical solution of a spherical cap and the modelling of different mass elements
is possible. A comparison of the computation times shows that modelling by tesseroids with different methods produces the
most accurate results in an acceptable computation time. As a numerical example, the Marussi tensor of the topographic effect
is computed globally using tesseroids calculated by Gauss–Legendre cubature (3D) on the basis of a digital height model. The
order of magnitude in the radial-radial component is about ± 8 E.U.
Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. 相似文献
6.
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7.
8.
给出了由地面重力数据计算外空扰动重力矢量的公式，并根据Wong and Gore截断理论给出了外区重力异常对计算点影响的公式。根据外空扰动重力与地面数据分辨率及其覆盖范围之间的关系，将重力异常分成不同频段、不同分辨率，分别计算了截断误差。利用全球重力位模型，计算出不同频段的截断误差，并给出了各频段相应的积分半径。对于模拟和检验航空矢量重力数据有一定的参考价值。 相似文献
9.
Anthony A. Vassiliou 《Journal of Geodesy》1988,62(1):41-58
The aliasing effects in local gravity field computations are presented in this study. First the relation between the power
spectral density of a 2-D continuous signal and its corresponding sampled version is derived. Then the power spectral density
of the aliasing errors related to non band-limited signals is derived. Finally the variance of these aliasing errors is computed
using gravity anomalies at different grid spacings. This computation prerequires some known gravity anomaly power spectral
density model. The model used in this study corresponds to a second-order Gauss-Markov covariance function for the anomalous
potential.
Editor’s notice: Comments on this paper will follow in the next issue of Bulletin Géodésique. 相似文献
10.
海洋重力场特征参数在地球重力场逼近计算和海上测量优化设计中具有重要的应用价值。基于卫星测高重力在海域具有覆盖范围广且分布均匀的独特优势，提出了利用最新卫星测高重力数据集开展海洋重力场特征统计模型计算和分析的研究方案，给出了代表误差和协方差函数模型参数的计算公式，定义并研究了海洋广义布格重力异常的变化特征，提出了等精度和非等精度拟合经验协方差函数的计算模型。利用中国近海及西太平洋海区超过50万个5'×5'方块的1'×1'网格卫星测高重力异常数据，首次计算得到一组有代表性的中国周边海域重力场特征统计模型参数，较好地揭示了海洋重力场有别于陆地重力场的变化特征，利用海面船测重力数据对计算结果进行了可靠性检核，提出了相应的模型参数修正方案和使用建议。 相似文献
11.
There exist three types of convolution formulae for the efficient evaluation of gravity field convolution integrals, i.e., the planar 2D convolution, the spherical 2D convolution and the spherical 1D convolution. The largest drawback of both the planar and the spherical 2D FFT methods is that, due to the approximations in the kernel function, only inexact results can be achieved. Apparently, the reason is the meridian convergence at higher latitudes. As the meridians converge, the ??,?λ blocks do not form a rectangular grid, as is assumed in 2D FFT methods. It should be pointed out that the meridian convergence not only leads to an approximation error in the kernel function, but also causes an approximation error during the implementation of 2D FFT in computer. In order to meet the increasing need for precise determination of the vertica deflections, this paper derives a more precise planar 2D FFT formula for the computation of the vertical deflections. After having made a detailed comparison between the planar and the spherical 2D FFT formulae, we find out the main source of errors causing the loss in accuracy by applying the conventional spherical 2D FFT method. And then, a modified spherical 2D FFT formula for the computation of the vertical deflections is developed in this paper. A series of numerical tests have been carried out to illustrate the improvement made upon the old spherical 2D FFT. The second part of this paper is to discuss the influences of the spherical harmonic reference field, the limited capsize, and the singular integral on the computation of the vertical deflections. The results of the vertical deflections over China by applying the spherical 1D FFT formula with different integration radii have been compared to the astro-observed vertical deflections in the South China Sea to obtain a set of optimum deflection computation parameters. 相似文献
12.
The gravitational potential and its derivatives for the prism 总被引：24，自引：12，他引：12
As a simple building block, the right rectangular parallelepiped (prism) has an important role mostly in local gravity field
modelling studies when the so called flat-Earth approximation is sufficient. Its primary (methodological) advantage follows
from the simplicity of the rigorous and consistent analytical forms describing the different gravitation-related quantities.
The analytical forms provide numerical values for these quantities which satisfy the functional connections existing between
these quantities at the level of numerical precision applied. Closed expressions for the gravitational potential of the prism
and its derivatives (up to the third order) are listed for easy reference.
Received: 18 August 1999 / Accepted: 15 June 2000 相似文献
13.
重力测量数据存在地形数据产生的高频分量的影响,高精度地形数据正演重力梯度也能较好地反映重力局部高频特征。为获得高精度重力梯度数据,实现基准梯度数据库精确快速构建,研究了利用数字高程模型正演重力梯度的频率域快速计算方法,推导出基于余弦变换的Parker正演重力梯度理论公式。数值实验结果表明,余弦变换频率域正演方法平均绝对误差可达到0.5E左右精度要求,与傅里叶变换正演方法相比误差可减小3dB左右,与棱柱法等空间域正演方法相比,该方法计算规模小,速度优势明显。 相似文献
14.
H. Sünkel 《Journal of Geodesy》1981,55(1):31-40
GSPP is a computer program system which has been developed for the purposes of automatically determining and representing
gravity field surfaces like the geoid, the field of gravity anomalies or deviations of the vertical at prescribed altitude,
etc. The system processes gravity field information given by a heterogeneous set of linear functionals of the anomalous potential
superimposed by noise, and provides automatically gravity field surfaces in terms of profiles, contour maps and/or 3-dimensional
representations.
The solution is generally based on least-squares collocation; for a homogeneous data set, a simple weighted average interpolation
is available as well. Based on the given data, surface function values at the grid points of a regular rectangular grid are
predicted. The representation of the surfaces is smooth using bicubic spline functions.
GSPP has a control unit which performs all necessary decision processes and such reduces the user’s decision making to a minimum.
The system has been designed for geodetic purposes only; however, because of its versatility and flexibility it presents itself
also for applications in other geosciences. 相似文献
15.
广义球谐函数定积分计算方法的改进 总被引：1，自引：0，他引：1
运用球谐函数定积分的基本递推公式，推导了在重力场球谐综合与球谐分析中出现的广义球谐函数定积分的计算公式；给出了其适用于超高阶次的改良型递推公式。数值试验表明，该改良公式具有较高的计算精度和计算速度，解决了超高阶次广义球谐函数定积分计算的溢出问题，拓展了这类定积分的计算公式。他们的数值实现为利用位模型计算高分辨率扰动重力场元格网平均值、重力场球谐综合分析等奠定了基础。 相似文献
16.
在重力聚焦反演基础上提出多尺度源网聚焦反演算法.首先,对源网进行粗网格剖分,用共轭梯度法求解粗网格源网模型的聚焦解,直到拟合差下降至设定的数值;然后,将粗网格得到的密度映射到细网格;最后,以细网格模型为初始模型,进一步迭代直到拟合差下降至符合反演要求.模型试验结果显示,相比于固定源网反演,多尺度源网聚焦反演迭代的总耗时... 相似文献
17.
A density interface modeling method using polyhedral representation is proposed to construct 3-D models of spherical or ellipsoidal interfaces such as the terrain surface of the Earth and applied to forward calculating gravity effect of topography and bathymetry for regional or global applications. The method utilizes triangular facets to fit undulation of the target interface. The model maintains almost equal accuracy and resolution at different locations of the globe. Meanwhile, the exterior gravitational field of the model, including its gravity and gravity gradients, is obtained simultaneously using analytic solutions. Additionally, considering the effect of distant relief, an adaptive computation process is introduced to reduce the computational burden. Then features and errors of the method are analyzed. Subsequently, the method is applied to an area for the ellipsoidal Bouguer shell correction as an example and the result is compared to existing methods, which shows our method provides high accuracy and great computational efficiency. Suggestions for further developments and conclusions are drawn at last. 相似文献
18.
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
19.
A synthetic Earth Gravity Model Designed Specifically for Testing Regional Gravimetric Geoid Determination Algorithms 总被引：1，自引：0，他引：1
I. Baran M. Kuhn S. J. Claessens W. E. Featherstone S. A. Holmes P. Vaníček 《Journal of Geodesy》2006,80(1):1-16
A synthetic [simulated] Earth gravity model (SEGM) of the geoid, gravity and topography has been constructed over Australia specifically for validating regional gravimetric geoid determination theories, techniques and computer software. This regional high-resolution (1-arc-min by 1-arc-min) Australian SEGM (AusSEGM) is a combined source and effect model. The long-wavelength effect part (up to and including spherical harmonic degree and order 360) is taken from an assumed errorless EGM96 global geopotential model. Using forward modelling via numerical Newtonian integration, the short-wavelength source part is computed from a high-resolution (3-arc-sec by 3-arc-sec) synthetic digital elevation model (SDEM), which is a fractal surface based on the GLOBE v1 DEM. All topographic masses are modelled with a constant mass-density of 2,670 kg/m3. Based on these input data, gravity values on the synthetic topography (on a grid and at arbitrarily distributed discrete points) and consistent geoidal heights at regular 1-arc-min geographical grid nodes have been computed. The precision of the synthetic gravity and geoid data (after a first iteration) is estimated to be better than 30 μ Gal and 3 mm, respectively, which reduces to 1 μ Gal and 1 mm after a second iteration. The second iteration accounts for the changes in the geoid due to the superposed synthetic topographic mass distribution. The first iteration of AusSEGM is compared with Australian gravity and GPS-levelling data to verify that it gives a realistic representation of the Earth’s gravity field. As a by-product of this comparison, AusSEGM gives further evidence of the north–south-trending error in the Australian Height Datum. The freely available AusSEGM-derived gravity and SDEM data, included as Electronic Supplementary Material (ESM) with this paper, can be used to compute a geoid model that, if correct, will agree to in 3 mm with the AusSEGM geoidal heights, thus offering independent verification of theories and numerical techniques used for regional geoid modelling.Electronic Supplementary Material Supplementary material is available in the online version of this article at http://dx.doi.org/10.1007/s00190-005-0002-z 相似文献
20.
Gravity field terrain effect computations by FFT 总被引：2，自引：2，他引：2
René Forsberg 《Journal of Geodesy》1985,59(4):342-360
The widespread availability of detailed gridded topographic and bathymetric data for many areas of the earth has resulted
in a need for efficient terrain effect computation techniques, especially for applications in gravity field modelling. Compared
to conventional integration techniques, Fourier transform methods provide extremely efficient computations due to the speed
of the Fast Fourier Transform (FFT. The Fourier techniques rely on linearization and series expansions of the basically unlinear terrain effect integrals, typically
involving transformation of the heights/depths and their squares. TheFFT methods will especially be suited for terrain reduction of land gravity data and satellite altimetry geoid data.
In the paper the basic formulas will be outlined, and special emphasis will be put on the practial implementation, where a
special coarse/detailed grid pair formulation must be used in order to minimize the unavoidable edge effects ofFFT, and the special properties ofFFT are utilized to limit the actual number of data transformations needed. Actual results are presented for gravity and geoid
terrain effects in test areas of the USA, Greenland and the North Atlantic. The results are evaluated against a conventional
integration program: thus, e.g., in an area of East Greenland (with terrain corrections up to10 mgal), the accuracy ofFFT-computed terrain corrections in actual gravity stations showed anr.m.s. error of0.25 mgal, using height data from a detailed photogrammetric digital terrain model. Similarly, isostatic ocean geoid effects in the
Faeroe Islands region were found to be computed withr.m.s. errors around0.03 m 相似文献