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1.
Hussein Abd-Elmotaal 《Journal of Geodesy》1993,67(2):86-90
The representation of the topography is usually made by digital height models and digital density models. Therefore, one can produce the so-called digital Moho model (DMM) by applying a certain isostatic hypothesis. The attraction of such compensating masses is deducted. Also, some special cases are treated. The effect of neglecting the height of the computational point only on calculating the attraction of the compensating masses is studied. The results show that the height of the computational point must be taken into account on calculating the attraction of the compensating masses specially for high mountainous areas. 相似文献
2.
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
3.
The separation between the reference surfaces for orthometric heights and normal heights—the geoid and the quasigeoid—is typically
in the order of a few decimeters but can reach nearly 3 m in extreme cases. The knowledge of the geoid–quasigeoid separation
with centimeter accuracy or better, is essential for the realization of national and international height reference frames,
and for precision height determination in geodetic engineering. The largest contribution to the geoid–quasigeoid separation
is due to the distribution of topographic masses. We develop a compact formulation for the rigorous treatment of topographic
masses and apply it to determine the geoid–quasigeoid separation for two test areas in the Alps with very rough topography,
using a very fine grid resolution of 100 m. The magnitude of the geoid–quasigeoid separation and its accuracy, its slopes,
roughness, and correlation with height are analyzed. Results show that rigorous treatment of topographic masses leads to a
rather small geoid–quasigeoid separation—only 30 cm at the highest summit—while results based on approximations are often
larger by several decimeters. The accuracy of the topographic contribution to the geoid–quasigeoid separation is estimated
to be 2–3 cm for areas with extreme topography. Analysis of roughness of the geoid–quasigeoid separation shows that a resolution
of the modeling grid of 200 m or less is required to achieve these accuracies. Gravity and the vertical gravity gradient inside
of topographic masses and the mean gravity along the plumbline are modeled which are important intermediate quantities for
the determination of the geoid–quasigeoid separation. We conclude that a consistent determination of the geoid and quasigeoid
height reference surfaces within an accuracy of few centimeters is feasible even for areas with extreme topography, and that
the concepts of orthometric height and normal height can be consistently realized and used within this level of accuracy. 相似文献
4.
A new method is presented for the computation of the gravitational attraction of topographic masses when their height information is given on a regular grid. It is shown that the representation of the terrain relief by means of a bilinear surface not only offers a serious alternative to the polyhedra modeling, but also approaches even more smoothly the continuous reality. Inserting a bilinear approximation into the known scheme of deriving closed analytical expressions for the potential and its first-order derivatives for an arbitrarily shaped polyhedron leads to a one-dimensional integration with – apparently – no analytical solution. However, due to the high degree of smoothness of the integrand function, the numerical computation of this integral is very efficient. Numerical tests using synthetic data and a densely sampled digital terrain model in the Bavarian Alps prove that the new method is comparable to or even faster than a terrain modeling using polyhedra. 相似文献
5.
Comparisons between high-degree models of the Earth’s topographic and gravitational potential may give insight into the quality and resolution of the source data sets, provide feedback on the modelling techniques and help to better understand the gravity field composition. Degree correlations (cross-correlation coefficients) or reduction rates (quantifying the amount of topographic signal contained in the gravitational potential) are indicators used in a number of contemporary studies. However, depending on the modelling techniques and underlying levels of approximation, the correlation at high degrees may vary significantly, as do the conclusions drawn. The present paper addresses this problem by attempting to provide a guide on global correlation measures with particular emphasis on approximation effects and variants of topographic potential modelling. We investigate and discuss the impact of different effects (e.g., truncation of series expansions of the topographic potential, mass compression, ellipsoidal versus spherical approximation, ellipsoidal harmonic coefficient versus spherical harmonic coefficient (SHC) representation) on correlation measures. Our study demonstrates that the correlation coefficients are realistic only when the model’s harmonic coefficients of a given degree are largely independent of the coefficients of other degrees, permitting degree-wise evaluations. This is the case, e.g., when both models are represented in terms of SHCs and spherical approximation (i.e. spherical arrangement of field-generating masses). Alternatively, a representation in ellipsoidal harmonics can be combined with ellipsoidal approximation. The usual ellipsoidal approximation level (i.e. ellipsoidal mass arrangement) is shown to bias correlation coefficients when SHCs are used. Importantly, gravity models from the International Centre for Global Earth Models (ICGEM) are inherently based on this approximation level. A transformation is presented that enables a transformation of ICGEM geopotential models from ellipsoidal to spherical approximation. The transformation is applied to generate a spherical transform of EGM2008 (sphEGM2008) that can meaningfully be correlated degree-wise with the topographic potential. We exploit this new technique and compare a number of models of topographic potential constituents (e.g., potential implied by land topography, ocean water masses) based on the Earth2014 global relief model and a mass-layer forward modelling technique with sphEGM2008. Different to previous findings, our results show very significant short-scale correlation between Earth’s gravitational potential and the potential generated by Earth’s land topography (correlation +0.92, and 60% of EGM2008 signals are delivered through the forward modelling). Our tests reveal that the potential generated by Earth’s oceans water masses is largely unrelated to the geopotential at short scales, suggesting that altimetry-derived gravity and/or bathymetric data sets are significantly underpowered at 5 arc-min scales. We further decompose the topographic potential into the Bouguer shell and terrain correction and show that they are responsible for about 20 and 25% of EGM2008 short-scale signals, respectively. As a general conclusion, the paper shows the importance of using compatible models in topographic/gravitational potential comparisons and recommends the use of SHCs together with spherical approximation or EHCs with ellipsoidal approximation in order to avoid biases in the correlation measures. 相似文献
6.
L. E. Sjöberg 《Journal of Geodesy》2007,81(5):345-350
This study emphasizes that the harmonic downward continuation of an external representation of the Earth’s gravity potential
to sea level through the topographic masses implies a topographic bias. It is shown that the bias is only dependent on the
topographic density along the geocentric radius at the computation point. The bias corresponds to the combined topographic
geoid effect, i.e., the sum of the direct and indirect topographic effects. For a laterally variable topographic density function,
the combined geoid effect is proportional to terms of powers two and three of the topographic height, while all higher order
terms vanish. The result is useful in geoid determination by analytical continuation, e.g., from an Earth gravity model, Stokes’s
formula or a combination thereof. 相似文献
7.
地面固定式扫描点云首先要将自由坐标系的点云纳入国家坐标系,而单站扫描的点云数据量极大,无法在可视环境下进行拼接。针对现有方法对海量点云拼接的不足,提出一种基于探测球的固定式扫描海量点云自动定向方法,该方法通过数据关联技术读取海量点云、建立标靶搜索环、球拟合确定标靶候选点、全组合距离匹配法确定同名点及坐标转换参数解算等,完成点云的自动定向过程。通过实验验证文中算法的有效性及可行性。 相似文献
8.
9.
对大比例尺扫描地形图中的房屋自动识别，通过预处理、起始点搜索、断点连接、房屋角点检测及直角化这套处理流程，达到了较好的识别效果。 相似文献
10.
D. A. Smith 《Journal of Geodesy》2002,76(3):150-168
A new method for computing gravitational potential and attraction induced by distant, global masses on a global scale has
been developed. The method uses series expansions and the well known one-dimensional fast Fourier transform (1-D FFT) method.
It has been proven to be significantly faster than quadrature while being equally accurate. Various quantities were studied
to cover the two primary applications of the Stokes–Helmert scheme of modeling effects. These two applications (or paths),
given the names R/r/D and R/D/r, are briefly discussed, although the primary objective of the paper is to provide computational
information to either path, rather than choosing one path as preferable to the other. It is further shown that the impact
of masses outside a 4-degree cap can impact the absolute computation of the geoid at more than 1 cm, and should therefore
be included in all local geoid computations seeking that accuracy.
Received: 13 December 2000 / Accepted: 3 September 2001 相似文献
11.
本文讨论了根据重复水准、重力测量资料利用虚拟质点法计算水准面随时间的变化,提出了虚拟质点位置参数的优化方法(该法克服了司托克斯方法和配置法的缺点)。模拟计算表明,水准面位移的计算精度是很高的。 相似文献
12.
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
13.
There are two basic types of geodetic projections by which the points located on the Earth's surface can be projected onto
a reference ellipsoid. Because of the different principles of Helmert's and Pizzetti's methods two sets of horizontal and
vertical coordinates are obtained for the same set of surface points. The difference is investigated in terms of offsets of
horizontal coordinates. For an estimation of the offsets the field lines going through topographic masses are determined by
three different numerical methods in `flat Earth approximation' using a volume element model of the density distribution of
the lithosphere in a part of central Europe. The maximum horizontal offset reaches 20 cm on the investigated area at the level
of the geoid.
Received: 28 October 1998 / Accepted: 16 August 1999 相似文献
14.
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
15.
球形标靶的固定式扫描大点云自动定向方法 总被引：1，自引：0，他引：1
根据目前地面激光扫描数据获取速度快、数据量大、测量距离远、专用特殊材料制作的标靶识别距离近、点云定向数据处理相对滞后、自动化程度低、不能适应远距离地形测量的现状,提出了从大点云中(每站1亿点以上)自动探测远距离标靶的点云定向方法。该方法首先根据标靶控制点的工程测量坐标信息,搜索到标靶所在点云环,然后对各点云环进行扇形分区,快速探测标靶,获取标靶中心扫描坐标,最后平差计算扫描仪位置参数和姿态参数,实现点云坐标到工程测量坐标的转换。该方法在普通配置的计算机上得到实现,并成功用于远距离山区地形测量,其中定向标靶半径0.162m,标靶到扫描站距离在180~700m之间。 相似文献
16.
17.
18.
论述了数字地形图中产生高程点与等高线错误的可能原因,分析了高程点和等高线在地形图中的空间位置关系及作为判断条件的数学关系,论述了解决问题的办法和判断规则,展示了通过编制计算机程序实现找出其错误的核心代码,此研究对于减轻质检人员在检查数字地形图的高程点与等高线错误时的劳动强度和提高工作效率很有意义。 相似文献
19.
Far-zone effects for different topographic-compensation models based on a spherical harmonic expansion of the topography 总被引：1，自引：1，他引：0
The determination of the gravimetric geoid is based on the magnitude of gravity observed at the surface of the Earth or at
airborne altitude. To apply the Stokes’s or Hotine’s formulae at the geoid, the potential outside the geoid must be harmonic
and the observed gravity must be reduced to the geoid. For this reason, the topographic (and atmospheric) masses outside the
geoid must be “condensed” or “shifted” inside the geoid so that the disturbing gravity potential T fulfills Laplace’s equation everywhere outside the geoid. The gravitational effects of the topographic-compensation masses
can also be used to subtract these high-frequent gravity signals from the airborne observations and to simplify the downward
continuation procedures. The effects of the topographic-compensation masses can be calculated by numerical integration based
on a digital terrain model or by representing the topographic masses by a spherical harmonic expansion. To reduce the computation
time in the former case, the integration over the Earth can be divided into two parts: a spherical cap around the computation
point, called the near zone, and the rest of the world, called the far zone. The latter one can be also represented by a global
spherical harmonic expansion. This can be performed by a Molodenskii-type spectral approach. This article extends the original
approach derived in Novák et al. (J Geod 75(9–10):491–504, 2001), which is restricted to determine the far-zone effects for
Helmert’s second method of condensation for ground gravimetry. Here formulae for the far-zone effects of the global topography
on gravity and geoidal heights for Helmert’s first method of condensation as well as for the Airy-Heiskanen model are presented
and some improvements given. Furthermore, this approach is generalized for determining the far-zone effects at aeroplane altitudes.
Numerical results for a part of the Canadian Rocky Mountains are presented to illustrate the size and distributions of these
effects. 相似文献
20.
L. E. Sjöberg 《Journal of Geodesy》2004,78(1-2):34-39
Gravimetric geoid determination by Stokes formula requires that the effects of topographic masses be removed prior to Stokes integration. This step includes the direct topographic and the downward continuation (DWC) effects on gravity anomaly, and the computations yield the co-geoid height. By adding the effect of restoration of the topography, the indirect effect on the geoid, the geoid height is obtained. Unfortunately, the computations of all these topographic effects are hampered by the uncertainty of the density distribution of the topography. Usually the computations are limited to a constant topographic density, but recently the effects of lateral density variations have been studied for their direct and indirect effects on the geoid. It is emphasised that the DWC effect might also be significantly affected by a lateral density variation. However, instead of computing separate effects of lateral density variation for direct, DWC and indirect effects, it is shown in two independent ways that the total geoid effect due to the lateral density anomaly can be represented as a simple correction proportional to the lateral density anomaly and the elevation squared of the computation point. This simple formula stems from the fact that the significant long-wavelength contributions to the various topographic effects cancel in their sum. Assuming that the lateral density anomaly is within 20% of the standard topographic density, the derived formula implies that the total effect on the geoid is significant at the centimetre level for topographic elevations above 0.66 km. For elevations of 1000, 2000 and 5000 m the effect is within ± 2.2, ± 8.8 and ± 56.8 cm, respectively. For the elevation of Mt. Everest the effect is within ± 1.78 m. 相似文献