共查询到20条相似文献，搜索用时 171 毫秒
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针对通常的似大地水准面模型较少涉及海域的情况,该文基于重力数据和地形数据,采用顾及各类地形位及地形引力影响的第二类Helmert凝集法计算了珠海重力似大地水准面;利用高分辨率和高精度的地形数据来恢复大地水准面短波部分,提高了似大地水准面的精度;利用25个高精度全球卫星导航系统水准资料与重力似大地水准面进行了独立比较,其精度为0.012m;然后,采用球冠谐方法,将重力似大地水准面与25个全球卫星导航系统水准数据联合,建立了珠海市海陆统一的似大地水准面模型,其精度为0.008m;最后,利用15个全球卫星导航系统/水准点对似大地水准面模型进行了外部检核,精度为0.010m。 相似文献
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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
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《武汉大学学报(信息科学版)》2016,(3)
在分析现有地形影响处理方法的基础上,着重对以下3方面问题进行讨论:其一,在传统平面参考面的地形改正计算方法基础上,基于国际通用的GRS80椭球采用Tesseroid单元体积分法计算地形改正,以适用于山区和地形变化复杂地区的地形改正计算,推导了基于Tesseroid单元体的地形改正算法的泰勒级数展开公式,并验证该方法较传统方法的优越性。其二,目前,大地水准面计算中通常只考虑Molodensky一阶项影响,然而已有结果表明在山区二阶项的影响可达到分米级。针对目前厘米级大地水准面任务,基于Molodensky一阶项算法,给出了二阶项和三阶项对高程异常贡献的严密级数展开式。其三,本文详细讨论了利用地形改正值代替Molodensky级数解计算重力大地水准面的误差影响。 相似文献
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利用Engelis按SEASAT卫星测高资料得到的海面地形模型和Levitus按位水准得到的海面地形模型计算了我国沿海几个验潮站与青岛验潮站之间的海面地形,并与几何水准联测得到的这几个验潮站的平均海面的高差进行了比较。用这三种方法求得的我国大陆沿海海水面倾斜的趋势大体上是一致的。此外,在全球统一系统内计算大地水准面差距时,若在计算点附近(Ψ_0=10°)应用我国区域性重力异常,由于大地水准面差距零阶项N_0和海面地形的影响,可使N的误差达到0.4米,这对确定米级精度的大地水准面差距是有影响的。 相似文献
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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
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Gravity field convolutions without windowing and edge effects 总被引：5，自引：0，他引：5
A new set of formulas has been developed for the computation of geoid undulations and terrain corrections by FFT when the input gravity anomalies and heights are mean gridded values. The effects of the analytical and the discrete spectra of kernel functions and that of zero-padding on the computation of geoid undulations and terrain corrections are studied in detail.Numerical examples show that the discrete spectrum is superior to the analytically-defined one. By using the discrete spectrum and 100% zero-padding, the RMS differences are 0.000 m for the FFT geoid undulations and 0.200 to 0.000 mGal for the FFT terrain corrections compared with results obtained by numerical integration. 相似文献
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Lars E. Sjöberg 《Journal of Geodesy》1993,67(3):178-184
In view of the smallness of the atmospheric mass compared to the mass variations within the Earth, it is generally assumed in physical geodesy that the terrain effects are negligible. Subsequently most models assume a spherical or ellipsoidal layering of the atmosphere. The removal and restoring of the atmosphere in solving the exterior boundary value problems thus correspond to gravity and geoid corrections of the order of 0.9 mGal and -0.7 cm, respectively.We demonstrate that the gravity terrain correction for the removal of the atmosphere is of the order of 50µGal/km of elevation with a maximum close to 0.5 mGal at the top of Mount Everest. The corresponding effect on the geoid may reach several centimetres in mountainous regions. Also the total effect on geoid determination for removal and restoring the atmosphere may contribute significantly, in particular by long wavelengths. This is not the case for the quasi geoid in mountainous regions. 相似文献
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Review and numerical assessment of the direct topographical reduction in geoid determination 总被引：4，自引：0，他引：4
Recent papers in the geodetic literature promote the reduction of gravity for geoid determination according to the Helmert condensation technique where the entire reduction is made in place before downward continuation. The alternative approach, primarily developed by Moritz, uses two evaluation points, one at the Earths surface, the other on the (co-)geoid, for the direct topographic effect. Both approaches are theoretically legitimate and the derivations in each case make use of the planar approximation and a Lipschitz condition on height. Each method is re-formulated from first principles, yielding equations for the direct effect that contain only the spherical approximation. It is shown that neither method relies on a linear relationship between gravity anomalies and height (as claimed by some). Numerical tests, however, show that the practical implementations of these two approaches yield significant differences. Computational tests were performed in three areas of the USA, using 1×1 grids of gravity data and 30×30 grids of height data to compute the gravimetric geoid undulation, and GPS/leveled heights to compute the geometric geoid undulation. Using the latter as a control, analyses of the gravimetric undulations indicate that while in areas with smooth terrain no substantial differences occur between the gravity reduction methods, the Moritz–Pellinen (MP) approach is clearly superior to the Vanicek–Martinec (VM) approach in areas of rugged terrain. In theory, downward continuation is a significant aspect of either approach. Numerically, however, based on the test data, neither approach benefited by including this effect in the areas having smooth terrain. On the other hand, in the rugged, mountainous area, the gravimetric geoid based on the VM approach was improved slightly, but with the MP approach it suffered significantly. The latter is attributed to an inability to model the downward continuation of the Bouguer anomaly accurately in rugged terrain. Applying the higher-order, more accurate gravity reduction formulas, instead of their corresponding planar and linear approximations, yielded no improvement in the accuracy of the gravimetric geoid undulation based on the available data. 相似文献
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This paper deals with the problem of determining a scalar spherical field from its surface gradient, i.e., the modelling of geoid undulations from deflections of the vertical. Essential tools are integral formulae on the sphere based on Green’s function of the Beltrami operator. The determination of geoid undulations from deflections of the vertical is formulated as multiscale procedure involving scale-dependent regularized versions of the surface gradient of Green’s function. An advantage of the presented approach is that the multiscale method is based on locally supported wavelets. In consequence, local modelling of geoid undulations are calculable from locally available deflections of the vertical 相似文献
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地形改正与地形直接影响的转化关系 总被引：1，自引：0，他引：1
传统的第三边值问题的解算方法有Molodensky算法和Stokes-Helmert算法两种。在Molodensky算法中使用的地形改正和Stokes-Helmert算法中使用的直接影响均由大地水准面外地形产生,因而必然存在关系。本文通过推导给出了直接影响是地形改正、层间改正与压缩地形影响3项之和的结论。在此基础上,给出了直接影响的质量线平面积分算法、质量棱柱平面积分算法和地形改正的球面积分算法。此外本文还推导了布格球冠层间改正算法。通过实验得出,直接影响的质量线平面积分算法和质量棱柱平面积分算法与传统球面积分算法的差异分别为3.81和1.64 m Gal;地形改正球面积分算法与传统质量线、质量棱柱平面积分的差异分别为3.92和1.69 m Gal。该结果说明,本文推导的直接影响与地形改正的关系式是正确有效且实用的。 相似文献
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L. E. Sjöberg 《Journal of Geodesy》2000,74(2):255-268
The topographic potential and the direct topographic effect on the geoid are presented as surface integrals, and the direct
gravity effect is derived as a rigorous surface integral on the unit sphere. By Taylor-expanding the integrals at sea level
with respect to topographic elevation (H) the power series of the effects is derived to arbitrary orders. This study is primarily limited to terms of order H
2. The limitations of the various effects in the frequently used planar approximations are demonstrated. In contrast, it is
shown that the spherical approximation to power H
2 leads to a combined topographic effect on the geoid (direct plus indirect effect) proportional to H˜2 (where terms of degrees 0 and 1 are missing) of the order of several metres, while the combined topographic effect on the
height anomaly vanishes, implying that current frequent efforts to determine the direct effect to this order are not needed.
The last result is in total agreement with Bjerhammar's method in physical geodesy. It is shown that the most frequently applied
remove–restore technique of topographic masses in the application of Stokes' formula suffers from significant errors both
in the terrain correction C (representing the sum of the direct topographic effect on gravity anomaly and the effect of continuing the anomaly to sea
level) and in the term t (mainly representing the indirect effect on the geoidal or quasi-geoidal height).
Received: 18 August 1998 / Accepted: 4 October 1999 相似文献
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Journal of Geodesy - ?The application of Stokes' formula to create geoid undulations requires no masses outside the geoid. However, due to the existence of the topography, terrain... 相似文献
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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
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Y. M. Wang 《Journal of Geodesy》1990,64(3):231-246
The method of analytical downward continuation has been used for solving Molodensky’s problem. This method can also be used
to reduce the surface free air anomaly to the ellipsoid for the determination of the coefficients of the spherical harmonic
expansion of the geopotential. In the reduction of airborne or satellite gradiometry data, if the sea level is chosen as reference
surface, we will encounter the problem of the analytical downward continuation of the disturbing potential into the earth,
too. The goal of this paper is to find out the topographic effect of solving Stoke’sboundary value problem (determination
of the geoid) by using the method of analytical downward continuation.
It is shown that the disturbing potential obtained by using the analytical downward continuation is different from the true
disturbing potential on the sea level mostly by a −2πGρh 2/p. This correction is important and it is very easy to compute
and add to the final results. A terrain effect (effect of the topography from the Bouguer plate) is found to be much smaller
than the correction of the Bouguer plate and can be neglected in most cases.
It is also shown that the geoid determined by using the Helmert’s second condensation (including the indirect effect) and
using the analytical downward continuation procedure (including the topographic effect) are identical. They are different
procedures and may be used in different environments, e.g., the analytical downward continuation procedure is also more convenient
for processing the aerial gravity gradient data.
A numerical test was completed in a rough mountain area, 35°<ϕ<38°, 240°<λ<243°. A digital height model in 30″×30″ point value
was used. The test indicated that the terrain effect in the test area has theRMS value ±0.2−0.3 cm for geoid. The topographic effect on the deflections of the vertical is around1 arc second. 相似文献
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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