关于重力大地水准面精度的探讨

从移去恢复法原理以及局部大地水准面精化残差拟合两个角度,分别得到了重力大地水准面精度估计的直接法与间接法,并通过实例分析了两种方法的误差评定结果。     

用重力异常逐级余差计算重力大地水准面

本文将计算重力大地水准面的频域方法推广至空域，提出了一种新的用重力数据和重力模型位系数联合确定大地水准面的方法。利用重力异常的逐级余差实施积分，使得通常的Ｓｔｏｋｅｓ积分方法具有明确的频域分析含义，可按精度要求确定出使用重力异常余差的块形大小及积分半径ψｏ。     

区域重力大地水准面确定的相对精度估计

以频域解析方法,研究由地面重力数据、全球住模型确定区域重力大地水准面的相对精度估计.首先由Stokes公式的数值积分推导地面重力数据与球谐系敬的精度关系;再由"移去-恢复"方法的空域截断逼近模式和协方差函数的球谐表达,分别推导内区地面重力数据之误差、外区全球位模型之误差与区域重力大地水准面之相对精度的解析关系;为便于计算,提出将内区地面重力数据和外区全球位模型的频域截断误差合并,再按频段重新划分为两部分:①全球范围--地面重力数据对应频率以上的截断;②外区范围--介于全球位模型最高频率与地面重力数据对应频率之间的截断,以经验阶方差模型分别估计之.模拟计算显示了地面重力数据之精度、分辨率、积分半径和全球位模型之精度、分辨率与区域重力大地水准面之相时精度的具体对应关系.本文研究同样适用于区域重力似大地水准面的确定.     

中国陆地似大地水准面计算模型介绍

本文叙述了中国陆地似大地水准面计算模型建立的方法、精度及发展前景。     

WZD94中国重力大地水准面研究

利用我国实测重力值计算完成了全国５＇×５＇格网平均空间重力异常，并结合重力场模型ＷＤＭ９４，利用国内外最新发展起来的快速谱算法确定了我国高分辨率５＇×５＇重力大地水准面ＷＺＤ９４。     

论相对论重力位及相对论大地水准面

讨论了相对论意义下的重力位及大地水准面,指出了等时率大地水准面的缺陷,建议今后采用等频面及等频大地水准面的概念,给出了等频大地水准面与经典大地水准面的差异,同时给出了等频大地水准面的近似表达式。     

海洋重力似大地水准面与区域测高似大地水准面的拟合问题

研究了将陆地重力似大地水准面与GPS水准似大地水准面拟合的处理方法推广到海洋的问题,首先从理论上证明了当存在海面地形,则海洋大地水准面与似大地水准面不重合,导出了在海洋上大地水准面差距与高程异常之间差值的公式,由此给出了求定平均海面相对于区域高程基准的正常高以及测高似大地水准面的计算公式。由于测高平均海面与GPS大地高有相近的精度,提出了将海洋重力似大地水准面与区域测高似大地水准面拟合的处理方法,并利用当前最新的海面地形模型和测高平均海面模型做了数值估计。     

利用空中平均重力异常确定区域大地水准面

提出了直接利用空中平均重力异常计算区域大地水准面的方法。模拟计算的结果表明, 该方法与传统的利用地面平均空间重力异常确定的大地水准面精度相当, 但其显著优点是勿需空中重力异常的向下解析延拓, 从而可以避免延拓误差对大地水准面精化的影响。     

中国陆海大地水准面拼接问题的理论探讨

探讨了建立新一代中国似大地水准面模型中的陆海大地水准面的拼接,分析了拼接差产生的原因,阐述了无缝拼接需要遵循的原则,提出了基于拟合拼接法的拼接方案.     

地形起伏对大地水准面的影响的探讨

通过一个实例得到两个重要的结论：1．计算地形起伏改正时应该使用公式δN=πGρhp^2/γ-Gρ/6γ∫∫（h^3-hp^3)/l^3dxdy而不能用公式δN=Gρ/γ∫∫（h-hp/l）dxdy-Gρ/6γ∫∫（h-hp）^3/l^3dxdy;2.在海拔较低的地区，即使地形起伏比较大，但是地形起伏改正数却很小，可以直接采用几何拟舍而无须考虑地形改正。     

泉州市新大地水准面精化研究

随着城市的扩大,泉州市在完成新一轮精度较好的GPS/水准网布测与数据处理的基础上,通过收集、整理泉州市及周边地区陆地重力测量资料、国内外先进的地球重力场模型,采用先进的(似)大地水准面确定理论与方法,完成了泉州市规划区精度优于3 cm的似大地水准面的确定工作.     

利用卫星重力梯度与地面数据确定地球重力场的分析

本文利用简捷的球谐分析方法讨论了重力场元在地面和空间的谱分布特征和向下延拓问题,分析了各类测量数据求定重力场的最高分辨率及精度。结果表明,在一个低轨道卫星上以适当的精度(优于10~(-2)E)的重力梯度测量可以获得空间分辨率为100公里、精度高于5mgal和10cm的重力场和大地水准面。     

Geoid models around Sognefjord using depth data

Bathymetry data from Sognefjord, Norway, have been included in a terrain model, and their influence on the geoid has been calculated. The test area, located in the western part of Norway, was chosen due to its deep fjords and high mountains. Inclusion of bathymetry data in the terrain model altered the computed gravimetric geoid by as much as a few decimeters. The effect was detectable to a distance of more than 100 km. All calculated geoids, both with and without bathymetry data in the terrain model, fit the geoidal heights determined by available Global Positioning System (GPS) and levelling heights at the sub-decimetre level. Contrary to expectations, the accuracy in geoid prediction was reduced when using bathymetric data. The geoid changes were largest over the fjord where no GPS points were located. Different methods on the same area [isostatic and Residual Terrain Model (RTM)-terrain reductions] showed differences of approximately 1 m. Rigorous distinction between quasigeoid and geoid was found to be essential in this kind of area. Received: 12 May 1997 / Accepted 7 May 1998     

Geoid, topography, and the Bouguer plate or shell

 Topography plays an important role in solving many geodetic and geophysical problems. In the evaluation of a topographical effect, a planar model, a spherical model or an even more sophisticated model can be used. In most applications, the planar model is considered appropriate: recall the evaluation of gravity reductions of the free-air, Poincaré–Prey or Bouguer kind. For some applications, such as the evaluation of topographical effects in gravimetric geoid computations, it is preferable or even necessary to use at least the spherical model of topography. In modelling the topographical effect, the bulk of the effect comes from the Bouguer plate, in the case of the planar model, or from the Bouguer shell, in the case of the spherical model. The difference between the effects of the Bouguer plate and the Bouguer shell is studied, while the effect of the rest of topography, the terrain, is discussed elsewhere. It is argued that the classical Bouguer plate gravity reduction should be considered as a mathematical construction with unclear physical meaning. It is shown that if the reduction is understood to be reducing observed gravity onto the geoid through the Bouguer plate/shell then both models give practically identical answers, as associated with Poincaré's and Prey's work. It is shown why only the spherical model should be used in the evaluation of topographical effects in the Stokes–Helmert solution of Stokes' boundary-value problem. The reason for this is that the Bouguer plate model does not allow for a physically acceptable condensation scheme for the topography. Received: 24 December 1999 / Accepted: 11 December 2000     

利用重力场模型和局部重力资料计算GPS水准高的精度探讨

利用大地水准面高，结合GPS测量的高程信息,直接计算GPS水准高，是一种全新诱人的解决方案。本文就这种方案，根据其核心技术－大地水面高的性质：长波长－全球重力场；中波长－局部重力资料，短波长－数据地形，对它的具体实现，适用范围以及精度分析作了详尽的探讨，在此基础上，提出一些GPS水准应用规范和要求，并利用实验数据对其进行验证。     

A synthetic Earth Gravity Model Designed Specifically for Testing Regional Gravimetric Geoid Determination Algorithms

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     

我国陆地垂线偏差的精化计算

主要阐述了全国局部地形改正和1′×1′平均法耶异常的计算方法;重力资料充分地区和重力资料不充分地区的垂线偏差计算方法。用214个天文点的天文大地垂线偏差与本文相应方法计算的垂线偏差的不符值,算得的4地区垂线偏差中误差平均值小于±2″。     

On the combination of gravity anomalies and gravity disturbances for geoid determination in Western Australia

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.     

地形对确定高精度局部大地水准面的影响

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Sjöberg方法计算地形对大地水准面的影响。