大地水准面差距计算方法的研究

本文首先证明了三种大地水准面差距计算方法(迈塞尔方法、文策尔方法、最小二乘配置法)之间的关系。通过对某盆地的大地水准面差距的计算及和多普勒结果的比较,得到了一些对计算我国大地水准面差距有益的结论。     

运用GPS曲面拟合高程精化锦州市区似大地水准面

利用已完成的锦州市区基础控制成果对锦州市似大地水准面精化进行了研究。介绍了GPS高程的应用理论,大地水准高的计算方法以及利用曲面拟合法计算大地水准面高,并对结果进行了分析,绘制出高程异常等值线图。     

一种确定大地水准面重力位漂移δW的方法

理论上,大地水准面上的重力位常数W0决定了大地水准面的形状及大小。源于大地水准面重力位W0的系统误差将直接导致大地水准面的漂移,如何精确确定W0一直是大地测量学家极为感兴趣的问题。本文基于虚拟压缩恢复法,提出了一种不同于传统的确定大地水准面重力位漂移δW的方法。     

大地水准面数值计算及结构分析

针对大地水准面精化问题,该文提出了基于大地水准面起伏几何性质构建精确大地水准面的方法。相对传统方法根据经验公式设计精化大地水准面分辨率,该文提出了一种顾及区域性特点的大地水准面分辨率设计方法,推导了构建厘米级大地水准面需要达到的空间分辨率计算公式。采用Alltrans EGM2008Calculator 1.00软件计算不同区域的大地水准面高程,并用坡度方法分析大地水准面的精细结构。最后以江西省大地水准面起伏为基础,采用该方法进行计算。结果表明:构建厘米级大地水准面需要达到的空间分辨率为7″,可为大地水准面精化研究提供参考。     

陆海交界区域厘米级精度似大地水准面的确定

为了得到我国某陆海交界区厘米级精度的区域（似）大地水准面,利用43个高精度GPS／水准点和1045个实测重力点数据对EGM96,WDM94和GFZ计算的局部重力（似）大地水准面进行了比较与评价。结果表明,在该测区用移去．恢复法确定重力（似）大地水准面时,EGM96应该是首选参考重力场模型。该测区处在陆海交界处,海域无GPS／水准数据。经比较发现,采用距离倒数加权平均法将该区重力似大地水准面拟合于GPS／水准数据比在大范围使用的多项式法效果更好。采用该方法计算的测区（似）大地水准面精度优于3cm。     

陆海交界区域厘米级精度似大地水准面的确定

为了得到我国某陆海交界区厘米级精度的区域(似)大地水准面,利用43个高精度GPS/水准点和1 045个实测重力点数据对EGM96,WDM94和GFZ计算的局部重力(似)大地水准面进行了比较与评价。结果表明,在该测区用移去-恢复法确定重力(似)大地水准面时,EGM96应该是首选参考重力场模型。该测区处在陆海交界处,海域无GPS/水准数据。经比较发现,采用距离倒数加权平均法将该区重力似大地水准面拟合于GPS/水准数据比在大范围使用的多项式法效果更好。采用该方法计算的测区(似)大地水准面精度优于3cm。     

河源市cm级似大地水准面模型的确定

综合利用地球重力场模型、数字高程模型、重力数据和高程异常数据,采用"移去-恢复"法和三次多项式拟合算法,确定了河源市cm级似大地水准面模型;研究了地形复杂的城市级似大地水准面模型计算的关键技术难点,并提出了优化方法。     

城市级似大地水准面模型确定的优化方法研究

以清远市cm级似大地水准面模型的确立为例,综合运用各种数据和拟合算法,通过计算和统计,探讨了采用"移去-恢复"法计算城市级似大地水准面模型的关键技术,并提出了优化建议.     

武汉市似大地水准面GPS水准建模与软件研制

本文针对高程异常格网线性内插模型在表达光滑曲面时出现的近似误差,提出了采用基于统计学习理论的机器学习方法,结合粗差检测技术和虚拟观测值,建立高精度GPS水准似大地水准面模型。武汉市GPS水准似大地水准面几何建模实例表明了方法的可靠性与优势。单机版、WEB版、PDA版系列软件的成功研制,最大限度地实现了似大地水准面模型的普及应用。     

配置法在局部大地水准面精化中的实例研究

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。     

A method to validate gravimetric-geoid computation software based on Stokes's integral formula

A method is presented with which to verify that the computer software used to compute a gravimetric geoid is capable of producing the correct results, assuming accurate input data. The Stokes, gravimetric terrain correction and indirect effect formulae are integrated analytically after applying a transformation to surface spherical coordinates centred on each computation point. These analytical results can be compared with those from geoid computation software using constant gravity data in order to verify its integrity. Results of tests conducted with geoid computation software are presented which illustrate the need for integration weighting factors, especially for those compartments close to the computation point. Received: 6 February 1996 / Accepted: 19 April 1997     

GPS-gravimetric geoid determination in Egypt

The main objective of this study is to improve the geoid by GPS/leveling data in Egypt. Comparisons of the gravimetric geoid with GPS/leveling data have been performed. On the basis of a gravimetric geoid fitted to GPS/leveling by the least square method, a smoothed geoid was obtained. A high-resolution geoid in Egypt was computed with a 2.5′×2.5′ grid by combining the data set of 2600 original point gravity values, 20″×30″ resolution Digital Terrain Model (DTM) grid and the spherical harmonic model EGM96. The method of computation involved the strict evaluation of the Stokes integral with 1D-FFT. The standard deviation of the difference between the gravimetric and the GPS/leveling geoid heights is ±0.47 m. The standard deviation after fitting of the gravimetric geoid to the GPS/leveling points is better than ±13 cm. In the future we will try to improve our geoid results in Egypt by increasing the density of gravimetric coverage.     

GPS-GRAVIMETRIC GEOID DETERMINATION IN EGYPT

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应用聚类分析方法进行实测重力数据的选点优化

针对局部(似)大地水准面的求解过程,将聚类分析方法用于重力观测数据的优化设计。根据重力场的变化特征,利用地形的双向坡度值作为分类属性,给出了实测重力数据可以较稀疏或必须稠密的判断依据。在一处丘陵地区进行了数值实验,结果表明,应用此方法在非均匀地删除掉近一半的实测重力数据之后,计算得到的(似)大地水准面变化的最大值为1.2 cm,最小值为-0.4 cm,平均值为0.3 cm,与未删除实测重力数据情况下获得的计算结果精度相当。由此验证了该方法的可行性,并为局部(似)大地水准面求解过程的优化设计提供了一条可借鉴的途径。     

Using gravity and topography-implied anomalies to assess data requirements for precise geoid computation

Many regions around the world require improved gravimetric data bases to support very accurate geoid modeling for the modernization of height systems using GPS. We present a simple yet effective method to assess gravity data requirements, particularly the necessary resolution, for a desired precision in geoid computation. The approach is based on simulating high-resolution gravimetry using a topography-correlated model that is adjusted to be consistent with an existing network of gravity data. Analysis of these adjusted, simulated data through Stokes’s integral indicates where existing gravity data must be supplemented by new surveys in order to achieve an acceptable level of omission error in the geoid undulation. The simulated model can equally be used to analyze commission error, as well as model error and data inconsistencies to a limited extent. The proposed method is applied to South Korea and shows clearly where existing gravity data are too scarce for precise geoid computation.     

Far-zone effects for different topographic-compensation models based on a spherical harmonic expansion of the topography

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.     

The effect on the geoid of lateral topographic density variations

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.     

GPS水准、天文重力水准与重力大地水准面多种数据联合处理的研究

针对我国大地水准面的研究状况,提出了在国家GPSB级网完成之后,利用GPS水准、天文重力水准与重力大地水准面3类数据确定我国高精度大地水准面的理论和方法。分析了3类数据的误差传播规律,给出了联合平差模型,并用一模拟网进行了试算。     

On the accuracy of modified Stokes's integration in high-frequency gravimetric geoid determination

 Two numerical techniques are used in recent regional high-frequency geoid computations in Canada: discrete numerical integration and fast Fourier transform. These two techniques have been tested for their numerical accuracy using a synthetic gravity field. The synthetic field was generated by artificially extending the EGM96 spherical harmonic coefficients to degree 2160, which is commensurate with the regular 5^′ geographical grid used in Canada. This field was used to generate self-consistent sets of synthetic gravity anomalies and synthetic geoid heights with different degree variance spectra, which were used as control on the numerical geoid computation techniques. Both the discrete integration and the fast Fourier transform were applied within a 6^∘ spherical cap centered at each computation point. The effect of the gravity data outside the spherical cap was computed using the spheroidal Molodenskij approach. Comparisons of these geoid solutions with the synthetic geoid heights over western Canada indicate that the high-frequency geoid can be computed with an accuracy of approximately 1 cm using the modified Stokes technique, with discrete numerical integration giving a slightly, though not significantly, better result than fast Fourier transform. Received: 2 November 1999 / Accepted: 11 July 2000     

The topographic bias by analytical continuation in physical geodesy

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.