大地水准而短议

介绍了大地水准面的定义,简单回顾了计算大地水准面研究的进展,扼要介绍了Stokes-Helmert方法,以及它对付不精确知道岩石密度的妙处,还评论了向下延拓的意义,最后展望了大地边值问题研究的前景.     

论(N-ζ)公式的内涵及推求N的精度

介绍了大地水准面(N)与似大地水准面(ξ)之差公式的推导方法，揭示了其物理内涵，论述了其在精化大地水准面中的重要作用。当似大地水准面精度达到cm级时，大地水准面也将达到同样的精度。     

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。     

GPS高程测量中大地水准面差距的计算

本文介绍了研究大地水准面的三种主要方法，及利用ＧＰＳ高程测量成果结合地表拟合技术求正高高程应用的情况。     

宁夏区大地水准面精化建立及检核的探讨

介绍了利用GPS组合法建立宁夏区似大地水准面的方案,研究了其数据处理方法和精度,简述了大地水准面检核的内容。     

越南测绘概览

本文简要介绍了越南大地控制网布设，大地基准建立，精密大地水准面确定，以及地图制图等方面的进展情况。     

等频大地水准面的概念及应用

阐述了等频大地水准面的概念及其理论基础，讨论了等频大地水准面与经典大地水准面的关系，提出了测定位差和高程差的新方法－引力或重力频移法，探讨了利用频移观测法解边值问题求定地球外部重力位的途径。     

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     

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；住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；住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。     

数字城市中大地水准面的功能与精化技术

由于数字城市可将城市上每一点的各种属性和信息进行有机组织,所以在信息化时代其重要性不言而喻。而大地水准面作为每一点高程的起算面,是数字城市能够准确提供基于地球空间坐标或城市空间坐标信息的保障,在一些应用领域由于需要知道点的海拔高也需要高精度大地水准面的支持。所以,就大地水准面在数字城市中提供高程基准的功能以及精化技术进行了深入的分析研究。介绍了典型的应用实例,并对构建数字城市的过程中有关大地水准面的精化提出了建议。     

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。     

Two deterministic and three stochastic modifications of Stokes’s formula: a case study for the Baltic countries

In regional gravimetric geoid determination, it is customary to use the modified Stokes formula that combines local terrestrial data with a global geopotential model. This study compares two deterministic and three stochastic modification methods for computing a regional geoid over the Baltic countries. The final selection of the best modification method is made by means of two accuracy estimates: the expected global mean square error of the geoid estimator, and the statistics of the post-fit residuals between the computed geoid models and precise GPS-levelling data. Numerical results show that the modification methods tested do not provide substantially different results, although the stochastic approaches appear formally better in the selected study area. The 2.8–5.3 cm (RMS) post-fit residuals to the GPS-levelling points indicate the suitability of the new geoid model for many practical applications. Moreover, the numerical comparisons reveal a one-dimensional offset between the regional vertical datum and the geoid models based upon the new GRACE-only geopotential model GGM01s. This gives an impression of a greater reliability of the new model compared to the earlier, EGM96-based and somewhat tilted regional geoid models for the same study area.     

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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Estimating geoid height change in North America: past, present and future

The forthcoming GRAV-D gravimetric geoid model over the United States is to be updated regularly to account for changes in geoid height. Its baseline precision is to be at the 10–20 mm level over non-mountainous regions. The aim of this study is to provide an estimate of the magnitude, time scale, and spatial footprint of geoid height change over North America, from mass redistribution processes of hydrologic, cryospheric and solid Earth nature. Geoid height changes from continental water storage changes over the past 50 years and predicted over the next century are evaluated and are highly dependent on the used model. Groundwater depletion from anthropogenic pumping in regional scale aquifers may lead to geoid changes of 10 mm magnitude every 50–100 years. The GRACE time varying gravity fields are used to (i) assess the errors in a glacial isostatic adjustment model, which, if used to correct the GRAV-D model, may induce errors at the 10 mm geoid height level after ~20 years, (ii), evaluate geoid height change over ice mass loss regions of North America, which, if they remain unchanged in the future, may lead to geoid height changes at the 10 mm level in under a decade and (iii), compute sea level rise and its effect on the geoid, which is found to be negligible. Coseismic gravitational changes from past North American earthquakes are evaluated, and lead to geoid change at the 10-mm level for only the largest thrust earthquakes. Finally, geoid change from volcanic processes are assessed and found to be significant with respect to the GRAV-D geoid model baseline precision for cataclysmic events, such as that of the 1980 Mt. St. Helens eruption. Recommendations on how to best monitor geoid change in the future are given.     

海洋重力大地水准面的确定

美国海洋卫星测高仪的出现,使应用Hotine积分确定海洋大地水准面成为现实。本文通过对Hotine积分及垂线偏差的计算公式进行改进,较好地改善了求和项的收敛性,减小了截断误差影响,并提出了利用Hotine函数和重力异常确定海洋大地水准面的方法。 实际计算表明:海洋重力大地水准面的精度在1米以内;卫星测高大地水准面间存在0.5米系统差;它和海底地形有一定的相关性,能较好地反映出海底地形的宏观特性。     

Precise geoid determination over Sweden using the Stokes–Helmert method and improved topographic corrections

 Four different implementations of Stokes' formula are employed for the estimation of geoid heights over Sweden: the Vincent and Marsh (1974) model with the high-degree reference gravity field but no kernel modifications; modified Wong and Gore (1969) and Molodenskii et al. (1962) models, which use a high-degree reference gravity field and modification of Stokes' kernel; and a least-squares (LS) spectral weighting proposed by Sj?berg (1991). Classical topographic correction formulae are improved to consider long-wavelength contributions. The effect of a Bouguer shell is also included in the formulae, which is neglected in classical formulae due to planar approximation. The gravimetric geoid is compared with global positioning system (GPS)-levelling-derived geoid heights at 23 Swedish Permanent GPS Network SWEPOS stations distributed over Sweden. The LS method is in best agreement, with a 10.1-cm mean and ±5.5-cm standard deviation in the differences between gravimetric and GPS geoid heights. The gravimetric geoid was also fitted to the GPS-levelling-derived geoid using a four-parameter transformation model. The results after fitting also show the best consistency for the LS method, with the standard deviation of differences reduced to ±1.1 cm. For comparison, the NKG96 geoid yields a 17-cm mean and ±8-cm standard deviation of agreement with the same SWEPOS stations. After four-parameter fitting to the GPS stations, the standard deviation reduces to ±6.1 cm for the NKG96 geoid. It is concluded that the new corrections in this study improve the accuracy of the geoid. The final geoid heights range from 17.22 to 43.62 m with a mean value of 29.01 m. The standard errors of the computed geoid heights, through a simple error propagation of standard errors of mean anomalies, are also computed. They range from ±7.02 to ±13.05 cm. The global root-mean-square error of the LS model is the other estimation of the accuracy of the final geoid, and is computed to be ±28.6 cm. Received: 15 September 1999 / Accepted: 6 November 2000     

高原山区局部大地水准面精化方法研究

局部大地水准面精化的实质是精确计算出大地水准面的起伏变化情况。一般情况下,需要密度足够的重力数据,依重力异常密集计算大地水准面差距或高程异常。但是在大陆西部高原山区重力点密度是不够的,无法达到大地水准面精化的目的。本文从理论上证实了用地形和岩石密度数据进行局部大地水准面精化的可行性。     

Models for Fitting Gravimetric Geoids and GPS Results

The aim of this investigation is to study how to use a gravimetric(quasi) geoid for levelling by GPS data in an optimal way.The advent of precise geodetic GPS has made the use of a technique possible,which might be called GPS- gravimetric geoid determination.In this approach,GPS heights above the reference ellipsoid are determined for points whose levelled (orthometric) height H is above sea level people have already surveyed;for these points,we thus have the values of the geoid undulation N.These values are then used to constrain the geoid undulations N‘ obtained from the gravimetric solution.     

高精度局域大地水准面对布测GPS水准和重力的要求

给定局域（似）大地水准面所要求的精度后，对该局域中应该布测GPS水准网的密度和精度进行了研究，并对不同地形类型的载我中，重力扰动对该局域（似）大地水准面精度的影响进行了讨论，并提出了相应布测量密度的要求。