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1.
为解决世界各国高程基准差异的问题,提出联合卫星重力场模型、地面重力数据、GNSS大地高、局部高程基准的正高或正常高,按大地边值问题法确定局部高程基准重力位差的方法。首先推导了利用传统地面"有偏"重力异常确定高程基准重力位差的方法;接着利用改化Stokes核函数削弱"有偏"重力异常的影响,并联合卫星重力场模型和地面"有偏"重力数据,得到独立于任何局部高程基准的重力水准面,以此来确定局部高程基准重力位差;最后利用GNSS+水准数据和重力大地水准面确定了美国高程基准与全球高程基准W0的重力位差为-4.82±0.05 m2s-2。 相似文献
2.
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
3.
R. H. Rapp 《Journal of Geodesy》1997,71(5):282-289
This paper suggests that potential coefficient models of the Earth's gravitational potential be used to calculate height
anomalies which are then reduced to geoid undulations where such quantities are needed for orthometric height determination
and vertical datum definition through a potential coefficient realization of the geoid. The process of the conversion of the
height anomaly into a geoid undulation is represented by a height anomaly gradient term and the usual N–ζ term that is dependent on elevation and the Bouguer anomaly. Using a degree 360 expansion of 30′ elevations and the OSU91A
potential coefficient model, a degree 360 representation of the correction terms was computed. The magnitude of N–ζ reached –3.4 m in the Himalaya Mountains with smaller, but still significant, magnitudes in other mountainous regions.
Received: 6 May 1996; Accepted: 30 October 1996 相似文献
4.
M. C. Santos P. Vaníček W. E. Featherstone R. Kingdon A. Ellmann B. -A. Martin M. Kuhn R. Tenzer 《Journal of Geodesy》2006,80(12):691-704
Following our earlier definition of the rigorous orthometric height [J Geod 79(1-3):82–92 (2005)] we present the derivation and calculation of the differences between this and the Helmert orthometric height, which is embedded in the vertical datums used in numerous countries. By way of comparison, we also consider Mader and Niethammer’s refinements to the Helmert orthometric height. For a profile across the Canadian Rocky Mountains (maximum height of ~2,800 m), the rigorous correction to Helmert’s height reaches ~13 cm, whereas the Mader and Niethammer corrections only reach ~3 cm. The discrepancy is due mostly to the rigorous correction’s consideration of the geoid-generated gravity disturbance. We also point out that several of the terms derived here are the same as those used in regional gravimetric geoid models, thus simplifying their implementation. This will enable those who currently use Helmert orthometric heights to upgrade them to a more rigorous height system based on the Earth’s gravity field and one that is more compatible with a regional geoid model. 相似文献
5.
从高程系统定义出发,探讨高程基准面的重力等位性质,测试分析不同类型高程系统地面点高程之间的差异,考察GNSS代替水准与实际水准测量成果的一致性,进而提出新的GNSS代替水准算法。主要结论包括:(1)当精度要求达到厘米级水平时,正常高的基准面也应是大地水准面。中国国家1985高程基准采用正常高系统,其高程基准面是过青岛零点的大地水准面。(2)近地空间中等解析正高面与大地水准面平行,GNSS代替水准能直接测定地面点的解析正高,但正常高系统更有利于描述地势和地形起伏。(3)本文给出的GNSS代替水准测定近地点正常高算法,大地高误差对正常高结果的影响比大地水准面误差大,前者影响约为后者的1.5倍。 相似文献
6.
讨论了建立全球统一高程系统的若干基本问题,包括正常高的几何定义和重力定义,区域水准测量高程系统的全球统一问题以及大地水准面位W_0的确定。结果表明:(1)几何水准高程和重力定义的正常高存在差别,由GNSS/重力得到的正常高并不等于几何水准给出的正常高,而要加上一与高程有关的改正项,并且在山区这一改正不可忽略;(2)由GNSS/重力/区域几何水准融合可以给出一个相对的全球统一高程系统,而要得到绝对的统一系统,还须知道大地水准面的位W_0;(3)现代大地测量技术可以以一定精度求出W_0,但它是时变的,因此只能定义出某个历元的全球绝对统一高程系统。 相似文献
7.
2020珠峰高程测量,首次确定并发布了基于国际高程参考系统(IHRS)的珠峰正高。在珠峰地区实现国际高程参考系统,采用的方案是建立珠峰区域高精度重力大地水准面。利用地球重力场谱组合理论和基于数据驱动的谱权确定方法,测试优选参考重力场模型及其截断阶数和球冠积分半径等关键参数,联合航空和地面重力等数据建立了珠峰区域重力似大地水准面模型,61点高精度GNSS水准高程异常检核表明,模型精度达3.8 cm,加入航空重力数据后模型精度提升幅度达51.3%。提出顾及高差改正的峰顶高程异常内插方法,采用顾及地形质量影响的高程异常——大地水准面差距转换改正严密公式,使用峰顶实测地面重力数据,基于国际高程参考系统定义的重力位值W0和GRS80参考椭球,最终确定了国际高程参考系统中的高精度珠峰峰顶大地水准面差距。 相似文献
8.
The rigorous determination of orthometric heights 总被引：1，自引：2，他引：1
The main problem of the rigorous definition of the orthometric height is the evaluation of the mean value of the Earth’s gravity acceleration along the plumbline within the topography. To find the exact relation between rigorous orthometric and Molodensky’s normal heights, the mean gravity is decomposed into: the mean normal gravity, the mean values of gravity generated by topographical and atmospheric masses, and the mean gravity disturbance generated by the masses contained within geoid. The mean normal gravity is evaluated according to Somigliana–Pizzetti’s theory of the normal gravity field generated by the ellipsoid of revolution. Using the Bruns formula, the mean values of gravity along the plumbline generated by topographical and atmospheric masses can be computed as the integral mean between the Earth’s surface and geoid. Since the disturbing gravity potential generated by masses inside the geoid is harmonic above the geoid, the mean value of the gravity disturbance generated by the geoid is defined by applying the Poisson integral equation to the integral mean. Numerical results for a test area in the Canadian Rocky Mountains show that the difference between the rigorously defined orthometric height and the Molodensky normal height reaches ∼0.5 m. 相似文献
9.
Fast and accurate relative positioning for baselines less than 20 km in length is possible using dual-frequency Global Positioning
System (GPS) receivers. By measuring orthometric heights of a few GPS stations by differential levelling techniques, the geoid
undulation can be modelled, which enables GPS to be used for orthometric height determination in a much faster and more economical
way than terrestrial methods. The geoid undulation anomaly can be very useful for studying tectonic structure. GPS, levelling
and gravity measurements were carried out along a 200-km-long highly undulating profile, at an average elevation of 4000 m,
in the Ladak region of NW Himalaya, India. The geoid undulation and gravity anomaly were measured at 28 common GPS-levelling
and 67 GPS-gravity stations. A regional geoid low of nearly −4 m coincident with a steep negative gravity gradient is compatible
with very recent findings from other geophysical studies of a low-velocity layer 20–30 km thick to the north of the India–Tibet
plate boundary, within the Tibetan plate. Topographic, gravity and geoid data possibly indicate that the actual plate boundary
is situated further north of what is geologically known as the Indus Tsangpo Suture Zone, the traditionally supposed location
of the plate boundary. Comparison of the measured geoid with that computed from OSU91 and EGM96 gravity models indicates that
GPS alone can be used for orthometric height determination over the Higher Himalaya with 1–2 m accuracy.
Received: 10 April 1997 / Accepted: 9 October 1998 相似文献
10.
11.
为实现中国和尼泊尔共同宣布珠峰高程,我国于2019—2020年开展了珠峰高程测量工作,并于2020年5月27日完成峰顶测量。首次在珠峰北侧区域实施航空重力测量、开展峰顶地面重力测量,首次联合航空和地面重力等数据确定了基于国际高程参考系统(international height reference system,IHRS)的珠峰区域重力似大地水准面模型和峰顶大地水准面差距。此次珠峰测量,各种先进测量装备尤其是国产测量仪器全面担纲,通过多种技术手段相互验证和严密检核计算,确保了珠峰高程测量成果的精度和可靠性。最后,中尼双方合作开展数据处理,共同确定珠峰峰顶雪面正高(海拔高)为8848.86 m。 相似文献
12.
Lars E. Sjöberg 《Journal of Geodesy》2006,79(12):675-681
The application of Stokes’s formula to determine the geoid height requires that topographic and atmospheric masses be mathematically removed prior to Stokes integration. This corresponds to the applications of the direct topographic and atmospheric effects. For a proper geoid determination, the external masses must then be restored, yielding the indirect effects. Assuming an ellipsoidal layering of the atmosphere with 15% increase in its density towards the poles, the direct atmospheric effect on the geoid height is estimated to be −5.51 m plus a second-degree zonal harmonic term with an amplitude of 1.1 cm. The indirect effect is +5.50 m and the total geoid correction thus varies between −1.2 cm at the equator to 1.9 cm at the poles. Finally, the correction needed to the atmospheric effect if Stokes’s formula is used in a spherical approximation, rather than an ellipsoidal approximation, of the Earth varies between 0.3 cm and 4.0 cm at the equator and pole, respectively. 相似文献
13.
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
14.
H. Nahavandchi 《Journal of Geodesy》2002,76(6-7):345-352
It is suggested that a spherical harmonic representation of the geoidal heights using global Earth gravity models (EGM) might
be accurate enough for many applications, although we know that some short-wavelength signals are missing in a potential coefficient
model. A `direct' method of geoidal height determination from a global Earth gravity model coefficient alone and an `indirect'
approach of geoidal height determination through height anomaly computed from a global gravity model are investigated. In
both methods, suitable correction terms are applied. The results of computations in two test areas show that the direct and
indirect approaches of geoid height determination yield good agreement with the classical gravimetric geoidal heights which
are determined from Stokes' formula. Surprisingly, the results of the indirect method of geoidal height determination yield
better agreement with the global positioning system (GPS)-levelling derived geoid heights, which are used to demonstrate such
improvements, than the results of gravimetric geoid heights at to the same GPS stations. It has been demonstrated that the
application of correction terms in both methods improves the agreement of geoidal heights at GPS-levelling stations. It is
also found that the correction terms in the direct method of geoidal height determination are mostly similar to the correction
terms used for the indirect determination of geoidal heights from height anomalies.
Received: 26 July 2001 / Accepted: 21 February 2002 相似文献
15.
GPS高程转换方法和正常高计算 总被引：13，自引：0，他引：13
GPS测量所提供的高程为相对于WGS-84椭球的GPS大地高，而我国使用的是正常高。大地高等于正常高与高程异常之和，要使GPS高程在工程实际中得到应用，必须先求出高程异常，进而获得正常高。结合GPS测量和水准测量资料，用神经网络方法和二次多项式曲面拟合方法拟合高程异常，对拟合精度进行了分析比较，得出了有实用价值的结论。 相似文献
16.
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. 相似文献
17.
The analytical continuation bias in geoid determination using potential coefficients and terrestrial gravity data 总被引：1，自引：1，他引：0
J. Ågren 《Journal of Geodesy》2004,78(4-5):314-332
One important application of an Earth Gravity Model (EGM) is to determine the geoid. Since an EGM is represented by an external-type series of spherical harmonics, a biased geoid model is obtained when the EGM is applied inside the masses in continental regions. In order to convert the downward-continued height anomaly to the corresponding geoid undulation, a correction has to be applied for the analytical continuation bias of the geoid height. This technique is here called the geoid bias method. A correction for the geoid bias can also be utilised when an EGM is combined with terrestrial gravity data, using the combined approach to topographic corrections. The geoid bias can be computed either by a strict integral formula, or by means of one or more terms in a binomial expansion. The accuracy of the lowest binomial terms is studied numerically. It is concluded that the first term (of power H2) can be used with high accuracy up to degree 360 everywhere on Earth. If very high mountains are disregarded, then the use of the H2 term can be extended up to maximum degrees as high as 1800. It is also shown that the geoid bias method is practically equal to the technique applied by Rapp, which utilises the quasigeoid-to-geoid separation. Another objective is to carefully consider how the combined approach to topographic corrections should be interpreted. This includes investigations of how the above-mentioned H2 term should be computed, as well as how it can be improved by a correction for the residual geoid bias. It is concluded that the computation of the combined topographic effect is efficient in the case that the residual geoid bias can be neglected, since the computation of the latter is very time consuming. It is nevertheless important to be able to compute the residual bias for individual stations. For reasonable maximum degrees, this can be used to check the quality of the H2 approximation in different situations.Acknowledgement The author would like to thank Prof. L.E. Sjöberg for several ideas and for reading two draft versions of the paper. His support and constructive remarks have improved its quality considerably. The valuable suggestions from three unknown reviewers are also appreciated. 相似文献
18.
2005年我国对珠穆朗玛峰高程进行了新的测定,为此在珠峰及其邻近地区开展了大规模的大地测量数据获取和数据处理工作。相对于1975年珠峰测高,2005年在珠峰以北地区的地面控制和珠峰高程测定中采用了GPS技术,采用了雷达探测技术测定珠峰峰顶冰雪覆盖层的深度,利用地球重力场模型、重力和数字地形数据、以及GPS水准等资料,精化珠峰地区的大地水准面,提高了测量珠峰高程和探测峰顶冰雪覆盖层深度的精度和可靠性。由此测得珠峰峰顶雪面正常高为8 846.67 M,珠峰峰顶雪面正高(海拔高)为8 847.93 M,珠峰峰顶岩面正高为8 844.43 M,珠峰峰顶相应点的冰雪层厚度为3.50 M。 相似文献
19.
20.
最小二乘配置法中局部协方差函数的计算 总被引：3，自引：1，他引：2
随着 GPS日益广泛的应用及精度的不断提高 ,在有些实际应用中利用 GPS来代替传统的水准测量进行高程控制已成为可能 ,这也进一步提出了对高精度大地水准面的需求。快速傅立叶变换 (FFT)是目前计算大地水准面比较常用的方法之一 ,但需要将重力观测量进行内插得到规则格网上的平均重力异常。利用最小二乘配置法计算大地水准面可直接利用已有的观测值进行计算 ,同时可综合利用不同类型的数据 ,如重力异常和垂线偏差等计算大地水准面 ,因此最小二乘配置法仍有广泛的应用 ,但制约最小二乘配置应用的关键问题是局部协方差函数的计算。将主要讨论最小二乘配置法中局部协方差函数的计算 ,使所用的协方差函数能更好地反映已知的数据 ,从而获得更精确的结果。 相似文献