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1.
The determination of gravimetric deflections of the vertical for the area of Greece is attempted by combining a spherical hamonics model and gravity nomalies using the method of least squares collocation. The components of deflections of the vertical are estimated on a grid with spacing 15′ in latitude and 20′ in longitude covering only the continental area of Greece, where a sufficient number of point gravity anomalies is available. In order to test the accuracy of the determination, gravimetric deflections of the vertical are computed at stations where astrogeodetic data are available. The results show that in a large region of rugged topography and irregular potential field, the prediction is possible with a standard deviation of 18% ... 28% of the root mean square variation of the observations, without taking into account the topography. Furthermore, the estimation of some systematic differences between observed and computed deflections of the vertical is attempted. 相似文献
2.
S. Ono 《Journal of Geodesy》1987,61(1):41-59
The main objective of the present work is to present methods to obtain detailed surveys of the shape of the quasigeoid and of deflections of the vertical from the point of view of three-dimensional constituting and rigorous computing of the astrogeodetic network. The error of an astrogravimetric leveling line in the most general case, i.e., in the shape of a polygon has been estimated. This error can be tested and checked by comparison of gravimetric deflections of the vertical with astrogeodetic deflections, i.e., by computation of the error of astrogeodetic gravimetric deflection of the vertical. The astrogeodetic deflections of the vertical required for the horizontal angle correction in triangulation and traverse are easily obtained by interpolation. An example of astrogravimetric leveling demonstrates the possibility to carry out an astrogravimetric leveling with any required accuracy, for example, with the accuracy of ±1 ml/1000 km. In connection with height determination from PGS a procedure of constituting a well-distributed set of fiducial ground stations by using high-precision astrogravimetric methods together with millimeter-level accuracy astrogravimetric leveling to test various space systems observations has been suggested. 相似文献
3.
Confirming regional 1 cm differential geoid accuracy from airborne gravimetry: the Geoid Slope Validation Survey of 2011 总被引：3，自引：3，他引：0
Dru A. Smith Simon A. Holmes Xiaopeng Li Sébastien Guillaume Yan Ming Wang Beat Bürki Daniel R. Roman Theresa M. Damiani 《Journal of Geodesy》2013,87(10-12):885-907
A terrestrial survey, called the Geoid Slope Validation Survey of 2011 (GSVS11), encompassing leveling, GPS, astrogeodetic deflections of the vertical (DOV) and surface gravity was performed in the United States. The general purpose of that survey was to evaluate the current accuracy of gravimetric geoid models, and also to determine the impact of introducing new airborne gravity data from the ‘Gravity for the Redefinition of the American Vertical Datum’ (GRAV-D) project. More specifically, the GSVS11 survey was performed to determine whether or not the GRAV-D airborne gravimetry, flown at 11 km altitude, can reduce differential geoid error to below 1 cm in a low, flat gravimetrically uncomplicated region. GSVS11 comprises a 325 km traverse from Austin to Rockport in Southern Texas, and includes 218 GPS stations ( $\sigma _{\Delta h }= 0.4$ cm over any distance from 0.4 to 325 km) co-located with first-order spirit leveled orthometric heights ( $\sigma _{\Delta H }= 1.3$ cm end-to-end), including new surface gravimetry, and 216 astronomically determined vertical deflections $(\sigma _{\mathrm{DOV}}= 0.1^{\prime \prime })$ . The terrestrial survey data were compared in various ways to specific geoid models, including analysis of RMS residuals between all pairs of points on the line, direct comparison of DOVs to geoid slopes, and a harmonic analysis of the differences between the terrestrial data and various geoid models. These comparisons of the terrestrial survey data with specific geoid models showed conclusively that, in this type of region (low, flat) the geoid models computed using existing terrestrial gravity, combined with digital elevation models (DEMs) and GRACE and GOCE data, differential geoid accuracy of 1 to 3 cm (1 $\sigma )$ over distances from 0.4 to 325 km were currently being achieved. However, the addition of a contemporaneous airborne gravity data set, flown at 11 km altitude, brought the estimated differential geoid accuracy down to 1 cm over nearly all distances from 0.4 to 325 km. 相似文献
4.
E. W. Grafarend 《Journal of Geodesy》2001,75(7-8):363-390
In a comparison of the solution of the spherical horizontal and vertical boundary value problems of physical geodesy it is
aimed to construct downward continuation operators for vertical deflections (surface gradient of the incremental gravitational
potential) and for gravity disturbances (vertical derivative of the incremental gravitational potential) from points on the
Earth's topographic surface or of the three-dimensional (3-D) Euclidean space nearby down to the international reference sphere
(IRS). First the horizontal and vertical components of the gravity vector, namely spherical vertical deflections and spherical
gravity disturbances, are set up. Second, the horizontal and vertical boundary value problem in spherical gravity and geometry
space is considered. The incremental gravity vector is represented in terms of vector spherical harmonics. The solution of
horizontal spherical boundary problem in terms of the horizontal vector-valued Green function converts vertical deflections
given on the IRS to the incremental gravitational potential external in the 3-D Euclidean space. The horizontal Green functions
specialized to evaluation and source points on the IRS coincide with the Stokes kernel for vertical deflections. Third, the
vertical spherical boundary value problem is solved in terms of the vertical scalar-valued Green function. Fourth, the operators
for upward continuation of vertical deflections given on the IRS to vertical deflections in its external 3-D Euclidean space
are constructed. Fifth, the operators for upward continuation of incremental gravity given on the IRS to incremental gravity
to the external 3-D Euclidean space are generated. Finally, Meissl-type diagrams for upward continuation and regularized downward
continuation of horizontal and vertical gravity data, namely vertical deflection and incremental gravity, are produced.
Received: 10 May 2000 / Accepted: 26 February 2001 相似文献
5.
I. N. Tziavos 《Journal of Geodesy》1987,61(2):177-197
Mean gravity anomalies, deflections of the vertical, and a geopotential model complete to degree and order180 are combined in order to determine geoidal heights in the area bounded by [34°≦ϕ≤42°, 18°≦λ≦28°]. Moreover, employing point
gravity anomalies simultaneously with the above data, an attempt is made to predict deflections of the vertical in the same
area. The method used in the computations is least squares collocation. Using empirical covariance functions for the data,
the suitable errors for the different sources of observations, and the optimum cap radius around each point of evaluation,
an accuracy better than±0.60m for geoidal heights and±1″.5 for deflections of the vertical is obtained taking into account existing systematic effects. This accuracy refers to the
comparison between observed and predicted values. 相似文献
6.
Johannes Ihde 《Journal of Geodesy》1981,55(2):99-110
The investigations refer to the compartment method by using mean terrestrial free air anomalies only. Three main error influences of remote areas (distance from the fixed point >9°) on height anomalies and deflections of the vertical are being regarded:
- The prediction errors of mean terrestrial free air anomalies have the greatest influence and amount to about ±0″.2 in each component for deflections of the vertical and to ±3 m for height anomalies;
- The error of the compartment method, which originates from converting the integral formulas of Stokes and Vening-Meinesz into summation formulas, can be neglected if the anomalies for points and gravity profiles are compiled to 5°×5° mean values.
- The influences of the mean gravimetric correction terms of Arnold—estimated for important mountains of the Earth by means of an approximate formula—on height anomalies may amount to 1–2 m and on deflections of the vertical to 0″0.5–0″.1, and, therefore, they have to be taken into account for exact calculations.
7.
重力异常和垂线偏差是测高卫星非常重要的产品。二者的精度指标对于未来的测高卫星方案设计至关重要。本文利用球谐函数来对重力异常和垂线偏差的精度指标进行讨论,首先从理论上推导了重力异常和垂线偏差误差的近似匹配关系,然后通过6个超高阶重力场模型验证了有关结论的正确性。数值试验表明:垂线偏差误差和重力异常误差满足近似的比例关系,即若垂线偏差各方位向等精度测量,且假定精度均为1μrad,则所对应的重力异常精度约为1.4mGal;反之,若重力异常的精度为1mGal,则所对应的垂线偏差的精度约为0.7μrad。 相似文献
8.
测线布设是海洋重力测量中海区技术设计的主要内容,在保证测图精度和提高测量效率方面起着关键作用。目前测线间距依据测量任务而定,没有充分顾及测区重力异常的变化特性。结合海洋重力测量的特点,利用EGM2008模型重力异常作为测线布设的先验信息,在满足测量成果精度要求的前提下,估算测线布设间距。利用实测数据检验估算的测线布设间距的合理性,结果表明,利用EGM2008模型估算的测线间距布设测线能满足海洋重力测量的精度要求,为确定海洋重力测量测线布设间距提供量化依据。 相似文献
9.
高程异常、垂线偏差及空中扰动引力矢量是大地测量和空间技术最常用的一组重力场参数,本文在分析了以上三种参数的计算误差源以后,详细论证了计算这些参数对积分面积元的不同要求。在此基础上,本文尝试将高斯积分应用于地球重力场数值计算中,试验结果表明,这样做不仅提高了计算速度和精度,而且能够在一定程度上克服重力场元数值积分的奇异性。 相似文献
10.
Fitting gravimetric geoid models to vertical deflections 总被引：2，自引：2，他引：0
Regional gravimetric geoid and quasigeoid models are now commonly fitted to GPS-levelling data, which simultaneously absorbs
levelling, GPS and quasi/geoid errors due to their inseparability. We propose that independent vertical deflections are used
instead, which are not affected by this inseparability problem. The formulation is set out for geoid slopes and changes in
slopes. Application to 1,080 astrogeodetic deflections over Australia for the AUSGeoid98 model shows that it is feasible,
but the poor quality of the historical astrogeodetic deflections led to some unrealistic values. 相似文献
11.
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12.
There exist three types of convolution formulae for the efficient evaluation of gravity field convolution integrals, i.e., the planar 2D convolution, the spherical 2D convolution and the spherical 1D convolution. The largest drawback of both the planar and the spherical 2D FFT methods is that, due to the approximations in the kernel function, only inexact results can be achieved. Apparently, the reason is the meridian convergence at higher latitudes. As the meridians converge, the ??,?λ blocks do not form a rectangular grid, as is assumed in 2D FFT methods. It should be pointed out that the meridian convergence not only leads to an approximation error in the kernel function, but also causes an approximation error during the implementation of 2D FFT in computer. In order to meet the increasing need for precise determination of the vertica deflections, this paper derives a more precise planar 2D FFT formula for the computation of the vertical deflections. After having made a detailed comparison between the planar and the spherical 2D FFT formulae, we find out the main source of errors causing the loss in accuracy by applying the conventional spherical 2D FFT method. And then, a modified spherical 2D FFT formula for the computation of the vertical deflections is developed in this paper. A series of numerical tests have been carried out to illustrate the improvement made upon the old spherical 2D FFT. The second part of this paper is to discuss the influences of the spherical harmonic reference field, the limited capsize, and the singular integral on the computation of the vertical deflections. The results of the vertical deflections over China by applying the spherical 1D FFT formula with different integration radii have been compared to the astro-observed vertical deflections in the South China Sea to obtain a set of optimum deflection computation parameters. 相似文献
13.
14.
GRACE、GOCE卫星重力计划的实施,对确定高精度重力场模型具有重要贡献。联合GRACE、GOCE卫星数据建立的重力场模型和我国均匀分布的649个GPS/水准数据可以确定我国高程基准重力位,但我国高程基准对应的参考面为似大地水准面,是非等位面,将似大地水准面转化为大地水准面后确定的大地水准面重力位为62 636 854.395 3m~2s~(-2),为提高高阶项对确定大地水准面的贡献,利用高分辨率重力场模型EGM2008扩展GRACE/GOCE模型至2190阶,同时将重力场模型和GPS/水准数据统一到同一参考框架和潮汐系统,最后利用扩展后的模型确定的我国大地水准面重力位为62 636 852.751 8m~2s~(-2)。其中组合模型TIM_R4+EGM2008确定的我国85高程基准重力位值62 636 852.704 5m~2s~(-2)精度最高。重力场模型截断误差对确定我国大地水准面的影响约16cm,潮汐系统影响约4~6cm。 相似文献
15.
Astronomical-topographic levelling using high-precision astrogeodetic vertical deflections and digital terrain model data 总被引：2，自引：1，他引：1
At the beginning of the twenty-first century, a technological change took place in geodetic astronomy by the development of
Digital Zenith Camera Systems (DZCS). Such instruments provide vertical deflection data at an angular accuracy level of 0.̋1
and better. Recently, DZCS have been employed for the collection of dense sets of astrogeodetic vertical deflection data in
several test areas in Germany with high-resolution digital terrain model (DTM) data (10–50 m resolution) available. These
considerable advancements motivate a new analysis of the method of astronomical-topographic levelling, which uses DTM data
for the interpolation between the astrogeodetic stations. We present and analyse a least-squares collocation technique that
uses DTM data for the accurate interpolation of vertical deflection data. The combination of both data sets allows a precise
determination of the gravity field along profiles, even in regions with a rugged topography. The accuracy of the method is
studied with particular attention on the density of astrogeodetic stations. The error propagation rule of astronomical levelling
is empirically derived. It accounts for the signal omission that increases with the station spacing. In a test area located
in the German Alps, the method was successfully applied to the determination of a quasigeoid profile of 23 km length. For
a station spacing from a few 100 m to about 2 km, the accuracy of the quasigeoid was found to be about 1–2 mm, which corresponds
to a relative accuracy of about 0.05−0.1 ppm. Application examples are given, such as the local and regional validation of
gravity field models computed from gravimetric data and the economic gravity field determination in geodetically less covered
regions. 相似文献
16.
重点围绕远程飞行器飞行轨道控制保障需求,开展了空中扰动引力计算和地面重力异常测量精度指标及海洋重力测量测线布设方案的分析与论证。首先通过解析和简化飞行器导航误差解表达式,定量估计了地球重力场对远程飞行器飞行轨迹的影响,并以一定量值的落点偏差为限定指标,研究论证了空中扰动引力的计算精度要求。在此基础上,通过对地面重力异常截断误差及数据传播误差的估计和分析,研究确定了地面/海面网格平均重力异常的观测分辨率和计算精度指标。以此为依据,提出了相对应的海洋重力测量测线布设方案,并通过数值计算验证了所提方案的合理性和有效性。 相似文献
17.
Johannes Bouman 《Journal of Geodesy》2012,86(4):287-304
The vertical gradients of gravity anomaly and gravity disturbance can be related to horizontal first derivatives of deflection
of the vertical or second derivatives of geoidal undulations. These are simplified relations of which different variations
have found application in satellite altimetry with the implicit assumption that the neglected terms—using remove-restore—are
sufficiently small. In this paper, the different simplified relations are rigorously connected and the neglected terms are
made explicit. The main neglected terms are a curvilinear term that accounts for the difference between second derivatives
in a Cartesian system and on a spherical surface, and a small circle term that stems from the difference between second derivatives
on a great and small circle. The neglected terms were compared with the dynamic ocean topography (DOT) and the requirements
on the GOCE gravity gradients. In addition, the signal root-mean-square (RMS) of the neglected terms and vertical gravity
gradient were compared, and the effect of a remove-restore procedure was studied. These analyses show that both neglected
terms have the same order of magnitude as the DOT gradient signal and may be above the GOCE requirements, and should be accounted
for when combining altimetry derived and GOCE measured gradients. The signal RMS of both neglected terms is in general small
when compared with the signal RMS of the vertical gravity gradient, but they may introduce gradient errors above the spherical
approximation error. Remove-restore with gravity field models reduces the errors in the vertical gravity gradient, but it
appears that errors above the spherical approximation error cannot be avoided at individual locations. When computing the
vertical gradient of gravity anomaly from satellite altimeter data using deflections of the vertical, the small circle term
is readily available and can be included. The direct computation of the vertical gradient of gravity disturbance from satellite
altimeter data is more difficult than the computation of the vertical gradient of gravity anomaly because in the former case
the curvilinear term is needed, which is not readily available. 相似文献
18.
全面分析重力测量的各种误差和目前能达到的精度后，对垂直形变监测中引入重力观测值的可行性进行了具体研究。结果表明，若仅是为了测定点的垂直位移的高程速率，增加重力测量数据后对形变分析的精度增益十分有限。但是对于大跨度垂直形变监测和局部地区突发性垂直形变测定，重力测量方法可以及时掌握垂直形变的趋势 相似文献
19.
Summary Using a data set of 260 000 gravity anomalies it is shown that common characteristics for a local covariance function exist
in an area as large as Canada excluding the Rocky Mountains. After eliminating global features by referencing the data to
the GEM-10 satellite solution, the shape of the covariance function is remarkably consistent from one sample area to the next.
The determination of the essential parameters and the fitting of the covariance function are discussed in detail.
To test the reliability of the derived function, deflections of the vertical are estimated at about 230 stations where astrogeodetic
data are available. Results show that the standard error obtained from the discrepancies is about1″ for each component and that the error covariance matrix of least-squares collocation reflects this accuracy remarkably well. 相似文献
20.
本文提出了我国新旧重力系统实施转换的三种方法。其中平差法理论严谨,充分顾及了重力系统差异的物理意义,并可获得足够的信息,以估算旧网的实际精度;插值法为实地转换,系统转换误差小,计算简便,是较理想的实用模型;回归法是两套系统的平滑拟合,采用全国统一的转换模型,计算工作量最小。三种方法亦可结合使用。 相似文献