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1.
S. Ono 《Journal of Geodesy》1985,59(3):275-288
In order to solve the problems of determining the shape of a part of the earth of national or continental extent, that is,
of rigorous constituting and computing of the astrogeodetic network, it is required to determine gravimetric deflections of
the vertical with an accuracy of, say, 0″.3. For this it is adequate to carry out additional gravity surveys in the neighborhoods
of computation points, in addition to a given uniform gravity survey (normal density gravity survey).
The study offers a method to determine the optimal distribution of gravity stations in such a gravity survey, which guarantees
a given accuracy of computed gravimetric deflections of the vertical for a given statistical condition which characterizes
the variation of the gravity field. The approach used here is based on the concept of the error of representation and the
error propagation of Vening Meinesz integrals. 相似文献
2.
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 总被引：1，自引：0，他引：1
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 相似文献
3.
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
4.
F. L. Clarke 《Journal of Geodesy》1981,55(1):1-16
Comparisons of gravimetric and astrogeodetic deflections of the vertical in the Australian region indicate that the former
are affected by position dependent systematic errors, even after orientation onto the Australian Geodetic Datum. These are
probably due to errors in the predicted mean anomalies for gravimetrically unsurveyed oceanic regions to the east, south and
west of the continent. Deflection component residuals (astrogeodetic minus oriented gravimetric) at 83 control stations are
made the observables in a set of observation equations, based on the Vening Meinesz equations, from which pseudocorrections
to the mean anomalies for a set of arbitrarily selected surface elements are computed. These pseudocorrections compensate
for prediction errors in much larger unsurveyed regions. Their effects on individual deflection components are calculated
using the Vening Meinesz equations. Statistical tests indicate that pseudocorrections computed for four large offshore elements
and six smaller elements in unsurveyed areas produce corrections to the gravimetric deflections which make the ξ and η components
in seconds of arc consistent with normally distributed populations N (0.00, 0.702). 相似文献
5.
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
6.
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
7.
Prediction of vertical deflections from high-degree spherical harmonic synthesis and residual terrain model data 总被引：6，自引：4，他引：2
Christian Hirt 《Journal of Geodesy》2010,84(3):179-190
This study demonstrates that in mountainous areas the use of residual terrain model (RTM) data significantly improves the
accuracy of vertical deflections obtained from high-degree spherical harmonic synthesis. The new Earth gravitational model
EGM2008 is used to compute vertical deflections up to a spherical harmonic degree of 2,160. RTM data can be constructed as
difference between high-resolution Shuttle Radar Topography Mission (SRTM) elevation data and the terrain model DTM2006.0
(a spherical harmonic terrain model that complements EGM2008) providing the long-wavelength reference surface. Because these
RTM elevations imply most of the gravity field signal beyond spherical harmonic degree of 2,160, they can be used to augment
EGM2008 vertical deflection predictions in the very high spherical harmonic degrees. In two mountainous test areas—the German
and the Swiss Alps—the combined use of EGM2008 and RTM data was successfully tested at 223 stations with high-precision astrogeodetic
vertical deflections from recent zenith camera observations (accuracy of about 0.1 arc seconds) available. The comparison
of EGM2008 vertical deflections with the ground-truth astrogeodetic observations shows root mean square (RMS) values (from
differences) of 3.5 arc seconds for ξ and 3.2 arc seconds for η, respectively. Using a combination of EGM2008 and RTM data for the prediction of vertical deflections considerably reduces
the RMS values to the level of 0.8 arc seconds for both vertical deflection components, which is a significant improvement
of about 75%. Density anomalies of the real topography with respect to the residual model topography are one factor limiting
the accuracy of the approach. The proposed technique for vertical deflection predictions is based on three publicly available
data sets: (1) EGM2008, (2) DTM2006.0 and (3) SRTM elevation data. This allows replication of the approach for improving the
accuracy of EGM2008 vertical deflection predictions in regions with a rough topography or for improved validation of EGM2008
and future high-degree spherical harmonic models by means of independent ground truth data. 相似文献
8.
A. M. C. Srivastava 《Journal of Geodesy》1984,58(4):510-517
The astrogeodetic—gravimetric method based on the principle of least—squares solution has been used to determine the geocentric
Indian geodetic datum making use of the available nongeocentric astrogeodetic data and the gravimetric geocentric geoidal
heights in the form of smoothened values. Everett's method of interpolation has been used to obtain the smoothened geoidal
heights at the astrogeodetic stations in India from the available generalized values at 1°×1° corners. The values of the geoidal
height and deflections of the vertical at the geodetic datum Kalianpur H.S. so obtained have the negligible difference from
the values computed earlier by the same method using directly computed gravimetric geoidal heights at the astrogeodetic stations,
indicating that the use of the interpolated values in the astrogeodetic—gravimetric method employed would be an economical
approach of absolute orientation of a nongeocentric system if the gravimetric geoidal heights are available at 1°×1° corners
in the area of interest. 相似文献
9.
D. Arabelos 《Journal of Geodesy》1985,59(2):109-123
The evaluation of deflections of the vertical for the area of Greece is attempted using a combination of topographic and astrogeodetic
data. Tests carried out in the area bounded by 35°≤ϕ≤42°, 19°≤λ≤27° indicate that an accuracy of ±3″.3 can be obtained in
this area for the meridian and prime vertical deflection components when high resolution topographic data in the immediate
vicinity of computation points are used, combined with high degree spherical harmonic expansions of the geopotential and isostatic
reduction potential. This accuracy is about 25% better than the corresponding topographic-Moho deflection components which
are evaluated using topographic and Moho data up to 120 km around each station, without any combination with the spherical
harmonic expansion of the geopotential or isostatic reduction potential. The accuracy in both cases is increased to about
2″.6 when the astrogeodetic data available in the area mentioned above are used for the prediction of remaining values. Furthermore
the estimation of datum-shift parameters is attempted using least squares collocation. 相似文献
10.
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
11.
1 ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｆａｓｔＦｏｕｒｉｅｒｔｒａｎｓｆｏｒｍ (ＦＦＴ)ｔｅｃｈｎｉｑｕｅｉｓａｖｅｒｙｐｏｗｅｒｆｕｌｔｏｏｌｆｏｒｔｈｅｅｆｆｉｃｉｅｎｔｅｖａｌｕａｔｉｏｎｏｆｇｒａｖｉｔｙｆｉｅｌｄｃｏｎｖｏｌｕｔｉｏｎｉｎｔｅｇｒａｌｓ.Ｔｈａｎｋｓｔｏｔｈｅｇｏｏｄｃｏｍｐｕｔａｔｉｏｎｅｆｆｉｃｉｅｎｃｙ ,ｔｈｅＦＦＴｔｅｃｈｎｉｑｕｅ ,ｉｎｔｈｅｍｉｄ＿1 980ｓ ,ｂｅｇａｎｔｏｆｉｎｄｗｉｄｅｓｐｒｅａｄｕｓｅｉｎｇｅｏｉｄｄｅｔｅｒｍｉｎａｔｉｏｎ ,ｗｈｅｎｃｏｍｐａｒ… 相似文献
12.
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
13.
14.
Y. M. Wang C. Becker G. Mader D. Martin X. Li T. Jiang S. Breidenbach C. Geoghegan D. Winester S. Guillaume B. Bürki 《Journal of Geodesy》2017,91(10):1261-1276
Three Geoid Slope Validation Surveys were planned by the National Geodetic Survey for validating geoid improvement gained by incorporating airborne gravity data collected by the “Gravity for the Redefinition of the American Vertical Datum” (GRAV-D) project in flat, medium and rough topographic areas, respectively. The first survey GSVS11 over a flat topographic area in Texas confirmed that a 1-cm differential accuracy geoid over baseline lengths between 0.4 and 320 km is achievable with GRAV-D data included (Smith et al. in J Geod 87:885–907, 2013). The second survey, Geoid Slope Validation Survey 2014 (GSVS14) took place in Iowa in an area with moderate topography but significant gravity variation. Two sets of geoidal heights were computed from GPS/leveling data and observed astrogeodetic deflections of the vertical at 204 GSVS14 official marks. They agree with each other at a \({\pm }1.2\,\, \hbox {cm}\) level, which attests to the high quality of the GSVS14 data. In total, four geoid models were computed. Three models combined the GOCO03/5S satellite gravity model with terrestrial and GRAV-D gravity with different strategies. The fourth model, called xGEOID15A, had no airborne gravity data and served as the benchmark to quantify the contribution of GRAV-D to the geoid improvement. The comparisons show that each model agrees with the GPS/leveling geoid height by 1.5 cm in mark-by-mark comparisons. In differential comparisons, all geoid models have a predicted accuracy of 1–2 cm at baseline lengths from 1.6 to 247 km. The contribution of GRAV-D is not apparent due to a 9-cm slope in the western 50-km section of the traverse for all gravimetric geoid models, and it was determined that the slopes have been caused by a 5 mGal bias in the terrestrial gravity data. If that western 50-km section of the testing line is excluded in the comparisons, then the improvement with GRAV-D is clearly evident. In that case, 1-cm differential accuracy on baselines of any length is achieved with the GRAV-D-enhanced geoid models and exhibits a clear improvement over the geoid models without GRAV-D data. GSVS14 confirmed that the geoid differential accuracies are in the 1–2 cm range at various baseline lengths. The accuracy increases to 1 cm with GRAV-D gravity when the west 50 km line is not included. The data collected by the surveys have high accuracy and have the potential to be used for validation of other geodetic techniques, e.g., the chronometric leveling. To reach the 1-cm height differences of the GSVS data, a clock with frequency accuracy of \(10^{-18}\) is required. Using the GSVS data, the accuracy of ellipsoidal height differences can also be estimated. 相似文献
15.
基于重力场水平分量-垂线偏差对地形信息敏感的特点,根据边值理论由重力与地形数据确定格网垂线偏差模型,在此基础上,首先利用三维重力矢量-格网垂线偏差与格网重力异常,联合格网高程数据求得格网点间高程异常差,然后通过GPS/水准点的控制,构成紧密的几何条件,进行严密平差,从而获得高分辨率、高精度似大地水准面的数值模型。按照本文方法,利用我国6600多个GPS/水准点、1'×1'的格网垂线偏差、格网重力异常、格网高程数据,整体平差计算了我国陆海统一的似大地水准面模型,经GPS/水准点检核,全国似大地水准面的绝对精度达到了4 cm,相对精度优于7 cm。 相似文献
16.
17.
给出了数字天顶摄影仪的基本结构和垂线偏差测量的基本算法,结合仪器和测量过程,分析了垂线偏差测量误差。数字天顶摄影仪的自动化程度和测量精度都高于传统的天文大地测量。 相似文献
18.
Arabinda Sharma K. N. Tiwari P. B. S. Bhadoria 《Journal of the Indian Society of Remote Sensing》2009,37(1):139-146
Digital elevation models (DEM) are becoming increasingly important as tools in hydrological research and water resources management.
Since error and uncertainty are inherently associated with spatial data, a complete evaluation of a DEM is of utmost importance
before it is put into subsequent analysis. The present paper offers an innovative approach for quality assessment of contour
interpolated DEMs of different resolutions. Five most frequently cited interpolation methods viz., TIN with linear interpolation,
Inverse Distance Weighing, Thin Plate Spline, Ordinary Kriging and TOPOGRID were selected for gridding of contours at five
different resolutions i.e., 30m, 45m, 60m, 75m and 90m. In order to compare the quality of interpolated DEMs, a qualitative
and quantitative evaluation of inter-polated DEMs for their vertical, horizontal and shape accuracy were carried out. It was
found that different interpolation methods produced DEMs with different levels of artifacts. The analyses of vertical accuracy
suggested that the variations were not pronounced in nature. However, the quantitative comparisons for horizontal and shape
accuracy showed that there was a high level of disparity with significant differences among the interpolated DEMs. 相似文献
19.
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
20.
Accuracy analysis of vertical deflection data observed with the Hannover Digital Zenith Camera System TZK2-D 总被引：4，自引：1，他引：3
This paper analyses the accuracy of vertical deflection measurements carried out with the Digital Zenith Camera System TZK2-D,
an astrogeodetic state-of-the-art instrumentation developed at the University of Hannover. During 107 nights over a period
of 3.5 years, the system was used for repeated vertical deflection observations at a selected station in Hannover. The acquired
data set consists of about 27,300 single measurements and covers 276 h of observation time, respectively. For the data collected
at an earlier stage of development (2003 to 2004), the accuracy of the nightly mean values has been found to be about 0′′.10−0′′.12.
Due to applying a refined observation strategy since 2005, the accuracy of the vertical deflection measurements was enhanced
into the unprecedented range of 0′′.05 − 0′′.08. Accessing the accuracy level of 0′′.05 requires usually 1 h of observational
data, while the 0′′.08 accuracy level is attained after 20 min measurement time. In comparison to the analogue era of geodetic
astronomy, the accuracy of vertical deflection observations is significantly improved by about one order of magnitude. 相似文献