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1.
The short wavelength geoid undulations, caused by topography, amount to several decimeters in mountainous areas. Up to now these effects are computed by means of digital terrain models in a grid of 100–500m. However, for many countries these data are not yet available or their collection is too expensive. This problem can be overcome by considering the special behaviour of the gravity potential along mountain slopes. It is shown that 90 per cent of the topographic effects are represented by a simple summation formula, based on the average height differences and distances between valleys and ridges along the geoid profiles, δN=[30.H.D.+16.(H−H′).D] in mm/km, (error<10%), whereH, H′, D are estimated in a map to the nearest 0.2km. The formula is valid for asymmetric sides of valleys (H, H′) and can easily be corrected for special shapes. It can be used for topographic refinement of low resolution geoids and for astrogeodetic projects. The “slope method” was tested in two alpine areas (heights up to 3800m, astrogeodetic deflection points every 170km 2) and resulted in a geoid accuracy of ±3cm. In first order triangulation networks (astro points every 1000km 2) or for gravimetric deflections the accuracy is about 10cm per 30km. Since a map scale of 1∶500.000 is sufficient, the method is suitable for developing countries, too.  相似文献   

2.
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   

3.
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   

4.
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   

5.
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   

6.
Summary A special application of T. Krarup’s theory of collocation (least squares estimation) to astrogeodetic determinations of the geoid is treated.  相似文献   

7.
This paper deals with the problem of determining a scalar spherical field from its surface gradient, i.e., the modelling of geoid undulations from deflections of the vertical. Essential tools are integral formulae on the sphere based on Green’s function of the Beltrami operator. The determination of geoid undulations from deflections of the vertical is formulated as multiscale procedure involving scale-dependent regularized versions of the surface gradient of Green’s function. An advantage of the presented approach is that the multiscale method is based on locally supported wavelets. In consequence, local modelling of geoid undulations are calculable from locally available deflections of the vertical  相似文献   

8.
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.
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   

10.
李厚朴  边少锋 《测绘学报》2011,40(6):730-735
为提高利用Molodensky公式反演测高大地水准面中央区效应的精度,视中央区为矩形域,将垂线偏差分量表示成双二次多项式插值形式,引入非奇异变换,推导出了大地水准面的计算公式。垂线偏差理论模型下的分析表明本文导出公式误差为零,而传统公式的误差与纬度以及垂线偏差子午分量与卯酉分量之间的比值有关;以中纬度区域分辨率为2'*2'的垂线偏差数据为背景场进行了实际计算,结果表明在反演计算点本身所在的1个网格对大地水准面的贡献时,传统公式与本文导出公式计算结果差值的最大值达数厘米。本文导出公式可为测高大地水准面的高精度反演提供理论依据。  相似文献   

11.
The international ellipsoid, 1924, was locally fitted to the Indian geoid in 1927. An attempt is here made to obtain the initial values for the Indian geodetic datum (I.G.D.) in absolute terms by gravimetric method using the available gravity material. The values obtained independently by the author’s least-squares solution technique, making use of the available astrogeodetic data in India, were also utilized in the results of the present determination.  相似文献   

12.
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   

13.
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   

14.
The Bruns formula is generalized to three dimensions with the derivation of equations expressing the height anomaly vector or the geoid undulation vector as a function of the disturbing gravity potential and its spatial derivatives. It is shown that the usual scalar Bruns formula provides not the separation along the normal to the reference ellipsoid but the component of the relevant spatial separation along the local direction of normal gravity. The above results which hold for any type of normal potential are specialized for the usual Somigliana-Pizzetti normal field so that the components of the geoid undulation vector are expressed as functions of the parameters of the reference ellipsoid, the disturbing potential and its spatial derivatives with respect to three types of curvilinear coordinates, ellipsoidal, geodetic and spherical. Finally the components of the geoid undulation vector are related to the deflections of the vertical in a spherical approximation.  相似文献   

15.
郑汉球 《测绘学报》1991,20(4):260-268
  相似文献   

16.
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   

17.
A new computational procedure for derivation of marine geoid on a 2.5′×2.5′grid in a non-tidal system over the South China Sea and the Philippine Sea from multi-satellite altimeter sea surface heights is discussed. Single-and dual-satellite crossovers were performed, and components of deflections of the vertical were determined at the crossover positions using Sand-well's computational theory, and gridded onto a 2.5′×2.5′resolution grid by employing the Shepard's interpolation procedure. 2.5′×2.5′grid of EGM96-derived components of deflections of the vertical and geoid heights were then used as reference global geopotential model quantities in a remove-restore procedure to implement the Molodensky-like formula via 1D-FFT technique to predict the geoid heights over the South China Sea and the Philippine Sea from the gridded altimeter-derived components of deflec-tions of the vertical. Statistical comparisons between the altimeter-and the EGM96- derived geoid heights showed that there was a root-mean-square agreement of ±0.35 m between them in a region of less tectonically active geological structures. However, over areas of tectonically active structures such as the Philippine trench, differences of about -19.9 m were obtained.  相似文献   

18.
The problem of improving the geoid from satellite altimetry is formulated and studied within the scope of geophysical fluid dynamics. The oceanic levelling is defined by analogy to the astrogeodetic levelling and it is used to determine the sea surface topography as a function of current velocity, atmospheric pressure and viscosity. Simulating strong currents like the Gulf Stream or the Kuroshio the numerical treatment of the oceanic levelling shows that the sea surface topography can come up to an order of magnitude of1–2 m, whereby the results depend on latitude and slightly on the actual pressure conditions.  相似文献   

19.
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   

20.
在板块边缘的冲撞地区重力场的求定   总被引：7，自引：2，他引：7  
陈俊勇  刘允诺 《测绘学报》1994,23(4):241-246
在陆地上，板块边的冲撞地区一般都是呈现地形复杂，地表和地下的质量分布不均衡、有强烈的地壳运动和构造运动，因此，该地区的重力场（重力异常、垂线偏差，大地水准面）变化剧烈。对它的归算和推估都需要作特殊的考虑。本文以位于欧亚板块和印度板块边缘冲撞地区的珠穆朗玛峰测区的重力场求定为例，进行讨论。  相似文献   

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