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1.
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   

2.
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   

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   

4.
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   

5.
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   

6.
We present results from a new vertical deflection (VD) traverse observed in Perth, Western Australia, which is the first of its kind in the Southern Hemisphere. A digital astrogeodetic QDaedalus instrument was deployed to measure VDs with \({\sim }\)0.2\(''\) precision at 39 benchmarks with a \({{\sim }}1~\hbox {km}\) spacing. For the conversion of VDs to quasigeoid height differences, the method of astronomical–topographical levelling was applied, based on topographical information from the Shuttle Radar Topography Mission. The astronomical quasigeoid heights are in 20–30 mm (RMS) agreement with three independent gravimetric quasigeoid models, and the astrogeodetic VDs agree to 0.2–0.3\(''\) (north–south) and 0.6–0.9\(''\) (east–west) RMS. Tilt-like biases of \({\sim }1\,\,\hbox {mm}\) over \({\sim }1\,\,\hbox {km}\) are present for all quasigeoid models within \({\sim }20\,\,\hbox {km}\) of the coastline, suggesting inconsistencies in the coastal zone gravity data. The VD campaign in Perth was designed as a low-cost effort, possibly allowing replication in other Southern Hemisphere countries (e.g., Asia, Africa, South America and Antarctica), where VD data are particularly scarce.  相似文献   

7.
A global geopotential model, like EGM2008, is not capable of representing the high-frequency components of Earth’s gravity field. This is known as the omission error. In mountainous terrain, omission errors in EGM2008, even when expanded to degree 2,190, may reach amplitudes of 10 cm and more for height anomalies. The present paper proposes the utilisation of high-resolution residual terrain model (RTM) data for computing estimates of the omission error in rugged terrain. RTM elevations may be constructed as the difference between the SRTM (Shuttle Radar Topography Mission) elevation model and the DTM2006.0 spherical harmonic topographic expansion. Numerical tests, carried out in the German Alps with a precise gravimetric quasigeoid model (GCG05) and GPS/levelling data as references, demonstrate that RTM-based omission error estimates improve EGM2008 height anomaly differences by 10 cm in many cases. The comparisons of EGM2008-only height anomalies and the GCG05 model showed 3.7 cm standard deviation after a bias-fit. Applying RTM omission error estimates to EGM2008 reduces the standard deviation to 1.9 cm which equates to a significant improvement rate of 47%. Using GPS/levelling data strongly corroborates these findings with an improvement rate of 49%. The proposed RTM approach may be of practical value to improve quasigeoid determination in mountainous areas without sufficient regional gravity data coverage, e.g., in parts of Asia, South America or Africa. As a further application, RTM omission error estimates will allow refined validation of global gravity field models like EGM2008 from GPS/levelling data.  相似文献   

8.
Recently, four global geopotential models (GGMs) were computed and released based on the first 2 months of data collected by the Gravity field and steady-state Ocean Circulation Explorer (GOCE) dedicated satellite gravity field mission. Given that GOCE is a technologically complex mission and different processing strategies were applied to real space-collected GOCE data for the first time, evaluation of the new models is an important aspect. As a first assessment strategy, we use terrestrial gravity data over Switzerland and Australia and astrogeodetic vertical deflections over Europe and Australia as ground-truth data sets for GOCE model evaluation. We apply a spectral enhancement method (SEM) to the truncated GOCE GGMs to make their spectral content more comparable with the terrestrial data. The SEM utilises the high-degree bands of EGM2008 and residual terrain model data as a data source to widely bridge the spectral gap between the satellite and terrestrial data. Analysis of root mean square (RMS) errors is carried out as a function of (i) the GOCE GGM expansion degree and (ii) the four different GOCE GGMs. The RMS curves are also compared against those from EGM2008 and GRACE-based GGMs. As a second assessment strategy, we compare global grids of GOCE GGM and EGM2008 quasigeoid heights. In connection with EGM2008 error estimates, this allows location of regions where GOCE is likely to deliver improved knowledge on the Earth’s gravity field. Our ground truth data sets, together with the EGM2008 quasigeoid comparisons, signal clear improvements in the spectral band ~160–165 to ~180–185 in terms of spherical harmonic degrees for the GOCE-based GGMs, fairly independently of the individual GOCE model used. The results from both assessments together provide strong evidence that the first 2 months of GOCE observations improve the knowledge of the Earth’s static gravity field at spatial scales between ~125 and ~110 km, particularly over parts of Asia, Africa, South America and Antarctica, in comparison with the pre-GOCE-era.  相似文献   

9.
Flight test results from a strapdown airborne gravity system   总被引：3，自引：0，他引：3  
In June 1995, a flight test was carried out over the Rocky Mountains to assess the accuracy of airborne gravity for geoid determination. The gravity system consisted of a strapdown inertial navigation system (INS), two GPS receivers with zero baseline on the airplane and multiple GPS master stations on the ground, and a data logging system. To the best of our knowledge, this was the first time that a strapdown INS has been used for airborne gravimetry. The test was designed to assess repeatability as well as accuracy of airborne gravimetry in a highly variable gravity field. An east-west profile of 250 km across the Rocky Mountains was chosen and four flights over the same ground track were made. The flying altitude was about 5.5km, i.e., between 2.5 and 5.0km above ground, and the average flying speed was about 430km/h. This corresponds to a spatial resolution (half wavelength of cutoff frequency) of 5.07.0km when using filter lengths between 90 and 120s. This resolution is sufficient for geoid determination, but may not satisfy other applications of airborne gravimetry. The evaluation of the internal and external accuracy is based on repeated flights and comparison with upward continued ground gravity using a detailed terrain model. Gravity results from repeated flight lines show that the standard deviation between flights is about 2mGal for a single profile and a filter length of 120s, and about 3mGal for a filter length of 90s. The standard deviation of the difference between airborne gravity upward continued ground gravity is about 3mGal for both filter lengths. A critical discussion of these results and how they relate to the different transfer functions applied, is given in the paper. Two different mathematical approaches to airborne scalar gravimetry are applied and compared, namely strapdown inertial scalar gravimetry (SISG) and rotation invariant scalar gravimetry (RISG). Results show a significantly better performance of the SISG approach for a strapdown INS of this accuracy class. Because of major differences in the error model of the two approaches, the RISG method can be used as an effective reliability check of the SISG method. A spectral analysis of the residual errors of the flight profiles indicates that a relative geoid accuracy of 23cm over distances of 200km (0.1 ppm) can be achieved by this method. Since these results present a first data analysis, it is expected that further improvements are possible as more refined modelling is applied. Received: 19 August 1996 / Accepted: 12 May 1997  相似文献   

10.
Any errors in digital elevation models (DEMs) will introduce errors directly in gravity anomalies and geoid models when used in interpolating Bouguer gravity anomalies. Errors are also propagated into the geoid model by the topographic and downward continuation (DWC) corrections in the application of Stokes’s formula. The effects of these errors are assessed by the evaluation of the absolute accuracy of nine independent DEMs for the Iran region. It is shown that the improvement in using the high-resolution Shuttle Radar Topography Mission (SRTM) data versus previously available DEMs in gridding of gravity anomalies, terrain corrections and DWC effects for the geoid model are significant. Based on the Iranian GPS/levelling network data, we estimate the absolute vertical accuracy of the SRTM in Iran to be 6.5 m, which is much better than the estimated global accuracy of the SRTM (say 16 m). Hence, this DEM has a comparable accuracy to a current photogrammetric high-resolution DEM of Iran under development. We also found very large differences between the GLOBE and SRTM models on the range of −750 to 550 m. This difference causes an error in the range of −160 to 140 mGal in interpolating surface gravity anomalies and −60 to 60 mGal in simple Bouguer anomaly correction terms. In the view of geoid heights, we found large differences between the use of GLOBE and SRTM DEMs, in the range of −1.1 to 1 m for the study area. The terrain correction of the geoid model at selected GPS/levelling points only differs by 3 cm for these two DEMs.  相似文献   

11.
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   

12.
The AUSGeoid09 model of the Australian Height Datum   总被引：8，自引：6，他引：2  
AUSGeoid09 is the new Australia-wide gravimetric quasigeoid model that has been a posteriori fitted to the Australian Height Datum (AHD) so as to provide a product that is practically useful for the more direct determination of AHD heights from Global Navigation Satellite Systems (GNSS). This approach is necessary because the AHD is predominantly a third-order vertical datum that contains a ~1 m north-south tilt and ~0.5 m regional distortions with respect to the quasigeoid, meaning that GNSS-gravimetric-quasigeoid and AHD heights are inconsistent. Because the AHD remains the official vertical datum in Australia, it is necessary to provide GNSS users with effective means of recovering AHD heights. The gravimetric component of the quasigeoid model was computed using a hybrid of the remove-compute-restore technique with a degree-40 deterministically modified kernel over a one-degree spherical cap, which is superior to the remove-compute-restore technique alone in Australia (with or without a cap). This is because the modified kernel and cap combine to filter long-wavelength errors from the terrestrial gravity anomalies. The zero-tide EGM2008 global gravitational model to degree 2,190 was used as the reference field. Other input data are ~1.4 million land gravity anomalies from Geoscience Australia, 1′ × 1′ DNSC2008GRA altimeter-derived gravity anomalies offshore, the 9′′ × 9′′ GEODATA-DEM9S Australian digital elevation model, and a readjustment of Australian National Levelling Network (ANLN) constrained to the CARS2006 mean dynamic ocean topography model. To determine the numerical integration parameters for the modified kernel, the gravimetric component of AUSGeoid09 was compared with 911 GNSS-observed ellipsoidal heights at benchmarks. The standard deviation of fit to the GNSS-AHD heights is ±222 mm, which dropped to ±134 mm for the readjusted GNSS-ANLN heights showing that careful consideration now needs to be given to the quality of the levelling data used to assess gravimetric quasigeoid models. The publicly released version of AUSGeoid09 also includes a geometric component that models the difference between the gravimetric quasigeoid and the zero surface of the AHD at 6,794 benchmarks. This a posteriori fitting used least-squares collocation (LSC) in cross-validation mode to determine a correlation length of 75 km for the analytical covariance function, whereas the noise was taken from the estimated standard deviation of the GNSS ellipsoidal heights. After this LSC surface fitting, the standard deviation of fit reduced to ±30 mm, one-third of which is attributable to the uncertainty in the GNSS ellipsoidal heights.  相似文献   

13.
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   

14.
AUSGeoid2020 is a combined gravimetric–geometric model (sometimes called a “hybrid quasigeoid model”) that provides the separation between the Geocentric Datum of Australia 2020 (GDA2020) ellipsoid and Australia’s national vertical datum, the Australian Height Datum (AHD). This model is also provided with a location-specific uncertainty propagated from a combination of the levelling, GPS ellipsoidal height and gravimetric quasigeoid data errors via least squares prediction. We present a method for computing the relative uncertainty (i.e. uncertainty of the height between any two points) between AUSGeoid2020-derived AHD heights based on the principle of correlated errors cancelling when used over baselines. Results demonstrate AUSGeoid2020 is more accurate than traditional third-order levelling in Australia at distances beyond 3 km, which is 12 mm of allowable misclosure per square root km of levelling. As part of the above work, we identified an error in the gravimetric quasigeoid in Port Phillip Bay (near Melbourne in SE Australia) coming from altimeter-derived gravity anomalies. This error was patched using alternative altimetry data.  相似文献   

15.
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   

16.
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   

17.
 The use of GPS for height control in an area with existing levelling data requires the determination of a local geoid and the bias between the local levelling datum and the one implicitly defined when computing the local geoid. If only scarse gravity data are available, the heights of new data may be collected rapidly by determining the ellipsoidal height by GPS and not using orthometric heights. Hence the geoid determination has to be based on gravity disturbances contingently combined with gravity anomalies. Furthermore, existing GPS/levelling data may also be used in the geoid determination if a suitable general gravity field modelling method (such as least-squares collocation, LSC) is applied. A comparison has been made in the Aswan Dam area between geoids determined using fast Fourier transform (FFT) with gravity disturbances exclusively and LSC using only the gravity disturbances and the disturbances combined with GPS/levelling data. The EGM96 spherical harmonic model was in all cases used in a remove–restore mode. A total of 198 gravity disturbances spaced approximately 3 km apart were used, as well as 35 GPS/levelling points in the vicinity and on the Aswan Dam. No data on the Nasser Lake were available. This gave difficulties when using FFT, which requires the use of gridded data. When using exclusively the gravity disturbances, the agreement between the GPS/levelling data were 0.71 ± 0.17 m for FFT and 0.63 ± 0.15 for LSC. When combining gravity disturbances and GPS/levelling, the LSC error estimate was ±0.10 m. In the latter case two bias parameters had to be introduced to account for a possible levelling datum difference between the levelling on the dam and that on the adjacent roads. Received: 14 August 2000 / Accepted: 28 February 2001  相似文献   

18.
New Zealand uses 13 separate local vertical datums (LVDs) based on geodetic levelling from 12 different tide-gauges. We describe their unification using a regional gravimetric quasigeoid model and GPS-levelling data on each LVD. A novel application of iterative quasigeoid computation is used, where the LVD offsets computed from earlier models are used to apply additional gravity reductions from each LVD to that model. The solution converges after only three iterations yielding LVD offsets ranging from 0.24 to 0.58 m with an average standard deviation of ±0.08 m. The so-computed LVD offsets agree, within expected data errors, with geodetically levelled height differences at common benchmarks between adjacent LVDs. This shows that iterated quasigeoid models have a role in vertical datum unification.  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.
On the basis of gravity field model （EIGEN_CG01C）, together with multi-altimeter data, the improved deflection of the vertical gridded in 2＇×2＇ in China marginal sea and gridded in 5＇×5＇ in the global sea was determined by using the weighted method of along-track least squares, and the accuracy is better than 1.2^# in China marginal sea. As for the quality of the deflection of the vertical, it meets the challenge for the gravity field of high resolution and accuracy, it shows that, compared with the shipboard gravimetry in the sea, the accuracy of the gravity anomalies computed with the marine deflection of the vertical by inverse Vening-Meinesz formula is 7.75 m.s ^-2.  相似文献   

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