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1.
A detailed gravimetric geoid in the North Atlantic Ocean, named DGGNA-77, has been computed, based on a satellite and gravimetry derived earth potential model (consisting in spherical harmonic coefficients up to degree and order 30) and mean free air surface gravity anomalies (35180 1°×1° mean values and 245000 4′×4′ mean values). The long wavelength undulations were computed from the spherical harmonics of the reference potential model and the details were obtained by integrating the residual gravity anomalies through the Stokes formula: from 0 to 5° with the 4′×4′ data, and from 5° to 20° with the 1°×1° data. For computer time reasons the final grid was computed with half a degree spacing only. This grid extends from the Gulf of Mexico to the European and African coasts. Comparisons have been made with Geos 3 altimetry derived geoid heights and with the 5′×5′ gravimetric geoid derived byMarsh andChang [8] in the northwestern part of the Atlantic Ocean, which show a good agreement in most places apart from some tilts which porbably come from the satellite orbit recovery.  相似文献   

2.
A gravimetric geoid computed using different techniques has been compared to a geoid derived from Geos-3 altimeter data in two 30°×30° areas: one in the Tonga Trench area and one in the Indian Ocean. The specific techniques used were the usual Stokes integration (using 1°×1° mean anomalies) with the Molodenskii truncation procedure; a modified Stokes integration with a modified truncation method; and computations using three sets of potential coefficients including one complete to degree 180. In the Tonga Trench area the standard deviation of the difference between the modified Stokes’ procedure and the altimeter geoid was ±1.1 m while in the Indian Ocean area the difference was ±0.6 m. Similar results were found from the 180×180 potential coefficient field. However, the differences in using the usual Stokes integration procedure were about a factor of two greater as was predicted from an error analysis. We conclude that there is good agreement at the ±1 m level between the two types of geoids. In addition, systematic differences are at the half-meter level. The modified Stokes procedure clearly is superior to the usual Stokes method although the 180×180 solution is of comparable accuracy with the computational effort six times less than the integration procedures.  相似文献   

3.
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   

4.
1　ＩｎｔｒｏｄｕｃｔｉｏｎＤｉｆｆｅｒｅｎｔｇｅｏｉｄｓｏｌｕｔｉｏｎｓｗｅｒｅｃａｒｒｉｅｄｏｕｔｆｏｒＥ ｇｙｐｔｕｓｉｎｇｈｅｔｅｒｏｇｅｎｅｏｕｓｄａｔａａｎｄｄｉｆｆｅｒｅｎｔｍｅｔｈｏｄｏｌｏｇｉｅｓ (Ｅｌ＿Ｔｏｋｈｅｙ ,1 993) .ＴｈｅｍａｉｎｇｏａｌｏｆｔｈｉｓｐａｐｅｒｉｓｔｏｄｅｔｅｒｍｉｎｅａｍｏｓｔａｃｃｕｒａｔｅｎｅｗｇｅｏｉｄｆｏｒＥｇｙｐｔｔａｋｉｎｇａｄｖａｎｔａｇｅｏｆａｎｅｗｕｐｄａｔｅｄｇｒａｖｉｔｙｄａｔａｂａｓｅ,ｔｈｅｉｎｆｏｒｍａｔｉｏｎｇｉｖｅｎｂｙ…  相似文献   

5.
 Four different implementations of Stokes' formula are employed for the estimation of geoid heights over Sweden: the Vincent and Marsh (1974) model with the high-degree reference gravity field but no kernel modifications; modified Wong and Gore (1969) and Molodenskii et al. (1962) models, which use a high-degree reference gravity field and modification of Stokes' kernel; and a least-squares (LS) spectral weighting proposed by Sj?berg (1991). Classical topographic correction formulae are improved to consider long-wavelength contributions. The effect of a Bouguer shell is also included in the formulae, which is neglected in classical formulae due to planar approximation. The gravimetric geoid is compared with global positioning system (GPS)-levelling-derived geoid heights at 23 Swedish Permanent GPS Network SWEPOS stations distributed over Sweden. The LS method is in best agreement, with a 10.1-cm mean and ±5.5-cm standard deviation in the differences between gravimetric and GPS geoid heights. The gravimetric geoid was also fitted to the GPS-levelling-derived geoid using a four-parameter transformation model. The results after fitting also show the best consistency for the LS method, with the standard deviation of differences reduced to ±1.1 cm. For comparison, the NKG96 geoid yields a 17-cm mean and ±8-cm standard deviation of agreement with the same SWEPOS stations. After four-parameter fitting to the GPS stations, the standard deviation reduces to ±6.1 cm for the NKG96 geoid. It is concluded that the new corrections in this study improve the accuracy of the geoid. The final geoid heights range from 17.22 to 43.62 m with a mean value of 29.01 m. The standard errors of the computed geoid heights, through a simple error propagation of standard errors of mean anomalies, are also computed. They range from ±7.02 to ±13.05 cm. The global root-mean-square error of the LS model is the other estimation of the accuracy of the final geoid, and is computed to be ±28.6 cm. Received: 15 September 1999 / Accepted: 6 November 2000  相似文献   

6.
 The AUSGeoid98 gravimetric geoid model of Australia has been computed using data from the EGM96 global geopotential model, the 1996 release of the Australian gravity database, a nationwide digital elevation model, and satellite altimeter-derived marine gravity anomalies. The geoid heights are on a 2 by 2 arc-minute grid with respect to the GRS80 ellipsoid, and residual geoid heights were computed using the 1-D fast Fourier transform technique. This has been adapted to include a deterministically modified kernel over a spherical cap of limited spatial extent in the generalised Stokes scheme. Comparisons of AUSGeoid98 with GPS and Australian Height Datum (AHD) heights across the continent give an RMS agreement of ±0.364 m, although this apparently large value is attributed partly to distortions in the AHD. Received: 10 March 2000 / Accepted: 21 February 2001  相似文献   

7.
In this study, ERS-1 altimeter data over the Indian offshore have been processed for deriving marine geoid and gravity. Processing of altimeter data involves corrections for various atmospheric and oceanographic effects, stacking and averaging of repeat passes, cross-over correction, removal of deeper earth and bathymetric effects, spectral analyses and conversion of geoid into free-air gravity anomaly. Methods for generation of residual geoid and free-air gravity anomaly using high resolution ERS-1 168 day repeat altimeter data were developed. High resolution detailed geoid maps, gravity anomaly and their spectral components have been generated over the Indian offshore using ERS-I altimeter data and ARCGIS system. A number of known megastructures over the study area have been successfully interpreted e.g. Bombay High, Saurastra platform, 90° east ridge etc. from these maps.  相似文献   

8.
《Journal of Geodesy》1961,61(1):245-264
Since the presentation of “The Hough Ellipsoid” at the Toronto meeting in 1957, the astro-geodetic geoid was extended into the Caribbean, India, and Japan. The two hemispheres were tentatively connected across the North Atlantic by a reasonable assumption about the unknown geoid profile there. A series of solutions for a world ellipsoid and world datum was made, with and without enforcing the flattening of 1/298.3, with and without gravimetric orientation. The resulting ellipsoids are very small, with an equatorial radius of around 6378 160 m. The agreement between astro-geodetic and gravimetric geoid profiles is greatly improved by the small ellipsoid.  相似文献   

9.
A synthetic [simulated] Earth gravity model (SEGM) of the geoid, gravity and topography has been constructed over Australia specifically for validating regional gravimetric geoid determination theories, techniques and computer software. This regional high-resolution (1-arc-min by 1-arc-min) Australian SEGM (AusSEGM) is a combined source and effect model. The long-wavelength effect part (up to and including spherical harmonic degree and order 360) is taken from an assumed errorless EGM96 global geopotential model. Using forward modelling via numerical Newtonian integration, the short-wavelength source part is computed from a high-resolution (3-arc-sec by 3-arc-sec) synthetic digital elevation model (SDEM), which is a fractal surface based on the GLOBE v1 DEM. All topographic masses are modelled with a constant mass-density of 2,670 kg/m3. Based on these input data, gravity values on the synthetic topography (on a grid and at arbitrarily distributed discrete points) and consistent geoidal heights at regular 1-arc-min geographical grid nodes have been computed. The precision of the synthetic gravity and geoid data (after a first iteration) is estimated to be better than 30 μ Gal and 3 mm, respectively, which reduces to 1 μ Gal and 1 mm after a second iteration. The second iteration accounts for the changes in the geoid due to the superposed synthetic topographic mass distribution. The first iteration of AusSEGM is compared with Australian gravity and GPS-levelling data to verify that it gives a realistic representation of the Earth’s gravity field. As a by-product of this comparison, AusSEGM gives further evidence of the north–south-trending error in the Australian Height Datum. The freely available AusSEGM-derived gravity and SDEM data, included as Electronic Supplementary Material (ESM) with this paper, can be used to compute a geoid model that, if correct, will agree to in 3 mm with the AusSEGM geoidal heights, thus offering independent verification of theories and numerical techniques used for regional geoid modelling.Electronic Supplementary Material Supplementary material is available in the online version of this article at http://dx.doi.org/10.1007/s00190-005-0002-z  相似文献   

10.
The determination of the gravimetric geoid is based on the magnitude of gravity observed at the surface of the Earth or at airborne altitude. To apply the Stokes’s or Hotine’s formulae at the geoid, the potential outside the geoid must be harmonic and the observed gravity must be reduced to the geoid. For this reason, the topographic (and atmospheric) masses outside the geoid must be “condensed” or “shifted” inside the geoid so that the disturbing gravity potential T fulfills Laplace’s equation everywhere outside the geoid. The gravitational effects of the topographic-compensation masses can also be used to subtract these high-frequent gravity signals from the airborne observations and to simplify the downward continuation procedures. The effects of the topographic-compensation masses can be calculated by numerical integration based on a digital terrain model or by representing the topographic masses by a spherical harmonic expansion. To reduce the computation time in the former case, the integration over the Earth can be divided into two parts: a spherical cap around the computation point, called the near zone, and the rest of the world, called the far zone. The latter one can be also represented by a global spherical harmonic expansion. This can be performed by a Molodenskii-type spectral approach. This article extends the original approach derived in Novák et al. (J Geod 75(9–10):491–504, 2001), which is restricted to determine the far-zone effects for Helmert’s second method of condensation for ground gravimetry. Here formulae for the far-zone effects of the global topography on gravity and geoidal heights for Helmert’s first method of condensation as well as for the Airy-Heiskanen model are presented and some improvements given. Furthermore, this approach is generalized for determining the far-zone effects at aeroplane altitudes. Numerical results for a part of the Canadian Rocky Mountains are presented to illustrate the size and distributions of these effects.  相似文献   

11.
The contribution of bathymetry to the prediction of quantities related to the gravity field (e.g., gravity anomalies, geoid heights) is discussed in an extended test area of the central Mediterranean Sea. Sea gravity anomalies and a priori statistical characteristics of depths are used in a least-squares collocation procedure in order to produce new depths, giving a better smoothing of the gravity field when using a remove-restore procedure. The effect of the bottom topography on gravity-field modeling is studied using both the original and the new depths through a residual terrain modeling reduction. The numerical tests show a considerable smoothing of the sea gravity anomalies and the available altimeter heights when the new depth information is taken into account according to the covariance analysis performed. Moreover, geoid heights are computed by combining the sea gravity anomalies either with the original depths or with the new ones, using as a reference surface the OSU91A geopotential model. Comparing the computed geoid heights with adjusted altimeter sea-surface heights (SSHs), better results are obtained when subtracting the attraction of the new depth information. Similar results are obtained when predicting gravity anomalies from altimeter SSHs where the terrain effect on altimetry is based on the new bottom topography. Received: 10 September 1996 / Accepted: 4 August 1997  相似文献   

12.
1　ＩｎｔｒｏｄｕｃｔｉｏｎＴｏｄｅｖｅｌｏｐｔｈｅｏｃｅａｎｗｉｄｅｌｙａｎｄｄｅｅｐｌｙ ,ｗｅｎｅｅｄａｂｕｎｄａｎｔｏｃｅａｎｉｎｆｏｒｍａｔｉｏｎ .Ａｓａｎｅｓｓｅｎｔｉａｌｐａｒｔｏｆｓｕｃｈｉｎｆｏｒｍａｔｉｏｎ ,ｓｅａｆｌｏｏｒｔｏｐｏｇｒａｐｈｙｐｌａｙｓａｖｅｒｙｉｍｐｏｒｔａｎｔｒｏｌｅｉｎａｖａｒｉｅｔｙｏｆｍａｒｉｎｅａｃｔｉｖｉｔｉｅｓ .Ｈｏｗｅｖｅｒ,ｔｈｅｈｉｇｈｃｏｓｔｆｏｒｏｃｅａｎｂａｔｈｙｍｅｔｒｉｃｓｕｒｖｅｙｉｎｇｌｉｍｉｔｓｔｈｅａｐｐｌｉｃａｔｉｏｎｏ…  相似文献   

13.
Bathymetry data from Sognefjord, Norway, have been included in a terrain model, and their influence on the geoid has been calculated. The test area, located in the western part of Norway, was chosen due to its deep fjords and high mountains. Inclusion of bathymetry data in the terrain model altered the computed gravimetric geoid by as much as a few decimeters. The effect was detectable to a distance of more than 100 km. All calculated geoids, both with and without bathymetry data in the terrain model, fit the geoidal heights determined by available Global Positioning System (GPS) and levelling heights at the sub-decimetre level. Contrary to expectations, the accuracy in geoid prediction was reduced when using bathymetric data. The geoid changes were largest over the fjord where no GPS points were located. Different methods on the same area [isostatic and Residual Terrain Model (RTM)-terrain reductions] showed differences of approximately 1 m. Rigorous distinction between quasigeoid and geoid was found to be essential in this kind of area. Received: 12 May 1997 / Accepted 7 May 1998  相似文献   

14.
A method is presented with which to verify that the computer software used to compute a gravimetric geoid is capable of producing the correct results, assuming accurate input data. The Stokes, gravimetric terrain correction and indirect effect formulae are integrated analytically after applying a transformation to surface spherical coordinates centred on each computation point. These analytical results can be compared with those from geoid computation software using constant gravity data in order to verify its integrity. Results of tests conducted with geoid computation software are presented which illustrate the need for integration weighting factors, especially for those compartments close to the computation point. Received: 6 February 1996 / Accepted: 19 April 1997  相似文献   

15.
This paper discusses an altimeter data processing technique designed to compute time series of the mesoscale dynamic sea surface and to produce mean sea surfaces and surface variability. The technique has been applied to Geosat data collected over the North and South Atlantic and the South Indian Ocean. The computed mean sea surfaces show a high correlation with ocean bottom topography, whereas the variability is found to be associated with mesoscale ocean currents. High variability levels are spotted near the Gulfstream Extension and the Agulhas Return Current.Detailed examination of the sea surface and related flow field time series made it possible to identify a large number of eddies and to keep track of them in both the nort-west and south-east Atlantic. Additionally, some of the eddy characteristics have been resolved such as translation and swirl velocity. It is found that the eddy motion is affected by ocean bottom slopes.  相似文献   

16.
The method of analytical downward continuation has been used for solving Molodensky’s problem. This method can also be used to reduce the surface free air anomaly to the ellipsoid for the determination of the coefficients of the spherical harmonic expansion of the geopotential. In the reduction of airborne or satellite gradiometry data, if the sea level is chosen as reference surface, we will encounter the problem of the analytical downward continuation of the disturbing potential into the earth, too. The goal of this paper is to find out the topographic effect of solving Stoke’sboundary value problem (determination of the geoid) by using the method of analytical downward continuation. It is shown that the disturbing potential obtained by using the analytical downward continuation is different from the true disturbing potential on the sea level mostly by a −2πGρh 2/p. This correction is important and it is very easy to compute and add to the final results. A terrain effect (effect of the topography from the Bouguer plate) is found to be much smaller than the correction of the Bouguer plate and can be neglected in most cases. It is also shown that the geoid determined by using the Helmert’s second condensation (including the indirect effect) and using the analytical downward continuation procedure (including the topographic effect) are identical. They are different procedures and may be used in different environments, e.g., the analytical downward continuation procedure is also more convenient for processing the aerial gravity gradient data. A numerical test was completed in a rough mountain area, 35°<ϕ<38°, 240°<λ<243°. A digital height model in 30″×30″ point value was used. The test indicated that the terrain effect in the test area has theRMS value ±0.2−0.3 cm for geoid. The topographic effect on the deflections of the vertical is around1 arc second.  相似文献   

17.
A 2×2 arc-minute resolution geoid model, CARIB97, has been computed covering the Caribbean Sea. The geoid undulations refer to the GRS-80 ellipsoid, centered at the ITRF94 (1996.0) origin. The geoid level is defined by adopting the gravity potential on the geoid as W 0=62 636 856.88 m2/s2 and a gravity-mass constant of GM=3.986 004 418×1014 m3/s2. The geoid model was computed by applying high-frequency corrections to the Earth Gravity Model 1996 global geopotential model in a remove-compute-restore procedure. The permanent tide system of CARIB97 is non-tidal. Comparison of CARIB97 geoid heights to 31 GPS/tidal (ITRF94/local) benchmarks shows an average offset (h–H–N) of 51 cm, with an Root Mean Square (RMS) of 62 cm about the average. This represents an improvement over the use of a global geoid model for the region. However, because the measured orthometric heights (H) refer to many differing tidal datums, these comparisons are biased by localized permanent ocean dynamic topography (PODT). Therefore, we interpret the 51 cm as partially an estimate of the average PODT in the vicinity of the 31 island benchmarks. On an island-by-island basis, CARIB97 now offers the ability to analyze local datum problems which were previously unrecognized due to a lack of high-resolution geoid information in the area. Received: 2 January 1998 / Accepted: 18 August 1998  相似文献   

18.
On the adjustment of combined GPS/levelling/geoid networks   总被引：12，自引：7，他引：5  
A detailed treatment of adjustment problems in combined global positioning system (GPS)/levelling/geoid networks is given. The two main types of `unknowns' in this kind of multi-data 1D networks are usually the gravimetric geoid accuracy and a 2D spatial field that describes all the datum/systematic distortions among the available height data sets. An accurate knowledge of the latter becomes especially important when we consider employing GPS techniques for levelling purposes with respect to a local vertical datum. Two modelling alternatives for the correction field are presented, namely a pure deterministic parametric model, and a hybrid deterministic and stochastic model. The concept of variance component estimation is also proposed as an important statistical tool for assessing the actual gravimetric geoid noise level and/or testing a priori determined geoid error models. Finally, conclusions are drawn and recommendations for further study are suggested. Received: 9 September 1998 / Accepted: 8 June 1999  相似文献   

19.
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   

20.
The crossover adjustment plays a central role in the processing of satellite altimeter measurements. The usual procedure is to form sea surface height differences at crossover points, solve for the radial orbit error (with due attention to the singular nature of the estimation problem) and then to construct altimetric sea-level maps using the mean sea surface heights at the crossover points. Our approach is very different, to make direct use of measurements at crossover points without differencing and to estimate simultaneously orbit parameters, mean sea surface height and sea surface height variability in a single, unified adjustment. The technique is suited for repeat data over an area small enough that adjoining passes may be considered to be parallel and to permit the solution of a set of linear equations of dimension equal to the number of crossover points. The size of the numerical problem is almost independent of the number of repeat cycles of the altimeter mission. Explicit recognition is given to the rank defect of the least-squares estimation problem; we show that, for an orbit model with r parameters, the rank defect of the local crossover problem is exactly r 2. The defect may be overcome by choosing an appropriate set of constraints – either giving a best fit of mean sea surface heights to a reference surface, or minimising orbit parameters, or a minimum norm solution in which both mean sea surface heights and orbit parameters are minimised. There is no need to choose a reference pass, all passes are treated equally and data gaps are easily accommodated. Numerical results are presented for the south-western Indian Ocean, based on the first 2 years of altimeter data from the Geosat Exact Repeat Mission. Received: 31 May 1996 / Accepted: 19 April 1997  相似文献   

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