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1.
Gravimetric geoid undulations have been computed by the modified Molodensky truncation method (the Meissl procedure) and by the method of least squares spectral combination by optimal kernels (the Wenzel procedure). These undulations have been compared in two manners. One comparison used Doppler-derived undulation-at 65 stations in the United States as references. A second comparison used Geos-3 derived undulations in 30°×30° areas in the Indian Ocean and Tonga Trench as references. the mean difference of undulation-computed by the Wenzel procedure was 0.6 m smaller than that of the Meissl procedure when compared to the Doppler derived undulations. The standard deviations of the differences of both procedures appeared to be not significantly different. There are no significant changes in the mean differences of both procedures when compared to Geos-3 derived undulations. The standard deviations of the differences computed by the Wenzel procedure were of the order of 0.2 m smaller than those computed by the Meissl procedure.  相似文献   

2.
The vertical component obtained from the Global Positioning System (GPS) observations is from the ellipsoid (a mathematical surface), and therefore needs to be converted to the orthometric height, which is from the geoid (represented by the mean sea level). The common practice is to use existing bench marks (around the four corners of a project area and interpolate for the rest of the area), but in many areas bench marks may not be available, in which case an existing geoid undulation is used. Present available global geoid undulation values are not generally as detailed as needed, and in many areas they are not known better than ±1 to ±5 m, because of many limitations. This article explains the difficulties encountered in obtaining precise geoid undulation with some example computations, and proposes a technique of applying corrections to the best available global geoid undulations using detailed free-air gravity anomalies (within a 2° × 2° area) to get relative centimeter accuracy. Several test computations have been performed to decide the optimal block sizes and the effective spherical distances to compute the regional and the local effects of gravity anomalies on geoid undulations by using the Stokes integral. In one test computation a 2° × 2° area was subdivided into smaller surface elements. A difference of 37.34 ± 1.6 cm in geoid undulation was obtained over the same 2° × 2° area when 1° × 1° block sizes were replaced by a combination of 5' × 5' and 1' × 1' subdivision integration elements (block sizes).  相似文献   

3.
Two models describing potential coefficient behavior are used to estimate the root mean square geoid undulation by wavelength. Four wavelength types were defined: long wavelengths: ℓ=2 to 10; intermediate wavelengths: ℓ=11 to 100; short wavelengths: ℓ=101 to 1000; and very short wavelengths: ℓ=1001 to ∞. By one representation of potential coefficient behavior the intermediate wavelength geoid information was ±5.64 m, short wavelength, ±0.66 m, and the very short wavelength, ±0.05 m. The procedures of this paper were applied to an actual residual undulation computation using detailed gravity material.  相似文献   

4.
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   

5.
This paper studies the use of two new methods for gravimetric geoid undulation computations: The Molodenskii's and Sjöberg's methods that both modify the original Stokes'function so that certainrms errors are minimized. These new methods were checked against the traditional methods of Stokes' and Meissl's modification with the criterion of the globalrms undulation error that each method implies. Sjöberg's method gave consistently the smallest globalrms undulation error of all the other methods for capsizes 0° to 10°. However with the exception of Stokes' method, for capsizes between 0° to 5°, all the methods gave approximately (within±5cm) the same globalrms undulation error. Actual gravity data within a cap of 2° and potential coefficient information were then combined to compute the undulation of 39 laser stations distributed around the world. Therms discrepancy between the gravimetric undulations using all the four methods and the undulations computed as the ellipsoidal minus the orthometric height of 28 at the above stations was±1.70,±1.65,±1.66,±1.65m for the Stokes', Meissl's, Molodenskii's and Sjöberg's method respectively. For five oceanic laser stations where no terrestrial gravity data was available, theGEOS-3/SEASAT altimeter sea surface heights were used to compute the undulations of these stations in a collocation method. Therms discrepancy between the altimeter derived undulation and the ellipsoidal mirus orthometric value of the undulation was ±1.30m for the above five laser stations.  相似文献   

6.
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   

7.
Using the spherical harmonic representations of the earth's disturbing potential and its functionals, we derive the inverse Vening Meinesz formula, which converts deflection of the vertical to gravity anomaly using the gradient of the H function. The deflection-geoid formula is also derived that converts deflection to geoidal undulation using the gradient of the C function. The two formulae are implemented by the 1D FFT and the 2D FFT methods. The innermost zone effect is derived. The inverse Vening Meinesz formula is employed to compute gravity anomalies and geoidal undulations over the South China Sea using deflections from Seasat, Geosat, ERS-1 and TOPEX//POSEIDON satellite altimetry. The 1D FFT yields the best result of 9.9-mgal rms difference with the shipborne gravity anomalies. Using the simulated deflections from EGM96, the deflection-geoid formula yields a 4-cm rms difference with the EGM96-generated geoid. The predicted gravity anomalies and geoidal undulations can be used to study the tectonic structure and the ocean circulations of the South China Sea. Received: 7 April 1997 / Accepted: 7 January 1998  相似文献   

8.
核幔边界（core-mantle boundary,CMB）是地球内部最重要的物理化学界面之一,地核和地幔通过核幔边界发生多种相互作用,这对地球重力场、地球自转及地磁场等都能产生重要影响。大地水准面异常是地球重力场的重要观测量,反映了地球内部的物质密度异常及界面变化等重要信息。推导了通过大地水准面异常反演核幔边界起伏的公式,利用2~4阶大地水准面异常反演了大尺度核幔边界起伏形态。结果显示,核幔边界起伏的径向幅度达±5 km、与Morelli的地震层析成像结果的幅度接近,但在形态上略有差异。以高为5 km、底边长为1 000 km的棱柱体模型模拟计算了核幔边界密度异常引起的大地水准面异常响应,结果与观测大地水准面异常比较接近。  相似文献   

9.
A preliminary gravimetric geoid with respect to the International Spheroid and the latest astro-geodetic geoid computed on the Everest and International Spheroids are given in the form of undulation maps over the Indian Sub—continent. 10x10 mean free-air anomalies (modified) on the Geodetic Reference System, 1967 (GRS-67) are also given for the whole country in the form of a chart. For the purpose of computing the gravimetric geoid, 50x50 mean free-air anomalies were used outside the area bounded by latitudes 00 to 400 N and longitudes 600 to 1000 E and 10x10 mean free-air anomalies within these limits. The anomalies partly computed by Survey of India and mostly collected from other sources (such as B.G.I.) were utilised for this purpose. The astro-geodetic geoid is based on the astronomical data observed in India up to 1978.  相似文献   

10.
 This paper suggests that potential coefficient models of the Earth's gravitational potential be used to calculate height anomalies which are then reduced to geoid undulations where such quantities are needed for orthometric height determination and vertical datum definition through a potential coefficient realization of the geoid. The process of the conversion of the height anomaly into a geoid undulation is represented by a height anomaly gradient term and the usual N–ζ term that is dependent on elevation and the Bouguer anomaly. Using a degree 360 expansion of 30′ elevations and the OSU91A potential coefficient model, a degree 360 representation of the correction terms was computed. The magnitude of N–ζ reached –3.4 m in the Himalaya Mountains with smaller, but still significant, magnitudes in other mountainous regions. Received: 6 May 1996; Accepted: 30 October 1996  相似文献   

11.
A set of2261 5°×5° mean anomalies were used alone and with satellite determined harmonic coefficients of the Smithsonian' Institution to determine the geopotential expansion to various degrees. The basic adjustment was carried out by comparing a terrestrial anomaly to an anomaly determined from an assumed set of coefficients. The (14, 14) solution was found to agree within ±3 m of a detailed geoid in the United States computed using1°×1° anomalies for an inner area and satellite determined anomalies in an outer area. Additional comparisons were made to the input anomaly field to consider the accuracy of various harmonic coefficient solutions. A by-product of this investigation was a new γE=978.0463 gals in the Potsdam system or978.0326 gals in an absolute system if −13.7 mgals is taken as the Potsdam correction. Combining this value of γE withf=1/298.25, KM=3.9860122·10 22 cm 3 /sec 2 , the consistent equatorial radius was found to be6378143 m.  相似文献   

12.
利用多颗卫星的测高数据,经共线平均及交叉点平差,建立浙江深海海域2.5′×2.5′格网分辨率的平均海面高模型,在扣除海面地形影响后得到海域的大地水准面起伏,并与EGM2008所得计算结果进行对比;利用移去-恢复技术及SVR方法,联合验潮站GPS/水准数据与EGM2008大地水准面模型,计算浙江近岸海域大地水准面起伏;最终建立浙江海域2.5′×2.5′格网分辨率的大地水准面模型。  相似文献   

13.
Minimization and estimation of geoid undulation errors   总被引：2，自引：1，他引：1  
The objective of this paper is to minimize the geoid undulation errors by focusing on the contribution of the global geopotential model and regional gravity anomalies, and to estimate the accuracy of the predicted gravimetric geoid.The geopotential model's contribution is improved by (a) tailoring it using the regional gravity anomalies and (b) introducing a weighting function to the geopotential coefficients. The tailoring and the weighting function reduced the difference (1) between the geopotential model and the GPS/levelling-derived geoid undulations in British Columbia by about 55% and more than 10%, respectively.Geoid undulations computed in an area of 40° by 120° by Stokes' integral with different kernel functions are analyzed. The use of the approximated kernels results in about 25 cm () and 190 cm (maximum) geoid errors. As compared with the geoid derived by GPS/levelling, the gravimetric geoid gives relative differences of about 0.3 to 1.4 ppm in flat areas, and 1 to 2.5 ppm in mountainous areas for distances of 30 to 200 km, while the absolute difference (1) is about 5 cm and 20 cm, respectively.A optimal Wiener filter is introduced for filtering of the gravity anomaly noise, and the performance is investigated by numerical examples. The internal accuracy of the gravimetric geoid is studied by propagating the errors of the gravity anomalies and the geopotential coefficients into the geoid undulations. Numerical computations indicate that the propagated geoid errors can reasonably reflect the differences between the gravimetric and GPS/levelling-derived geoid undulations in flat areas, such as Alberta, and is over optimistic in the Rocky Mountains of British Columbia.Paper presented at the IAG General Meeting, Beijing, China, August 8–13, 1993.  相似文献   

14.
An inverse Poisson integral technique has been used to determine a gravity field on the geoid which, when continued by analytic free space methods to the topographic surface, agrees with the observed field. The computation is performed in three stages, each stage refining the previous solution using data at progressively increasing resolution (1o×1o, 5′×5′, 5/8′×5/8′) from a decreasing area of integration. Reduction corrections are computed at 5/8′×5/8′ granularity by differencing the geoidal and surface values, smoothed by low-pass filtering and sub-sampled at 5′ intervals. This paper discusses 1o×1o averages of the reduction corrections thus obtained for 172 1o×1o squares in western North America. The 1o×1o mean reduction corrections are predominantly positive, varying from −3 to +15mgal, with values in excess of 5mgal for 26 squares. Their mean andrms values are +2.4 and 3.6mgal respectively and they correlate well with the mean terrain corrections as predicted byPellinen in 1962. The mean andrms contributions from the three stages of computation are: 1o×1o stage +0.15 and 0.7mgal; 5′×5′ stage +1.0 and 1.6mgal; and 5/8′×5/8′ stage +1.3 and 1.8mgal. These results reflect a tendency for the contributions to become larger and more systematically positive as the wavelengths involved become shorter. The results are discussed in terms of two mechanisms; the first is a tendency for the absolute values of both positive and negative anomalies to become larger when continued downwards and, the second, a non-linear rectification, due to the correlation between gravity anomaly and topographic height, which results in the values continued to a level surface being systematically more positive than those on the topography.  相似文献   

15.
Gravity field convolutions without windowing and edge effects   总被引：5，自引：0，他引：5  
A new set of formulas has been developed for the computation of geoid undulations and terrain corrections by FFT when the input gravity anomalies and heights are mean gridded values. The effects of the analytical and the discrete spectra of kernel functions and that of zero-padding on the computation of geoid undulations and terrain corrections are studied in detail.Numerical examples show that the discrete spectrum is superior to the analytically-defined one. By using the discrete spectrum and 100% zero-padding, the RMS differences are 0.000 m for the FFT geoid undulations and 0.200 to 0.000 mGal for the FFT terrain corrections compared with results obtained by numerical integration.  相似文献   

16.
Summary A local model of the geoid in NE Italy and its section along the Venice ground track of the ERS-1 satellite of the European Space Agency is presented. The observational data consist of geoid undulations determined with a network of 25 stations of known orthometric (by spirit leveling) and ellipsoidal (by GPS differential survey) and of 13 deflections of the vertical measured at sites of the network for which, besides the ellipsoidal (WGS84) coordinates, also astronomic coordinates were known. The network covers an area of 1×1 degrees and is tied to a vertical and horizontal datum: one vertex of the network is the tide gauge of Punta Salute, in Venice, providing a tie to a mean sea level; a second vertex is the site for mobile laser systems at Monte Venda, on the Euganei Hills, for which geocentric coordinates resulted from the analysis of several LAGEOS passes.The interpolation algorithm used to map sparse and heterogeneous data to a regular grid of geoid undulations is based on least squares collocation and the autocorrelation function of the geoid undulations is modeled by a third order Markov process on flat earth. The algorithm has been applied to the observed undulations and deflections of the vertical after subtraction of the corresponding predictions made on the basis of the OSU91A global geoid model of the Ohio State University, complete to degree and order 360. The locally improved geoid results by adding back, at the nodes of a regular grid, the predictions of the global field to the least squares interpolated values. Comparison of the model values with the raw data at the observing stations indicates that the mean discrepancy is virtually zero with a root mean square dispersion of 8 cm, assuming that the ellipsoidal heights and vertical deflections data are affected by a random error of 3 cm and 0.5 respectively. The corrections resulting from the local data and added to the background 360×360 global model are described by a smooth surface with excursions from the reference surface not larger than ±30 cm.  相似文献   

17.
Knudsen 《Journal of Geodesy》1987,61(2):145-160
The estimation of a local empirical covariance function from a set of observations was done in the Faeroe Islands region. Gravity and adjusted Seasat altimeter data relative to theGPM2 spherical harmonic approximation were selected holding one value in celles of1/8°×1/4° covering the area. In order to center the observations they were transformed into a locally best fitting reference system having a semimajor axis1.8 m smaller than the one ofGRS80. The variance of the data then was273 mgal 2 and0.12 m 2 respectively. In the calculations both the space domain method and the frequency domain method were used. Using the space domain method the auto-covariances for gravity anomalies and geoid heights and the cross-covariances between the quantities were estimated. Furthermore an empirical error estimate was derived. Using the frequency domain method the auto-covariances of gridded gravity anomalies was estimated. The gridding procedure was found to have a considerable smoothing effect, but a deconvolution made the results of the two methods to agree. The local covariance function model was represented by a Tscherning/Rapp degree-variance model,A/((i−1)(i−2)(i+24))(R B /R E )2i+2, and the error degree-variances related to the potential coefficient setGPM2. This covariance function was adjusted to fit the empirical values using an iterative least squares inversion procedure adjusting the factor A, the depth to the Bjerhammar sphere(R E −R B ), and a scale factor associated with the error degree-variances. Three different combinations of the empirical covariance values were used. The scale factor was not well determined from the gravity anomaly covariance values, and the depth to the Bjerhammar sphere was not well determined from geoid height covariance values only. A combination of the two types of auto-covariance values resulted in a well determined model.  相似文献   

18.
A new isostatic model of the lithosphere and gravity field   总被引：2，自引：0，他引：2  
Based on the analysis of various factors controlling isostatic gravity anomalies and geoid undulations, it is concluded that it is essential to model the lithospheric density structure as accurately as possible. Otherwise, if computed in the classical way (i.e. based on the surface topography and the simple Airy compensation scheme), isostatic anomalies mostly reflect differences of the real lithosphere structure from the simplified compensation model, and not necessarily the deviations from isostatic equilibrium. Starting with global gravity, topography and crustal density models, isostatic gravity anomalies and geoid undulations have been determined. The initial crust and upper-mantle density structure has been corrected in a least squares adjustment using gravity. To model the long-wavelength (>2000 km) features in the gravity field, the isostatic condition (i.e. equal mass for all columns above the compensation level) is applied in the adjustment to uncover the signals from the deep-Earth interior, including dynamic deformations of the Earths surface. The isostatic gravity anomalies and geoid undulations, rather than the observed fields, then represent the signals from mantle convection and deep density inhomogeneities including remnants of subducted slabs. The long-wavelength non-isostatic (i.e. the dynamic) topography was estimated to range from –0.4 to 0.5 km. For shorter wavelengths (<2000 km), the isostatic condition is not applied in the adjustment in order to obtain the non-isostatic topography due to regional deviations from classical Airy isostasy. The maximum deviations from Airy isostasy (–1.5 to 1 km) occur at currently active plate boundaries. As another result, a new global model of the lithosphere density distribution is generated. The most pronounced negative density anomalies in the upper mantle are found near large plume provinces, such as Iceland and East Africa, and in the vicinity of the mid-ocean ridge axes. Positive density anomalies in the upper mantle under the continents are not correlated with the cold and thick lithosphere of cratons, indicating a compensation mechanism due to thermal and compositional density.  相似文献   

19.
 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   

20.
Summary Satellite gradiometry is studied as a means to improve the geoid in local areas from a limited data coverage. Least-squares collocation is used for this purpose because it allows to combine heterogeneous data in a consistent way and to estimate the integrated effect of the attenuated spectrum. In this way accuracy studies can be performed in a general and reliable manner. It is shown that only three second-order gradients contribute significantly to the estimation of the geoidal undulations and that it is sufficient to have gradiometer data in a 5°×5° area around the estimation point. The accuracy of the geoid determination is strongly dependent on the degree and order of the reference field used. An accuracy of about ±1 m can be achieved with a reference field of (12, 12). There is an optimal satellite altitude for each reference field and this altitude may be higher than 300 km for a field of low degree and order. The influence of measuring errors is discussed and it is shown that only gradiometer data with accuracies better than ±0.05 E will give a significant improvement of the geoid. Finally, some results on the combination of satellite gradiometry and terrestrial gravity measurements are given. The proposed method seems to be well suited for local geoid determinations down to the meter range. It is especially interesting for unsurveyed and difficult areas because no terrestrial measurements are necessary. Furthermore, it has the practical advantage that only a local data coverage is needed.  相似文献   

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