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1.
Mean gravity anomalies, deflections of the vertical, and a geopotential model complete to degree and order180 are combined in order to determine geoidal heights in the area bounded by [34°≦ϕ≤42°, 18°≦λ≦28°]. Moreover, employing point gravity anomalies simultaneously with the above data, an attempt is made to predict deflections of the vertical in the same area. The method used in the computations is least squares collocation. Using empirical covariance functions for the data, the suitable errors for the different sources of observations, and the optimum cap radius around each point of evaluation, an accuracy better than±0.60m for geoidal heights and±1″.5 for deflections of the vertical is obtained taking into account existing systematic effects. This accuracy refers to the comparison between observed and predicted values.  相似文献   

2.
Terrestrial free-air gravity anomalies form a most essential data source in the framework of gravity field determination. Gravity anomalies depend on the datums of the gravity, vertical, and horizontal networks as well as on the definition of a normal gravity field; thus gravity anomaly data are affected in a systematic way by inconsistencies of the local datums with respect to a global datum, by the use of a simplified free-air reduction procedure and of different kinds of height system. These systematic errors in free-air gravity anomaly data cause systematic effects in gravity field related quantities like e.g. absolute and relative geoidal heights or height anomalies calculated from gravity anomaly data. In detail it is shown that the effects of horizontal datum inconsistencies have been underestimated in the past. The corresponding systematic errors in gravity anomalies are maximum in mid-latitudes and can be as large as the errors induced by gravity and vertical datum and height system inconsistencies. As an example the situation in Australia is evaluated in more detail: The deviations between the national Australian horizontal datum and a global datum produce a systematic error in the free-air gravity anomalies of about −0.10 mgal which value is nearly constant over the continent  相似文献   

3.
When planning a satellite gravity gradiometer (SGG) mission, it is important to know the quality of the quantities to be recovered at ground level as a function of e.g. satellite altitude, data type and sampling rate, and signal variance and noise. This kind of knowledge may be provided either using the formal error estimates of wanted quantities using least-squares collocation (LSC) or by comparing simulated data at ground level with results computed by methods like LSC or Fast Fourier Transform (FFT). Results of a regional gravity field recovery in a 10o×20o area surrounding the Alps using LSC and FFT are reported. Data used as observations in satellite altitude (202 or161 km) and for comparison at ground level were generated using theOSU86F coefficient set, complete to degree 360. These observations are referred to points across simulated orbits. The simulated quantities were computed for a 45 days mission period and 4 s sampling. A covariance function which also included terms above degree 360 was used for prediction and error estimation. This had the effect that the formal error standard deviation for gravity anomalies were considerably larger than the standard deviations of predicted minus simulated quantities. This shows the importance of using data with frequency content above degree 360 in simulation studies. Using data at202 km altitude the standard deviation of the predicted minus simulated data was equal to8.3 mgal for gravity and0.33 m for geoid heights.  相似文献   

4.
150多年来，重力均衡的理论已得到很大的发展，均衡异常与大地水准面差距在地球科学诸多学科中已得到了广泛的应用，各种均衡理论及其相应的重力异常在各种文献中已作了比较和评论；不同波长地形的重力效应，包括短波长的地形不能构成补偿也作了进一步研究。因此，在局部场中不宜用均衡补偿的方法作山区重力点值的推估，而曾经仅用地形（高程）的数据推估珠穆朗玛峰顶上的重力倒是适合的。  相似文献   

5.
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   

6.
为解决世界各国高程基准差异的问题,提出联合卫星重力场模型、地面重力数据、GNSS大地高、局部高程基准的正高或正常高,按大地边值问题法确定局部高程基准重力位差的方法。首先推导了利用传统地面"有偏"重力异常确定高程基准重力位差的方法;接着利用改化Stokes核函数削弱"有偏"重力异常的影响,并联合卫星重力场模型和地面"有偏"重力数据,得到独立于任何局部高程基准的重力水准面,以此来确定局部高程基准重力位差;最后利用GNSS+水准数据和重力大地水准面确定了美国高程基准与全球高程基准W0的重力位差为-4.82±0.05 m2s-2。  相似文献   

7.
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   

8.
Gravity field terrain effect computations by FFT   总被引：2，自引：2，他引：2  
The widespread availability of detailed gridded topographic and bathymetric data for many areas of the earth has resulted in a need for efficient terrain effect computation techniques, especially for applications in gravity field modelling. Compared to conventional integration techniques, Fourier transform methods provide extremely efficient computations due to the speed of the Fast Fourier Transform (FFT. The Fourier techniques rely on linearization and series expansions of the basically unlinear terrain effect integrals, typically involving transformation of the heights/depths and their squares. TheFFT methods will especially be suited for terrain reduction of land gravity data and satellite altimetry geoid data. In the paper the basic formulas will be outlined, and special emphasis will be put on the practial implementation, where a special coarse/detailed grid pair formulation must be used in order to minimize the unavoidable edge effects ofFFT, and the special properties ofFFT are utilized to limit the actual number of data transformations needed. Actual results are presented for gravity and geoid terrain effects in test areas of the USA, Greenland and the North Atlantic. The results are evaluated against a conventional integration program: thus, e.g., in an area of East Greenland (with terrain corrections up to10 mgal), the accuracy ofFFT-computed terrain corrections in actual gravity stations showed anr.m.s. error of0.25 mgal, using height data from a detailed photogrammetric digital terrain model. Similarly, isostatic ocean geoid effects in the Faeroe Islands region were found to be computed withr.m.s. errors around0.03 m  相似文献   

9.
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   

10.
The investigations refer to the compartment method by using mean terrestrial free air anomalies only. Three main error influences of remote areas (distance from the fixed point >9°) on height anomalies and deflections of the vertical are being regarded:
  1. The prediction errors of mean terrestrial free air anomalies have the greatest influence and amount to about ±0″.2 in each component for deflections of the vertical and to ±3 m for height anomalies;
  2. The error of the compartment method, which originates from converting the integral formulas of Stokes and Vening-Meinesz into summation formulas, can be neglected if the anomalies for points and gravity profiles are compiled to 5°×5° mean values.
  3. The influences of the mean gravimetric correction terms of Arnold—estimated for important mountains of the Earth by means of an approximate formula—on height anomalies may amount to 1–2 m and on deflections of the vertical to 0″0.5–0″.1, and, therefore, they have to be taken into account for exact calculations.
The computations of errors are carried out using a global covariance function of point free air anomalies.  相似文献   

11.
The Global Positioning System (GPS) is considered in conjunction with a strapdown Inertial Measurement Unit (IMU) for measuring the gravity vector. A comparison of this system in space and on an airborne platform shows the relative importance of each system element in these two different acceleration environments. With currently available instrumentation, the acceleration measurement accuracy is the deciding factor in space, while on an Earth-bound (including airborne) platform, the attitude error of the IMU is most critical. A simulation shows that GPS-derived accelerations in space can be accurate to better than 0.1mgal for a 30s integration time, leading to estimates of 1° mean gravity anomalies on the Earth's surface with an accuracy of 4–5 mgal. On an airborne platform, the horizontal gravity estimation error is tightly coupled to the attitude error of the platform, which can only be bounded by external attitude updates. Horizontal gravity errors of 5mgal are achievable if the attitude is maintained to an accuracy of 1arcsec.  相似文献   

12.
Summary Basically two different evaluation methods are available to compute geoid heights from residual gravity anomalies in the inner zone: numerical integration and least squares collocation.If collocation is not applied to a global gravity data set, as is usually the case in practice, its result will not be equal to the numerical integration result. However, the cross covariance function between geoid heights and gravity anomalies can be adapted such that the geoid contribution is computed only from a small gravity area up to a certain distance o from the computation point. Using this modification, identical results are obtained as from numerical integration.Applying this modification makes the results less dependent on the covariance function used. The difference between numerical integration and collocation is mainly caused by the implicitly extrapolated residual gravity anomaly values, outside the original data area. This extrapolated signal depends very much on the covariance function used, while the interpolated values within the original data area depend much less on it.As a sort of by-product, this modified collocation formula also leads to a new combination technique of numerical integration and collocation, in which the optimizing practical properties of both methods are fully exploited.Numerical examples are added as illustration.  相似文献   

13.
Crustal data of surface elevations and depth of Moho (and densities) can be utilized to form model-earth anomalies. These model-anomalies can closely approximate the free-air anomaly field of the earth, and could thus be used to predict the latter. A review of several such models is presented, with some elaboration on model developments, procedures, data analysis and accuracies. One of the models approaches a prediction accuracy of ±10 mgal for5°×5° mean free-air anomalies, whose r.m.s. value was about30% higher.  相似文献   

14.
 It is suggested that a spherical harmonic representation of the geoidal heights using global Earth gravity models (EGM) might be accurate enough for many applications, although we know that some short-wavelength signals are missing in a potential coefficient model. A `direct' method of geoidal height determination from a global Earth gravity model coefficient alone and an `indirect' approach of geoidal height determination through height anomaly computed from a global gravity model are investigated. In both methods, suitable correction terms are applied. The results of computations in two test areas show that the direct and indirect approaches of geoid height determination yield good agreement with the classical gravimetric geoidal heights which are determined from Stokes' formula. Surprisingly, the results of the indirect method of geoidal height determination yield better agreement with the global positioning system (GPS)-levelling derived geoid heights, which are used to demonstrate such improvements, than the results of gravimetric geoid heights at to the same GPS stations. It has been demonstrated that the application of correction terms in both methods improves the agreement of geoidal heights at GPS-levelling stations. It is also found that the correction terms in the direct method of geoidal height determination are mostly similar to the correction terms used for the indirect determination of geoidal heights from height anomalies. Received: 26 July 2001 / Accepted: 21 February 2002  相似文献   

15.
最小二乘配置法中局部协方差函数的计算   总被引：3，自引：1，他引：2  
文汉江 《测绘科学》2000,25(3):37-39
随着 GPS日益广泛的应用及精度的不断提高 ,在有些实际应用中利用 GPS来代替传统的水准测量进行高程控制已成为可能 ,这也进一步提出了对高精度大地水准面的需求。快速傅立叶变换 (FFT)是目前计算大地水准面比较常用的方法之一 ,但需要将重力观测量进行内插得到规则格网上的平均重力异常。利用最小二乘配置法计算大地水准面可直接利用已有的观测值进行计算 ,同时可综合利用不同类型的数据 ,如重力异常和垂线偏差等计算大地水准面 ,因此最小二乘配置法仍有广泛的应用 ,但制约最小二乘配置应用的关键问题是局部协方差函数的计算。将主要讨论最小二乘配置法中局部协方差函数的计算 ,使所用的协方差函数能更好地反映已知的数据 ,从而获得更精确的结果。  相似文献   

16.
Jakob Flury 《Journal of Geodesy》2006,79(10-11):624-640
The GRACE (gravity recovery and climate experiment) and GOCE (gravity field and steady-state ocean circulation explorer) dedicated gravity satellite missions are expected to deliver the long-wavelength scales of the Earth’s gravity field with extreme precision. For many applications in Earth sciences, future research activities will have to focus on a similar precision on shorter scales not recovered by satellite missions. Here, we investigate the signal power of gravity anomalies at such short scales. We derive an average degree variance and power spectral density model for topography-reduced gravity anomalies (residual terrain model anomalies and de-trended refined Bouguer anomalies), which is valid for wavelengths between 0.7 and 100  km. The model is based on the analysis of gravity anomalies from 13 test regions in various geographical areas and geophysical settings, using various power spectrum computation approaches. The power of the derived average topography-reduced model is considerably lower than the Tscherning–Rapp free air anomaly model. The signal power of the individual test regions deviates from the obtained average model by less than a factor of 4 in terms of square-root power spectral amplitudes. Despite the topographic reduction, the highest signal power is found in mountainous areas and the lowest signal power in flat terrain. For the derived average power spectral model, a validation procedure is developed based on least-squares prediction tests. The validation shows that the model leads to a good prediction quality and realistic error measures. Therefore, for least-squares prediction, the model could replace the use of autocovariance functions derived from local or regional data.  相似文献   

17.
Regional geopotential model improvement for the Iranian geoid determination   总被引：1，自引：0，他引：1  
Spherical harmonic expansions of the geopotential are frequently used for modelling the earth’s gravity field. Degree and order of recently available models go up to 360, corresponding to a resolution of about50 km. Thus, the high degree potential coefficients can be verified nowadays even by locally distributed sets of terrestrial gravity anomalies. These verifications are important when combining the short wavelength model impact, e.g. for regional geoid determinations by means of collocation solutions. A method based on integral formulae is presented, enabling the improvement of geopotential models with respect to non-global distributed gravity anomalies. To illustrate the foregoing, geoid computations are carried out for the area of Iran, introducing theGPM2 geopotential model in combination with available regional gravity data. The accuracy of the geoid determination is estimated from a comparison with Doppler and levelling data to ±1.4m.  相似文献   

18.
 Equations expressing the covariances between spherical harmonic coefficients and linear functionals applied on the anomalous gravity potential, T, are derived. The functionals are the evaluation functionals, and those associated with first- and second-order derivatives of T. These equations form the basis for the prediction of spherical harmonic coefficients using least-squares collocation (LSC). The equations were implemented in the GRAVSOFT program GEOCOL. Initially, tests using EGM96 were performed using global and regional sets of geoid heights, gravity anomalies and second-order vertical gravity gradients at ground level and at altitude. The global tests confirm that coefficients may be estimated consistently using LSC while the error estimates are much too large for the lower-order coefficients. The validity of an error estimate calculated using LSC with an isotropic covariance function is based on a hypothesis that the coefficients of a specific degree all belong to the same normal distribution. However, the coefficients of lower degree do not fulfil this, and this seems to be the reason for the too-pessimistic error estimates. In order to test this the coefficients of EGM96 were perturbed, so that the pertubations for a specific degree all belonged to a normal distribution with the variance equal to the mean error variance of the coefficients. The pertubations were used to generate residual geoid heights, gravity anomalies and second-order vertical gravity gradients. These data were then used to calculate estimates of the perturbed coefficients as well as error estimates of the quantities, which now have a very good agreement with the errors computed from the simulated observed minus calculated coefficients. Tests with regionally distributed data showed that long-wavelength information is lost, but also that it seems to be recovered for specific coefficients depending on where the data are located. Received: 3 February 2000 / Accepted: 23 October 2000  相似文献   

19.
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   

20.
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   

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