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1.
R. Kiamehr 《Journal of Geodesy》2006,79(10-11):602-612
The computation of regional gravimetric geoid models with reasonable accuracy, in developing countries, with sparse data is a difficult task that needs great care. Here we investigate the procedure for gathering, evaluating and combining different data for the determination of a gravimetric geoid model for Iran, where limited ground gravity data are available. Heterogeneous data, including gravity anomalies, the high-resolution Shuttle Radar Topography Mission global digital terrain model and different global geopotential models including recently published Gravity Recovery and Climate Experiment models, are combined through least-squares modification of the Stokes formula. The new gravimetric geoid model, IRG04, agrees considerably better with GPS/levelling than any of the other recent local geoid model in the area. Its RMS fit with GPS/levelling is 0.27 m and 3.8 ppm in the absolute and relative view, respectively. The relative accuracy of IRG04 is four times better than the most recently published global and regional geoid models available in this area. This progress shows the practical potential of the method of least-squares modification of Stokes’s formula in combination with heterogeneous data for regional geoid determination 相似文献
2.
Performance of three types of Stokes's kernel in the combined solution for the geoid 总被引:8,自引:6,他引:2
When regional gravity data are used to compute a gravimetric geoid in conjunction with a geopotential model, it is sometimes
implied that the terrestrial gravity data correct any erroneous wavelengths present in the geopotential model. This assertion
is investigated. The propagation of errors from the low-frequency terrestrial gravity field into the geoid is derived for
the spherical Stokes integral, the spheroidal Stokes integral and the Molodensky-modified spheroidal Stokes integral. It is
shown that error-free terrestrial gravity data, if used in a spherical cap of limited extent, cannot completely correct the
geopotential model. Using a standard norm, it is shown that the spheroidal and Molodensky-modified integration kernels offer
a preferable approach. This is because they can filter out a large amount of the low-frequency errors expected to exist in
terrestrial gravity anomalies and thus rely more on the low-frequency geopotential model, which currently offers the best
source of this information.
Received: 11 August 1997 / Accepted: 18 August 1998 相似文献
3.
A synthetic Earth Gravity Model Designed Specifically for Testing Regional Gravimetric Geoid Determination Algorithms 总被引:1,自引:0,他引:1
I. Baran M. Kuhn S. J. Claessens W. E. Featherstone S. A. Holmes P. Vaníček 《Journal of Geodesy》2006,80(1):1-16
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
4.
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
5.
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
6.
The determination of local geoid models has traditionally been carried out on land and at sea using gravity anomaly and satellite
altimetry data, while it will be aided by the data expected from satellite missions such as those from the Gravity field and
steady-state ocean circulation explorer (GOCE). To assess the performance of heterogeneous data combination to local geoid
determination, simulated data for the central Mediterranean Sea are analyzed. These data include marine and land gravity anomalies,
altimetric sea surface heights, and GOCE observations processed with the space-wise approach. A spectral analysis of the aforementioned
data shows their complementary character. GOCE data cover long wavelengths and account for the lack of such information from
gravity anomalies. This is exploited for the estimation of local covariance function models, where it is seen that models
computed with GOCE data and gravity anomaly empirical covariance functions perform better than models computed without GOCE
data. The geoid is estimated by different data combinations and the results show that GOCE data improve the solutions for
areas covered poorly with other data types, while also accounting for any long wavelength errors of the adopted reference
model that exist even when the ground gravity data are dense. At sea, the altimetric data provide the dominant geoid information.
However, the geoid accuracy is sensitive to orbit calibration errors and unmodeled sea surface topography (SST) effects. If
such effects are present, the combination of GOCE and gravity anomaly data can improve the geoid accuracy. The present work
also presents results from simulations for the recovery of the stationary SST, which show that the combination of geoid heights
obtained from a spherical harmonic geopotential model derived from GOCE with satellite altimetry data can provide SST models
with some centimeters of error. However, combining data from GOCE with gravity anomalies in a collocation approach can result
in the estimation of a higher resolution geoid, more suitable for high resolution mean dynamic SST modeling. Such simulations
can be performed toward the development and evaluation of SST recovery methods. 相似文献
7.
The objective of this study is to evaluate two approaches, which use different representations of the Earth’s gravity field for downward continuation (DC), for determining Helmert gravity anomalies on the geoid. The accuracy of these anomalies is validated by 1) analyzing conformity of the two approaches; and 2) converting them to geoid heights and comparing the resulting values to GPS-leveling data. The first approach (A) consists of evaluating Helmert anomalies at the topography and downward-continuing them to the geoid. The second approach (B) downward-continues refined Bouguer anomalies to the geoid and transforms them to Helmert anomalies by adding the condensed topographical effect. Approach A is sensitive to the DC because of the roughness of the Helmert gravity field. The DC effect on the geoid can reach up to 2 m in Western Canada when the Stokes kernel is used to convert gravity anomalies to geoid heights. Furthermore, Poisson’s equation for DC provides better numerical results than Moritz’s equation when the resulting geoid models are validated against the GPS-leveling. On the contrary, approach B is significantly less sensitive to the DC because of the smoothness of the refined Bouguer gravity field. In this case, the DC (Poisson’s and Moritz’s) contributes only at the decimeter level to the geoid model in Western Canada. The maximum difference between the geoid models from approaches A and B is about 5 cm in the region of interest. The differences may result from errors in the DC such as numerical instability. The standard deviations of the h−H−N for both approaches are about 8 cm at the 664 GPS-leveling validation stations in Western Canada. 相似文献
8.
用重力异常逐级余差计算重力大地水准面 总被引:1,自引:0,他引:1
本文将计算重力大地水准面的频域方法推广至空域,提出了一种新的用重力数据和重力模型位系数联合确定大地水准面的方法。利用重力异常的逐级余差实施积分,使得通常的Stokes积分方法具有明确的频域分析含义,可按精度要求确定出使用重力异常余差的块形大小及积分半径ψo。 相似文献
9.
DEM-induced errors in developing a quasi-geoid model for Africa 总被引:2,自引:0,他引:2
Errors in digital elevation models (DEMs) will introduce errors in geoid and quasi-geoid models, via their use in interpolating free-air gravity anomalies and (in the case of the quasi-geoid) their use in computing the Molodensky G
1 term. The effects of these errors and those of datum shifts are assessed using three independent DEMs for a test region in South Africa. It is shown that these effects are significant and that it is important to choose the best-possible DEM for use in geoid and quasi-geoid modelling.
Acknowledgments.The land gravity data used for this research were provided by the South African Council for Geoscience. Marine gravity anomalies were provided by the Danish National Survey and Cadastre (Kort & Matrikelstyrelsen). The GLOBE DEM was provided by the US National Geophysical Data Centre, and the CDSM DEM was provided by the South African Chief Directorate for Surveying and Mapping. The constructive comments of the reviewers are gratefully acknowledged. 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.
A. Ellmann 《Journal of Geodesy》2005,79(1-3):11-23
In regional gravimetric geoid determination, it is customary to use the modified Stokes formula that combines local terrestrial data with a global geopotential model. This study compares two deterministic and three stochastic modification methods for computing a regional geoid over the Baltic countries. The final selection of the best modification method is made by means of two accuracy estimates: the expected global mean square error of the geoid estimator, and the statistics of the post-fit residuals between the computed geoid models and precise GPS-levelling data. Numerical results show that the modification methods tested do not provide substantially different results, although the stochastic approaches appear formally better in the selected study area. The 2.8–5.3 cm (RMS) post-fit residuals to the GPS-levelling points indicate the suitability of the new geoid model for many practical applications. Moreover, the numerical comparisons reveal a one-dimensional offset between the regional vertical datum and the geoid models based upon the new GRACE-only geopotential model GGM01s. This gives an impression of a greater reliability of the new model compared to the earlier, EGM96-based and somewhat tilted regional geoid models for the same study area. 相似文献
12.
Gravity-field improvement in the Mediterranean Sea by estimating the bottom topography using collocation 总被引:4,自引:0,他引:4
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
13.
EGM96,WDM94和GPM98CR高阶地球重力场模型表示深圳局部重力场的比较与评价 总被引:9,自引:0,他引:9
为计算深圳精密重力大地水准面,利用62个高精度GPS水准点和4871个实测重力点数据对EGM96,WDM94和GPM98CR全球重力场模型表示深圳局部重力场进行了比较与评价。结果表明,由上述3个重力场模型计算的大地水准面高和重力异常与实测值之间存在明显的系统偏差,当采用GPS水准数据尽可能消除系统偏差以后,大地水准面高的精度得到显著提高,若应用移去-恢复技术确定深圳高精度大地水准面,则WDM94应该是首选的参考重力场模型。 相似文献
14.
W. E. Featherstone J. F. Kirby A. H. W. Kearsley J. R. Gilliland G. M. Johnston J. Steed R. Forsberg M. G. Sideris 《Journal of Geodesy》2001,75(5-6):313-330
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
15.
Erik de Min 《Journal of Geodesy》1995,69(4):223-232
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
16.
Computation of spherical harmonic coefficients and their error estimates using least-squares collocation 总被引:4,自引:0,他引:4
C. C. Tscherning 《Journal of Geodesy》2001,75(1):12-18
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
17.
The standard analytical approach which is applied for constructing geopotential models OSU86 and earlier ones, is based on
reducing the boundary value equation to a sphere enveloping the Earth and then solving it directly with respect to the potential
coefficients
n,m
. In an alternative procedure, developed by Jekeli and used for constructing the models OSU91 and EGM96, at first an ellipsoidal
harmonic series is developed for the geopotential and then its coefficients
n,m
e
are transformed to the unknown
n,m
. The second solution is more exact, but much more complicated. The standard procedure is modified and a new simple integral
formula is derived for evaluating the potential coefficients. The efficiency of the standard and new procedures is studied
numerically. In these solutions the same input data are used as for constructing high-degree parts of the EGM96 models. From
two sets of
n,m
(n≤360,|m|≤n), derived by the standard and new approaches, different spectral characteristics of the gravity anomaly and the geoid undulation
are estimated and then compared with similar characteristics evaluated by Jekeli's approach (`etalon' solution). The new solution
appears to be very close to Jekeli's, as opposed to the standard solution. The discrepancies between all the characteristics
of the new and `etalon' solutions are smaller than the corresponding discrepancies between two versions of the final geopotential
model EGM96, one of them (HDM190) constructed by the block-diagonal least squares (LS) adjustment and the other one (V068)
by using Jekeli's approach. On the basis of the derived analytical solution a new simple mathematical model is developed to
apply the LS technique for evaluating geopotential coefficients.
Received: 12 December 2000 / Accepted: 21 June 2001 相似文献
18.
J. C. Bhattacharji 《Journal of Geodesy》1984,58(1):31-36
The concept of an idealised earth having 1° averaged heights over its land surface is introduced as a means to improve upon
the existing geopotential coefficient solutions without the use of additional observed data, in order to provide more precise
knowledge of the earth’s gravity field in the form of 1° global geoid and 1° mean free-air gravity anomalies especially over
the mountainous regions with the visible topography condensed into the actual geoid, first by referring them to the idealised
earth and then by reducing the same to the actual earth on applying appropriate corrections for the differences between the
two earths. 相似文献
19.
Canadian gravimetric geoid model 2010 总被引:4,自引:1,他引:3
A new gravimetric geoid model, Canadian Gravimetric Geoid 2010 (CGG2010), has been developed to upgrade the previous geoid model CGG2005. CGG2010 represents the separation between the reference ellipsoid of GRS80 and the Earth’s equipotential surface of $W_0=62{,}636{,}855.69~\mathrm{m}^2\mathrm{s}^{-2}$ W 0 = 62 , 636 , 855.69 m 2 s ? 2 . The Stokes–Helmert method has been re-formulated for the determination of CGG2010 by a new Stokes kernel modification. It reduces the effect of the systematic error in the Canadian terrestrial gravity data on the geoid to the level below 2 cm from about 20 cm using other existing modification techniques, and renders a smooth spectral combination of the satellite and terrestrial gravity data. The long wavelength components of CGG2010 include the GOCE contribution contained in a combined GRACE and GOCE geopotential model: GOCO01S, which ranges from $-20.1$ ? 20.1 to 16.7 cm with an RMS of 2.9 cm. Improvement has been also achieved through the refinement of geoid modelling procedure and the use of new data. (1) The downward continuation effect has been accounted accurately ranging from $-22.1$ ? 22.1 to 16.5 cm with an RMS of 0.9 cm. (2) The geoid residual from the Stokes integral is reduced to 4 cm in RMS by the use of an ultra-high degree spherical harmonic representation of global elevation model for deriving the reference Helmert field in conjunction with a derived global geopotential model. (3) The Canadian gravimetric geoid model is published for the first time with associated error estimates. In addition, CGG2010 includes the new marine gravity data, ArcGP gravity grids, and the new Canadian Digital Elevation Data (CDED) 1:50K. CGG2010 is compared to GPS-levelling data in Canada. The standard deviations are estimated to vary from 2 to 10 cm with the largest error in the mountainous areas of western Canada. We demonstrate its improvement over the previous models CGG2005 and EGM2008. 相似文献
20.
The structure of normal matrices occurring in the problem of weighted least-squares spherical harmonic analysis of measurements
scattered on a sphere with random noises is investigated. Efficient algorithms for the formation of the normal matrices are
derived using fundamental relations inherent to the products of two surface spherical harmonic functions. The whole elements
of a normal matrix complete to spherical harmonic degree L are recursively obtained from its first row or first column extended to degree 2L with only O(L
4) computational operations. Applications of the algorithms to the formation of surface normal matrices from geoid undulations
and surface gravity anomalies are discussed in connection with the high-degree geopotential modeling.
Received: 22 March 1999 / Accepted: 23 December 1999 相似文献