共查询到20条相似文献,搜索用时 172 毫秒
1.
R. H. Rapp 《Journal of Geodesy》1997,71(5):282-289
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
2.
Fast and accurate relative positioning for baselines less than 20 km in length is possible using dual-frequency Global Positioning
System (GPS) receivers. By measuring orthometric heights of a few GPS stations by differential levelling techniques, the geoid
undulation can be modelled, which enables GPS to be used for orthometric height determination in a much faster and more economical
way than terrestrial methods. The geoid undulation anomaly can be very useful for studying tectonic structure. GPS, levelling
and gravity measurements were carried out along a 200-km-long highly undulating profile, at an average elevation of 4000 m,
in the Ladak region of NW Himalaya, India. The geoid undulation and gravity anomaly were measured at 28 common GPS-levelling
and 67 GPS-gravity stations. A regional geoid low of nearly −4 m coincident with a steep negative gravity gradient is compatible
with very recent findings from other geophysical studies of a low-velocity layer 20–30 km thick to the north of the India–Tibet
plate boundary, within the Tibetan plate. Topographic, gravity and geoid data possibly indicate that the actual plate boundary
is situated further north of what is geologically known as the Indus Tsangpo Suture Zone, the traditionally supposed location
of the plate boundary. Comparison of the measured geoid with that computed from OSU91 and EGM96 gravity models indicates that
GPS alone can be used for orthometric height determination over the Higher Himalaya with 1–2 m accuracy.
Received: 10 April 1997 / Accepted: 9 October 1998 相似文献
3.
Undulation and anomaly estimation using Geos-3 altimeter data without precise satellite orbits 总被引:1,自引:0,他引:1
The paper describes results obtained from the processing of 53 Geos-3 arcs of altimeter data obtained during the first weeks
after the launch of the satellite in April, 1975. The measurement from the satellite to the ocean surface was used to obtain
an approximate geoid undulation which was contaminated by long wavelength errors caused primarily by altimeter bias and orbit
error. This long wavelength error was reduced by fitting with a low degree polynomial the raw undulation data to the undulations
implied by the GEM 7 potential coefficients, in an adjustment process that included conditions on tracks that cross. The root
mean square crossover discrepancy before this adjustment was ±12.4 meters while after the adjustment it was ±0.9 m. These
adjusted undulations were used to construct a geoid map in the Geos-3 calibration area using a least squares filter to remove
remaining noise in the undulations. Comparing these undulations to ones computed from potential coefficients and terrestrial
gravity data indicates a mean difference of 0.25 m and a root mean square difference of ±1.92 m.
The adjusted undulations were also used to estimate several 5o, 2o, and 1o anomalies using the method of least squares collocation. The resulting predictions agreed well with known values although
the 1o x 1o anomalies could not be considered as reliably determined. 相似文献
4.
Bishwa Acharya 《GPS Solutions》1995,1(2):113-120
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
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.
Richard H. Rapp 《Journal of Geodesy》1980,54(2):149-163
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
7.
Vasilios K. Despotakis 《Journal of Geodesy》1989,63(4):342-358
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
8.
Essam Ghanem 《地球空间信息科学学报》2001,4(1):19-23
1 IntroductionDifferentgeoidsolutionswerecarriedoutforE gyptusingheterogeneousdataanddifferentmethodologies (El_Tokhey ,1 993) .ThemaingoalofthispaperistodetermineamostaccuratenewgeoidforEgypttakingadvantageofanewupdatedgravitydatabase,theinformationgivenby… 相似文献
9.
Richard H. Rapp 《Journal of Geodesy》1994,69(1):26-31
This paper discusses the separation between the reference surface of several vertical datums and the geoid. The data used includes a set of Doppler positioned stations, transformation parameters to convert the Doppler positions to ITRF90, and a potential coefficient model composed of the JGM-2 (NASA model) from degree 2 to 70 plus the OSU91A model from degree 71 to 360. The basic method of analysis is the comparison of a geometric geoid undulation derived from an ellipsoidal height and an orthometric height with the undulation computed from the potential coefficient model The mean difference can imply a bias of the datum reference surface with respect to the geoid. Vertical datums in the following countries were considered: England, Germany, United States, and Australia. The following numbers represent the bias values of each datum after adopting an equatorial radius of 6378136.3m: England (-87 cm), Germany (4 cm), United States (NGVD29 (-26 cm)), NAVD88 (-72 cm), Australia AHD (mainland, -68 cm); AHD (Tasmania, -98 cm). A negative sign indicates the datum reference surface is below the geoid. The 91 cm difference between the datums in England and Germany has been independently estimated as 80 cm. The 30 cm difference between AHD (mainland) and AHD (Tasmania) has been independently estimated as 40 cm. These bias values have been estimated from data where the geometric/ gravimetric geoid undulation difference standard deviation, at one station, is typically ±100 cm, although the mean difference is determined more accurately.The results of this paper can be improved and expanded with more accurate geocentric station positions, more accurate and consistent heights with respect to the local vertical datum, and a more accurate gravity field for the Earth. The ideas developed here provide insight on the determination of a world height system. 相似文献
10.
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
11.
Isaac Dadzie 《地球空间信息科学学报》2007,10(1):27-32
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
12.
Local geoid determination combining gravity disturbances and GPS/levelling: a case study in the Lake Nasser area, Aswan, Egypt 总被引:1,自引:0,他引:1
C. C. Tscherning Awar Radwan A. A. Tealeb S. M. Mahmoud M. Abd El-Monum Ramdan Hassan I. El-Syaed K. Saker 《Journal of Geodesy》2001,75(7-8):343-348
The use of GPS for height control in an area with existing levelling data requires the determination of a local geoid and
the bias between the local levelling datum and the one implicitly defined when computing the local geoid. If only scarse gravity
data are available, the heights of new data may be collected rapidly by determining the ellipsoidal height by GPS and not
using orthometric heights. Hence the geoid determination has to be based on gravity disturbances contingently combined with
gravity anomalies. Furthermore, existing GPS/levelling data may also be used in the geoid determination if a suitable general
gravity field modelling method (such as least-squares collocation, LSC) is applied. A comparison has been made in the Aswan
Dam area between geoids determined using fast Fourier transform (FFT) with gravity disturbances exclusively and LSC using
only the gravity disturbances and the disturbances combined with GPS/levelling data. The EGM96 spherical harmonic model was
in all cases used in a remove–restore mode. A total of 198 gravity disturbances spaced approximately 3 km apart were used,
as well as 35 GPS/levelling points in the vicinity and on the Aswan Dam. No data on the Nasser Lake were available. This gave
difficulties when using FFT, which requires the use of gridded data. When using exclusively the gravity disturbances, the
agreement between the GPS/levelling data were 0.71 ± 0.17 m for FFT and 0.63 ± 0.15 for LSC. When combining gravity disturbances
and GPS/levelling, the LSC error estimate was ±0.10 m. In the latter case two bias parameters had to be introduced to account
for a possible levelling datum difference between the levelling on the dam and that on the adjacent roads.
Received: 14 August 2000 / Accepted: 28 February 2001 相似文献
13.
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
14.
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
15.
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
16.
Spherical cap harmonic analysis: a comment on its proper use for local gravity field representation 总被引:1,自引:0,他引:1
Spherical cap harmonic analysis is the appropriate analytical technique for modelling Laplacian potential and the corresponding
field components over a spherical cap. This paper describes the use of this method by means of a least-squares approach for
local gravity field representation. Formulations for the geoid undulation and the components ξ, η of the deflection of the
vertical are derived, together with some warnings in the application of the technique. Although most of the formulations have
been given by another paper, these were confusing or even incorrect, mainly because of an improper application of the spherical
cap harmonic analysis.
Received: 16 January 1996 / Accepted: 17 March 1997 相似文献
17.
One of the aims of the Earth Explorer Gravity Field and Steady-State Ocean Circulation (GOCE) mission is to provide global
and regional models of the Earth's gravity field and of the geoid with high spatial resolution and accuracy. Using the GOCE
error model, simulation studies were performed in order to estimate the accuracy of datum transfer in different areas of the
Earth. The results showed that with the GOCE error model, the standard deviation of the height anomaly differences is about
one order of magnitude better than the corresponding value with the EGM96 error model. As an example, the accuracy of the
vertical datum transfer from the tide gauge of Amsterdam to New York was estimated equal to 57 cm when the EGM96 error model
was used, while in the case of GOCE error model this accuracy was increased to 6 cm. The geoid undulation difference between
the two places is about 76.5 m. Scaling the GOCE errors to the local gravity variance, the estimated accuracy varied between
3 and 7 cm, depending on the scaling model.
Received: 1 March 2000 / Accepted: 21 February 2001 相似文献
18.
Christopher Jekeli 《Journal of Geodesy》1980,54(2):137-147
Errors are considered in the outer zone contribution to oceanic undulation differences as obtained from a set of potential
coefficients complete to degree 180. It is assumed that the gravity data of the inner zone (a spherical cap), consisting of
either gravity anomalies or gravity disturbances, has negligible error. This implies that error estimates of the total undulation
difference are analyzed. If the potential coefficients are derived from a global field of 1°×1° mean anomalies accurate to
εΔg=10 mgal, then for a cap radius of 10°, the undulation difference error (for separations between 100 km and 2000 km) ranges
from 13 cm to 55 cm in the gravity anomaly case and from 6 cm to 36 cm in the gravity disturbance case. If εΔg is reduced to 1 mgal, these errors in both cases are less than 10 cm. In the absence of a spherical cap, both cases yield
identical error estimates: about 68 cm if εΔg=1 mgal (for most separations) and ranging from 93 cm to 160 cm if εΔg=10 mgal. Introducing a perfect 30-degree reference field, the latter errors are reduced to about 110 cm for most separations. 相似文献
19.
A methodology for precise determination of the fundamental geodetic parameter w
0, the potential value of the Gauss–Listing geoid, as well as its time derivative 0, is presented. The method is based on: (1) ellipsoidal harmonic expansion of the external gravitational field of the Earth
to degree/order 360/360 (130 321 coefficients; http://www.uni-stuttgard.de/gi/research/ index.html projects) with respect
to the International Reference Ellipsoid WGD2000, at the GPS positioned stations; and (2) ellipsoidal free-air gravity reduction
of degree/order 360/360, based on orthometric heights of the GPS-positioned stations. The method has been numerically tested
for the data of three GPS campaigns of the Baltic Sea Level project (epochs 1990.8,1993.4 and 1997.4). New w
0 and 0 values (w
0=62 636 855.75 ± 0.21 m2/s2, 0=−0.0099±0.00079 m2/s2 per year, w
0/&γmacr;=6 379 781.502 m,0/&γmacr;=1.0 mm/year, and &γmacr;= −9.81802523 m2/s2) for the test region (Baltic Sea) were obtained. As by-products of the main study, the following were also determined: (1)
the high-resolution sea surface topography map for the Baltic Sea; (2) the most accurate regional geoid amongst four different
regional Gauss–Listing geoids currently proposed for the Baltic Sea; and (3) the difference between the national height datums
of countries around the Baltic Sea.
Received: 14 August 2000 / Accepted: 19 June 2001 相似文献
20.
A detailed gravimetric geoid has been computed for the Nortwest Atlantic Ocean and Caribbean Sea area in support of the calibration
and evaluation of the GEOS-3 altimeter. This geoid, computed on a 15’ x 15’ grid was based upon a combination of surface gravity
data and the GSFC GEM-8 gravitational field model. This gravimetric geoid has been compared with passes of SKYLAB altimeter
data recorded in the Atlantic Ocean, and three typical passes are presented. The relative agreement of the two data types
is quite good with differences generally less than 2 meters for these passes. Sea surface manifestations of numerous short
wavelength (≈ 100 km) oceanographic features indicated in the altimeter data are also confirmed by the gravimetric geoid. 相似文献