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1.
With the advances in the field of GPS positioning and the global densification of permanent GPS tracking stations, it is now possible to determine at the highest level of accuracy the transformation parameters connecting various international terrestrial reference frame (ITRF) realizations. As a by-product of these refinements, not only the seven usual parameters of the similarity transformations between frames are available, but also their rates, all given at some epoch t k . This paper introduces rigorous matrix equations to estimate variance–covariance matrices for transformed coordinates at any epoch t based on a stochastic model that takes into consideration all a priori information of the parameters involved at epoch t k , and the coordinates and velocities at the reference frame initial epoch t 0. The results of this investigation suggest that in order to attain maximum accuracy, the agencies determining the 14-parameter transformations between reference frames should also publish their full variance–covariance matrix. Electronic Publication  相似文献   

2.
 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   

3.
Second-order derivatives of a general scalar function of position (F) with respect to the length elements along a family of local Cartesian axes are developed in the spheroidal and spherical coordinate systems. A link between the two kinds of formulations is established when the results in spherical coordinates are confirmed also indirectly, through a transformation from spheroidal coordinates. IfF becomesW (earth's potential) the six distinct second-order derivatives—which include one vertical and two horizontal gradients of gravity—relate the symmetric Marussi tensor to the curvature parameters of the field. The general formulas for the second-order derivatives ofF are specialized to yield the second-order derivatives ofU (standard potential) and ofT (disturbing potential), which allows the latter to be modeled by a suitable set of parameters. The second-order derivatives ofT in which the property ΔT=0 is explicitly incorporated are also given. According to the required precision, the spherical approximation may or may not be desirable; both kinds of results are presented. The derived formulas can be used for modeling of the second-order derivatives ofW orT at the ground level as well as at higher altitudes. They can be further applied in a rotating or a nonrotating field. The development in this paper is based on the tensor approach to theoretical geodesy, introduced by Marussi [1951] and further elaborated by Hotine [1969], which can lead to significantly shorter demonstrations when compared to conventional approaches.  相似文献   

4.
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   

5.
World Geodetic Datum 2000   总被引：7，自引：1，他引：6  
 Based on the current best estimates of fundamental geodetic parameters {W 0,GM,J 2,Ω} the form parameters of a Somigliana-Pizzetti level ellipsoid, namely the semi-major axis a and semi-minor axis b (or equivalently the linear eccentricity ) are computed and proposed as a new World Geodetic Datum 2000. There are six parameters namely the four fundamental geodetic parameters {W 0,GM,J 2,Ω} and the two form parameters {a,b} or {a,ɛ}, which determine the ellipsoidal reference gravity field of Somigliana-Pizzetti type constraint to two nonlinear condition equations. Their iterative solution leads to best estimates a=(6 378 136.572±0.053)m, b=(6 356 751.920 ± 0.052)m, ɛ=(521 853.580±0.013)m for the tide-free geoide of reference and a=(6 378 136.602±0.053)m, b=(6 356 751.860±0.052)m, ɛ=(521 854.674 ± 0.015)m for the zero-frequency tide geoid of reference. The best estimates of the form parameters of a Somigliana-Pizzetti level ellipsoid, {a,b}, differ significantly by −0.39 m, −0.454 m, respectively, from the data of the Geodetic Reference System 1980. Received: 1 February 1999 / Accepted: 31 August 1999  相似文献   

6.
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   

7.
Using TOPEX satellite altimetry, water-level-gauge data, and a geoid model, the geopotential, W 0, of the International Great Lakes Datum of 1985 (IGLD85) is determined. This is compared to an analogous determination using GPS and leveling data in the region. The two sets of data yield generally consistent results at the few-decimeter level and both indicate a tilt of about 33 cm in the computed datum across the region. On the basis of this and other studies, it is conjectured that the source of the tilt is a regional error in G99SSS. Further analysis of the altimetry and water-level data indicate that the geoid model, G99SSS, is in error by up to 20 cm at scales of about 100–150 km. In addition, the analysis of 8 years of altimeter and water-level data shows varying trends (up to 2 mm/yr) in crustal uplift throughout the region, generally consistent with an independent post-glacial rebound (PGR) model, ICE-4G. AcknowledgmentThis research was supported in part by the Ohio Sea Grant Program, grant no. NA86RG0053 (R/CE-5). A. Mainville kindly provided data and information for Canadian stations. The authors are grateful to M. Bursa, M. Poutanen, D. Zilkoski, and an anonymous reviewer for contributing significantly to the improvement of the paper.  相似文献   

8.
 Considering a GPS satellite and two terrestrial stations, two types of equations are derived relating the heights of the two stations to the measured data (frequency ratio or clock rate differences) and the coordinates and velocity components of all three participating objects. The potential possibilities of using such relations for the determination of heights (in terms of geopotential numbers or orthometric heights) are discussed. Received: 6 December 2000 / Accepted: 9 July 2001  相似文献   

9.
吴富梅  魏子卿  刘光明 《测绘学报》2018,47(10):1295-1300
确定局部高程基准相对大地水准面的垂直偏差是统一全球高程基准的重要途径。本文的目的是通过大港验潮站坐标直接确定我国高程基准的垂直偏差。首先给出通过大港验潮站坐标确定我国高程基准垂直偏差的基本原理,然后介绍测定大港验潮站平均海面坐标的方法及过程,接下来通过EGM2008和EIGEN-6C4重力场模型计算出的我国高程基准面的重力位,进而推算获得垂直偏差,并与我国东部地区GPS/水准数据的计算结果进行了比较。经分析发现,EGM2008模型计算结果的可靠性要好于EIGEN-6C4模型;利用大港验潮站坐标计算得到的我国高程基准相对大地水准面的垂直偏差为0.344 m,比利用我国东部261个GPS/水准点数据计算获得的偏差值小0.006 m。  相似文献   

10.
The TOPEX/Poseidon (T/P) satellite alti- meter mission marked a new era in determining the geopotential constant W 0. On the basis of T/P data during 1993–2003 (cycles 11–414), long-term variations in W 0 have been investigated. The rounded value W 0 = 62636856.0 ± 0.5) m 2 s −2 has already been adopted by the International Astronomical Union for the definition of the constant L G = W 0/c 2 = 6.969290134 × 10−10 (where c is the speed of light), which is required for the realization of the relativistic atomic time scale. The constant L G , based on the above value of W 0, is also included in the 2003 International Earth Rotation and Reference Frames Service conventions. It has also been suggested that W 0 is used to specify a global vertical reference system (GVRS). W 0 ensures the consistency with the International Terrestrial Reference System, i.e. after adopting W 0, along with the geocentric gravitational constant (GM), the Earth’s rotational velocity (ω) and the second zonal geopotential coefficient (J 2) as primary constants (parameters), then the ellipsoidal parameters (a,α) can be computed and adopted as derived parameters. The scale of the International Terrestrial Reference Frame 2000 (ITRF2000) has also been specified with the use of W 0 to be consistent with the geocentric coordinate time. As an example of using W 0 for a GVRS realization, the geopotential difference between the adopted W 0 and the geopotential at the Rimouski tide-gauge point, specifying the North American Vertical Datum 1988 (NAVD88), has been estimated.  相似文献   

11.
In GPS meteorology, the weighted mean temperature is usually obtained by using a linear function of the surface temperature T s. However, not every GPS station can measure the surface temperature. The current study explores the characteristics of surface temperature and weighted mean temperature based on the global pressure and temperature model (GPT) and the Bevis T m–T s relationship (T m =?a?+?bT s). A new global weighted mean temperature (GWMT) model has been built which directly uses three-dimensional coordinates and day of the year to calculate the weighted mean temperature. The data of year 2005–2009 from 135 radiosonde stations provided by the Integrated Global Radiosonde Archive were used to calculate the model coefficients, which have been validated through examples. The result shows that the GWMT model is generally better than the existing liner models in most areas according to the statistic indexes (namely, mean absolute error and root mean square). Then we calculated precipitable water vapor, and the result shows that GWMT model can also yield high precision PWV.  相似文献   

12.
 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   

13.
An algorithm for the determination of the spherical harmonic coefficients of the terrestrial gravitational field representation from the analysis of a kinematic orbit solution of a low earth orbiting GPS-tracked satellite is presented and examined. A gain in accuracy is expected since the kinematic orbit of a LEO satellite can nowadays be determined with very high precision, in the range of a few centimeters. In particular, advantage is taken of Newton's Law of Motion, which balances the acceleration vector with respect to an inertial frame of reference (IRF) and the gradient of the gravitational potential. By means of triple differences, and in particular higher-order differences (seven-point scheme, nine-point scheme), based upon Newton's interpolation formula, the local acceleration vector is estimated from relative GPS position time series. The gradient of the gravitational potential is conventionally given in a body-fixed frame of reference (BRF) where it is nearly time independent or stationary. Accordingly, the gradient of the gravitational potential has to be transformed from spherical BRF to Cartesian IRF. Such a transformation is possible by differentiating the gravitational potential, given as a spherical harmonics series expansion, with respect to Cartesian coordinates by means of the chain rule, and expressing zero- and first-order Ferrer's associated Legendre functions in terms of Cartesian coordinates. Subsequently, the BRF Cartesian coordinates are transformed into IRF Cartesian coordinates by means of the polar motion matrix, the precession–nutation matrices and the Greenwich sidereal time angle (GAST). In such a way a spherical harmonic representation of the terrestrial gravitational field intensity with respect to an IRF is achieved. Numerical tests of a resulting Gauss–Markov model document not only the quality and the high resolution of such a space gravity spectroscopy, but also the problems resulting from noise amplification in the acceleration determination process.  相似文献   

14.
The geoid gradient over the Darling Fault in Western Australia is extremely high, rising by as much as 38 cm over only 2 km. This poses problems for gravimetric-only geoid models of the area, whose frequency content is limited by the spatial distribution of the gravity data. The gravimetric-only version of AUSGeoid98, for instance, is only able to resolve 46% of the gradient across the fault. Hence, the ability of GPS surveys to obtain accurate orthometric heights is reduced. It is described how further gravity data were collected over the Darling Fault, augmenting the existing gravity observations at key locations so as to obtain a more representative geoid gradient. As many of the gravity observations were collected at stations with a well-known GRS80 ellipsoidal height, the opportunity arose to compute a geoid model via both the Stokes and the Hotine approaches. A scheme was devised to convert free-air anomaly data to gravity disturbances using existing geoid models, followed by a Hotine integration to geoid heights. Interestingly, these results depended very weakly upon the choice of input geoid model. The extra gravity data did indeed improve the fit of the computed geoid to local GPS/Australian Height Datum (AHD) observations by 58% over the gravimetric-only AUSGeoid98. While the conventional Stokesian approach to geoid determination proved to be slightly better than the Hotine method, the latter still improved upon the gravimetric-only AUSGeoid98 solution, supporting the viability of conducting gravity surveys with GPS control for the purposes of geoid determination. AcknowledgementsThe author would like to thank Will Featherstone, Ron Gower, Ron Hackney, Linda Morgan, Geoscience Australia, Scripps Oceanographic Institute and the three anonymous reviewers of this paper. This research was funded by the Australian Research Council.  相似文献   

15.
This paper is devoted to the spherical and spheroidal harmonic expansion of the gravitational potential of the topographic masses in the most rigorous way. Such an expansion can be used to compute gravimetric topographic effects for geodetic and geophysical applications. It can also be used to augment a global gravity model to a much higher resolution of the gravitational potential of the topography. A formulation for a spherical harmonic expansion is developed without the spherical approximation. Then, formulas for the spheroidal harmonic expansion are derived. For the latter, Legendre’s functions of the first and second kinds with imaginary variable are expanded in Laurent series. They are then scaled into two real power series of the second eccentricity of the reference ellipsoid. Using these series, formulas for computing the spheroidal harmonic coefficients are reduced to surface harmonic analysis. Two numerical examples are presented. The first is a spherical harmonic expansion to degree and order 2700 by taking advantage of existing software. It demonstrates that rigorous spherical harmonic expansion is possible, but the computed potential on the geoid shows noticeable error pattern at Polar Regions due to the downward continuation from the bounding sphere to the geoid. The second numerical example is the spheroidal expansion to degree and order 180 for the exterior space. The power series of the second eccentricity of the reference ellipsoid is truncated at the eighth order leading to omission errors of 25 nm (RMS) for land areas, with extreme values around 0.5 mm to geoid height. The results show that the ellipsoidal correction is 1.65 m (RMS) over land areas, with maximum value of 13.19 m in the Andes. It shows also that the correction resembles the topography closely, implying that the ellipsoidal correction is rich in all frequencies of the gravity field and not only long wavelength as it is commonly assumed.  相似文献   

16.
In this paper we examine OTL displacements detected by GPS stations of a dedicated campaign and validate ocean tide models. Our area of study is the continental shelf of Brittany and Cotentin in France. Brittany is one of the few places in the world where tides provoke loading displacements of ∼10–12 cm vertically and a few cm horizontally. Ocean tide models suffer from important discrepancies in this region. Seven global and regional ocean tide models were tested: FES2004 corrected for K2, TPXO.7.0, TPXO.6.2, GOT00.2, CSR4.0, NAO.99b and the most recent regional grids of the North East Atlantic (NEA2004). These gridded amplitudes and phases of ocean tides were convolved in order to get the predicted OTL displacements using two different algorithms. Data over a period of 3.5 months of 8 GPS campaign stations located on the north coast of Brittany are used, in order to evaluate the geographical distribution of the OTL effect. We have modified and implemented new algorithms in our GPS software, GINS 7.1. GPS OTL constituents are estimated based on 1-day batch solutions. We compare the observed GPS OTL constituents of M2, S2, N2 and K1 waves with the selected ocean tide models on global and regional grids. Large phase-lag and amplitude discrepancies over 20° and 1.5 cm in the vertical direction in the semi-diurnal band of M2 between predictions and GPS/models are detected in the Bay of Mont St-Michel. From a least squares spectral analysis of the GPS time-series, significant harmonic peaks in the integer multiples of the orbital periods of the GPS satellites are observed, indicating the existence of multipath effects in the GPS OTL constituents. The GPS OTL observations agree best with FES2004, NEA2004, GOT00.2 and CSR4.0 tide models.  相似文献   

17.
The North American Datum of 1983 (NAD 83) provides horizontal coordinates for more than 250,000 geodetic stations. These coordinates were derived by a least squares adjustment of existing terrestrial and space-based geodetic data. For pairs of first order stations with interstation distances between 10km and 100km, therms discrepancy between distances derived fromNAD 83 coordinates and distances derived from independentGPS data may be suitably approximated by the empirical rulee=0.008 K0.7 where e denotes therms discrepancy in meters and K denotes interstation distance in kilometers. For the same station pairs, therms discrepancy in azimuth may be approximated by the empirical rule e=0.020 K0.5. Similar formulas characterize therms discrepancies for pairs involving second and third order stations. Distance and orientation accuracies, moreover, are well within adopted standards. While these expressions indicate that the magnitudes of relative positional accuracies depend on station order, absolute positional accuracies are similar in magnitude for first, second, and third order stations. Adjustment residuals reveal a few local problems with theNAD 83 coordinates and with the weights assigned to certain classes of observations.  相似文献   

18.
Prior to Stokes integration, the gravitational effect of atmospheric masses must be removed from the gravity anomaly g. One theory for the atmospheric gravity effect on the geoid is the well-known International Association of Geodesy approach in connection with Stokes integral formula. Another strategy is the use of a spherical harmonic representation of the topography, i.e. the use of a global topography computed from a set of spherical harmonics. The latter strategy is improved to account for local information. A new formula is derived by combining the local contribution of the atmospheric effect computed from a detailed digital terrain model and the global contribution computed from a spherical harmonic model of the topography. The new formula is tested over Iran and the results are compared with corresponding results from the old formula which only uses the global information. The results show significant differences. The differences between the two formulas reach 17 cm in a test area in Iran.  相似文献   

19.
Very high-rate global positioning system (GPS) data has the capacity to quickly resolve seismically related ground displacements, thereby providing great potential for rapidly determining the magnitude and the nature of an earthquake’s rupture process and for providing timely warnings for earthquakes and tsunamis. The GPS variometric approach can measure ground displacements with comparable precision to relative positioning and precise point positioning (PPP) within a short period of time. The variometric approach is based on single-differencing over time of carrier phase observations using only the broadcast ephemeris and a single receiver to estimate velocities, which are then integrated to derive displacements. We evaluate the performance of the variometric approach to measure displacements using 50 Hz GPS data, which were recorded during the 2013 MW 6.6 Lushan earthquake and the 2011 MW 9.0 Tohoku-Oki earthquake. The comparison between 50 and 1 Hz seismic displacements demonstrates that 1 Hz solutions often fail to faithfully manifest the seismic waves containing high-frequency seismic signals due to aliasing, which is common for near-field stations of a moderate-magnitude earthquake. Results indicate that 10–50 Hz sampling GPS sites deployed close to the source or the ruptured fault are needed for measuring dynamic seismic displacements of moderate-magnitude events. Comparisons with post-processed PPP results reveal that the variometric approach can determine seismic displacements with accuracies of 0.3–4.1, 0.5–2.3 and 0.8–6.8 cm in the east, north and up components, respectively. Moreover, the power spectral density analysis demonstrates that high-frequency noises of seismic displacements, derived using the variometric approach, are smaller than those of PPP-derived displacements in these three components.  相似文献   

20.
 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   

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