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1.
 The Somigliana–Pizzetti gravity field (the International gravity formula), namely the gravity field of the level ellipsoid (the International Reference Ellipsoid), is derived to the sub-nanoGal accuracy level in order to fulfil the demands of modern gravimetry (absolute gravimeters, super conducting gravimeters, atomic gravimeters). Equations (53), (54) and (59) summarise Somigliana–Pizzetti gravity Γ(φ,u) as a function of Jacobi spheroidal latitude φ and height u to the order ?(10−10 Gal), and Γ(B,H) as a function of Gauss (surface normal) ellipsoidal latitude B and height H to the order ?(10−10 Gal) as determined by GPS (`global problem solver'). Within the test area of the state of Baden-Württemberg, Somigliana–Pizzetti gravity disturbances of an average of 25.452 mGal were produced. Computer programs for an operational application of the new international gravity formula with (L,B,H) or (λ,φ,u) coordinate inputs to a sub-nanoGal level of accuracy are available on the Internet. Received: 23 June 2000 / Accepted: 2 January 2001  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.
 The New Hebrides experiment consisted of setting up a pair of DORIS beacons in remote tropical islands in the southwestern Pacific, between 1993 and 1997. Because of orbitography requirements on TOPEX/Poséidon, the beacons were only transmitting to SPOT satellites. Root-mean-square (RMS) scatters at the centimeter level on the latitude and vertical components were achieved, but 2-cm RMS scatters affected the longitude component. Nevertheless, results of relative velocity (123 mm/year N250°) are very consistent with those obtained using the global positioning system (GPS) (126 mm/yr N246°). The co-seismic step (12 mm N60°) related to the Walpole event (M W = 7.7) is consistent with that derived from GPS (10 mm N30°) or from the centroid moment tensor (CMT) of the quake (12 mm N000°). Received: 19 November 1999 / Accepted: 17 May 2000  相似文献   

4.
 Global mean sea surface heights (SSHs) and gravity anomalies on a 2′×2′ grid were determined from Seasat, Geosat (Exact Repeat Mission and Geodetic Mission), ERS-1 (1.5-year mean of 35-day, and GM), TOPEX/POSEIDON (T/P) (5.6-year mean) and ERS-2 (2-year mean) altimeter data over the region 0∘–360∘ longitude and –80∘–80∘ latitude. To reduce ocean variabilities and data noises, SSHs from non-repeat missions were filtered by Gaussian filters of various wavelengths. A Levitus oceanic dynamic topography was subtracted from the altimeter-derived SSHs, and the resulting heights were used to compute along-track deflection of the vertical (DOV). Geoidal heights and gravity anomalies were then computed from DOV using the deflection-geoid and inverse Vening Meinesz formulae. The Levitus oceanic dynamic topography was added back to the geoidal heights to obtain a preliminary sea surface grid. The difference between the T/P mean sea surface and the preliminary sea surface was computed on a grid by a minimum curvature method and then was added to the preliminary grid. The comparison of the NCTU01 mean sea surface height (MSSH) with the T/P and the ERS-1 MSSH result in overall root-mean-square (RMS) differences of 5.0 and 3.1 cm in SSH, respectively, and 7.1 and 3.2 μrad in SSH gradient, respectively. The RMS differences between the predicted and shipborne gravity anomalies range from 3.0 to 13.4 mGal in 12 areas of the world's oceans. Received: 26 September 2001 / Accepted: 3 April 2002 Correspondence to: C. Hwang Acknowledgements. This research is partly supported by the National Science Council of ROC, under grants NSC89-2611-M-009-003-OP2 and NSC89-2211-E-009-095. This is a contribution to the IAG Special Study Group 3.186. The Geosat and ERS1/2 data are from NOAA and CERSAT/France, respectively. The T/P data were provided by AVISO. The CLS and GSFC00 MSS models were kindly provided by NASA/GSFC and CLS, respectively. Drs. Levitus, Monterey, and Boyer are thanked for providing the SST model. Dr. T. Gruber and two anonymous reviewers provided very detailed reviews that improved the quality of this paper.  相似文献   

5.
New solutions for the geodetic coordinate transformation   总被引：5，自引：2，他引：5  
 The Cartesian-to-geodetic-coordinate transformation is approached from a new perspective. Existence and uniqueness of geodetic representation are presented, along with a clear geometric picture of the problem and the role of the ellipse evolute. A new solution is found with a Newton-method iteration in the reduced latitude; this solution is proved to work for all points in space. Care is given to error propagation when calculating the geodetic latitude and height. Received: 9 August 2001 / Accepted: 27 March 2002 Acknowledgments. The author would like to thank the Clifford W.␣Tompson scholarship fund, Dr. Brian DeFacio, the University of Missouri College of Arts &Sciences, and the United States Air Force. He also thanks a reviewer for suggesting and providing a prototype MATLAB code. A MATLAB program for the iterative sequence is presented at the end of the paper (Appendix A).  相似文献   

6.
 This paper generalizes the Stokes formula from the spherical boundary surface to the ellipsoidal boundary surface. The resulting solution (ellipsoidal geoidal height), consisting of two parts, i.e. the spherical geoidal height N 0 evaluated from Stokes's formula and the ellipsoidal correction N 1, makes the relative geoidal height error decrease from O(e 2) to O(e 4), which can be neglected for most practical purposes. The ellipsoidal correction N 1 is expressed as a sum of an integral about the spherical geoidal height N 0 and a simple analytical function of N 0 and the first three geopotential coefficients. The kernel function in the integral has the same degree of singularity at the origin as the original Stokes function. A brief comparison among this and other solutions shows that this solution is more effective than the solutions of Molodensky et al. and Moritz and, when the evaluation of the ellipsoidal correction N 1 is done in an area where the spherical geoidal height N 0 has already been evaluated, it is also more effective than the solution of Martinec and Grafarend. Received: 27 January 1999 / Accepted: 4 October 1999  相似文献   

7.
 When standard boundary element methods (BEM) are used in order to solve the linearized vector Molodensky problem we are confronted with two problems: (1) the absence of O(|x|−2) terms in the decay condition is not taken into account, since the single-layer ansatz, which is commonly used as representation of the disturbing potential, is of the order O(|x|−1) as x→∞. This implies that the standard theory of Galerkin BEM is not applicable since the injectivity of the integral operator fails; (2) the N×N stiffness matrix is dense, with N typically of the order 105. Without fast algorithms, which provide suitable approximations to the stiffness matrix by a sparse one with O(N(logN) s ), s≥0, non-zero elements, high-resolution global gravity field recovery is not feasible. Solutions to both problems are proposed. (1) A proper variational formulation taking the decay condition into account is based on some closed subspace of co-dimension 3 of the space of square integrable functions on the boundary surface. Instead of imposing the constraints directly on the boundary element trial space, they are incorporated into a variational formulation by penalization with a Lagrange multiplier. The conforming discretization yields an augmented linear system of equations of dimension N+3×N+3. The penalty term guarantees the well-posedness of the problem, and gives precise information about the incompatibility of the data. (2) Since the upper left submatrix of dimension N×N of the augmented system is the stiffness matrix of the standard BEM, the approach allows all techniques to be used to generate sparse approximations to the stiffness matrix, such as wavelets, fast multipole methods, panel clustering etc., without any modification. A combination of panel clustering and fast multipole method is used in order to solve the augmented linear system of equations in O(N) operations. The method is based on an approximation of the kernel function of the integral operator by a degenerate kernel in the far field, which is provided by a multipole expansion of the kernel function. Numerical experiments show that the fast algorithm is superior to the standard BEM algorithm in terms of CPU time by about three orders of magnitude for N=65 538 unknowns. Similar holds for the storage requirements. About 30 iterations are necessary in order to solve the linear system of equations using the generalized minimum residual method (GMRES). The number of iterations is almost independent of the number of unknowns, which indicates good conditioning of the system matrix. Received: 16 October 1999 / Accepted: 28 February 2001  相似文献   

8.
The topographic potential and the direct topographic effect on the geoid are presented as surface integrals, and the direct gravity effect is derived as a rigorous surface integral on the unit sphere. By Taylor-expanding the integrals at sea level with respect to topographic elevation (H) the power series of the effects is derived to arbitrary orders. This study is primarily limited to terms of order H 2. The limitations of the various effects in the frequently used planar approximations are demonstrated. In contrast, it is shown that the spherical approximation to power H 2 leads to a combined topographic effect on the geoid (direct plus indirect effect) proportional to H˜2 (where terms of degrees 0 and 1 are missing) of the order of several metres, while the combined topographic effect on the height anomaly vanishes, implying that current frequent efforts to determine the direct effect to this order are not needed. The last result is in total agreement with Bjerhammar's method in physical geodesy. It is shown that the most frequently applied remove–restore technique of topographic masses in the application of Stokes' formula suffers from significant errors both in the terrain correction C (representing the sum of the direct topographic effect on gravity anomaly and the effect of continuing the anomaly to sea level) and in the term t (mainly representing the indirect effect on the geoidal or quasi-geoidal height). Received: 18 August 1998 / Accepted: 4 October 1999  相似文献   

9.
 Simplified techniques for high-degree spherical harmonic synthesis are extended to include gravitational potential second derivatives with respect to latitude. Received: 23 July 2001 / Accepted: 12 April 2002 Acknowledgement. The authors would like to thank Christian Tscherning for recommending Laplace's equation as an accuracy test. Our use of Legendre's differential equation, as the most direct means for extending our simplified synthesis methods to second-order derivatives, was a direct result of this suggestion. Correspondence to: S. A. Holmes  相似文献   

10.
 Since the beginning of the International Global Navigation Satellite System (GLONASS) Experiment, IGEX, in October 1998, the Center for Orbit Determination in Europe (CODE) has acted as an analysis center providing precise GLONASS orbits on a regular basis. In CODE's IGEX routine analysis the Global Positioning System (GPS) orbits and Earth rotation parameters are introduced as known quantities into the GLONASS processing. A new approach is studied, where data from the IGEX network are combined with GPS observations from the International GPS Service (IGS) network and all parameters (GPS and GLONASS orbits, Earth rotation parameters, and site coordinates) are estimated in one processing step. The influence of different solar radiation pressure parameterizations on the GLONASS orbits is studied using different parameter subsets of the extended CODE orbit model. Parameterization with three constant terms in the three orthogonal directions, D, Y, and X (D = direction satellite–Sun, Y = direction of the satellite's solar panel axis), and two periodic terms in the X-direction, proves to be adequate for GLONASS satellites. As a result of the processing it is found that the solar radiation pressure effect for the GLONASS satellites is significantly different in the Y-direction from that for the GPS satellites, and an extensive analysis is carried out to investigate the effect in detail. SLR observations from the ILRS network are used as an independent check on the quality of the GLONASS orbital solutions. Both processing aspects, combining the two networks and changing the orbit parameterization, significantly improve the quality of the determined GLONASS orbits compared to the orbits stemming from CODE's IGEX routine processing. Received: 10 May 2000 / Accepted: 9 October 2000  相似文献   

11.
Vector-based algorithms for the computation of azimuth, elevation and the ellipsoidal normal unit vector from 3D Cartesian coordinates are presented. As a by-product, the formulae for the ellipsoidal normal vector can also be used to iteratively transform rectangular Cartesian coordinates (X, Y, Z) into geodetic coordinates (φ, λ, h) for a height range from −5600 km to 108 km. Comparisons with existing methods indicate that the new transformation can compete with them.  相似文献   

12.
By using Halley’s third-order formula to find the root of a non-linear equation, we develop a new iterative procedure to solve an irrational form of the “latitude equation”, the equation to determine the geodetic latitude for given Cartesian coordinates. With a limit to one iteration, starting from zero height, and minimizing the number of divisions by means of the rational form representation of Halley’s formula, we obtain a new non-iterative method to transform Cartesian coordinates to geodetic ones. The new method is sufficiently precise in the sense that the maximum error of the latitude and the relative height is less than 6 micro-arcseconds for the range of height, −10 km ≤ h ≤ 30,000 km. The new method is around 50% faster than our previous method, roughly twice as fast as the well-known Bowring’s method, and much faster than the recently developed methods of Borkowski, Laskowski, Lin and Wang, Jones, Pollard, and Vermeille.  相似文献   

13.
Green's function solution to spherical gradiometric boundary-value problems   总被引：1，自引：1，他引：1  
 Three independent gradiometric boundary-value problems (BVPs) with three types of gradiometric data, {Γ rr }, {Γ r θ,Γ r λ} and {Γθθ−Γλλ,Γθλ}, prescribed on a sphere are solved to determine the gravitational potential on and outside the sphere. The existence and uniqueness conditions on the solutions are formulated showing that the zero- and the first-degree spherical harmonics are to be removed from {Γ r θ,Γ r λ} and {Γθθ−Γλλ,Γθλ}, respectively. The solutions to the gradiometric BVPs are presented in terms of Green's functions, which are expressed in both spectral and closed spatial forms. The logarithmic singularity of the Green's function at the point ψ=0 is investigated for the component Γ rr . The other two Green's functions are finite at this point. Comparisons to the paper by van Gelderen and Rummel [Journal of Geodesy (2001) 75: 1–11] show that the presented solution refines the former solution. Received: 3 October 2001 / Accepted: 4 October 2002  相似文献   

14.
 Ten days of GPS data from 1998 were processed to determine how the accuracy of a derived three-dimensional relative position vector between GPS antennas depends on the chord distance (denoted L) between these antennas and on the duration of the GPS observing session (denoted T). It was found that the dependence of accuracy on L is negligibly small when (a) using the `final' GPS satellite orbits disseminated by the International GPS Service, (b) fixing integer ambiguities, (c) estimating appropriate neutral-atmosphere-delay parameters, (d) 26 km ≤ L ≤ 300 km, and (e) 4 h ≤T ≤ 24 h. Under these same conditions, the standard error for the relative position in the north–south dimension (denoted S n and expressed in mm) is adequately approximated by the equation S n =k n /T  0.5 with k n =9.5 ± 2.1 mm · h0.5 and T expressed in hours. Similarly, the standard errors for the relative position in the east–west and in the up-down dimensions are adequately approximated by the equations S e =k e /T  0.5 and S u =k u /T  0.5, respectively, with k e =9.9 ± 3.1 mm · h0.5 and k u =36.5 ± 9.1 mm · h0.5. Received: 5 February 2001 / Accepted: 14 May 2001  相似文献   

15.
 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   

16.
Fast spherical collocation: theory and examples   总被引：2，自引：4，他引：2  
 It has long been known that a spherical harmonic analysis of gridded (and noisy) data on a sphere (with uniform error for a fixed latitude) gives rise to simple systems of equations. This idea has been generalized for the method of least-squares collocation, when using an isotropic covariance function or reproducing kernel. The data only need to be at the same altitude and of the same kind for each latitude. This permits, for example, the combination of gravity data at the surface of the Earth and data at satellite altitude, when the orbit is circular. Suppose that data are associated with the points of a grid with N values in latitude and M values in longitude. The latitudes do not need to be spaced uniformly. Also suppose that it is required to determine the spherical harmonic coefficients to a maximal degree and order K. Then the method will require that we solve K systems of equations each having a symmetric positive definite matrix of only N × N. Results of simulation studies using the method are described. Received: 18 October 2001 / Accepted: 4 October 2002 Correspondence to: F. Sansò  相似文献   

17.
 The weighted Procrustes algorithm is presented as a very effective tool for solving the three-dimensional datum transformation problem. In particular, the weighted Procrustes algorithm does not require any initial datum parameters for linearization or any iteration procedure. As a closed-form algorithm it only requires the values of Cartesian coordinates in both systems of reference. Where there is some prior information about the variance–covariance matrix of the two sets of Cartesian coordinates, also called pseudo-observations, the weighted Procrustes algorithm is able to incorporate such a quality property of the input data by means of a proper choice of weight matrix. Such a choice is based on a properly designed criterion matrix which is discussed in detail. Thanks to the weighted Procrustes algorithm, the problem of incorporating the stochasticity measures of both systems of coordinates involved in the seven parameter datum transformation problem [conformal group ℂ7(3)] which is free of linearization and any iterative procedure can be considered to be solved. Illustrative examples are given. Received: 7 January 2002 / Accepted: 9 September 2002 Correspondence to: E. W. Grafarend  相似文献   

18.
 The results from a global positioning system (GPS) experiment carried out in Brittany, France, in October 1999, aimed at measuring crustal displacements caused by ocean loading and quantifying their effects on GPS-derived tropospheric delay estimates, are presented. The loading effect in the vertical and horizontal position time series is identified, however with significant disagreement in amplitude compared to ocean loading model predictions. It is shown that these amplitude misfits result from spatial tropospheric heterogeneities not accounted for in the data processing. The effect of ocean loading on GPS-derived zenith total delay (ZTD) estimates is investigated and a scaling factor of 4.4 between ZTD and station height for a 10° elevation cut-off angle is found (i.e. a 4.4-cm station height error would map into a 1-cm ZTD error). Consequently, unmodeled ocean loading effects map into significant errors in ZTD estimates and ocean loading modeling must be properly implemented when estimating ZTD parameters from GPS data for meteorological applications. Ocean loading effects must be known with an accuracy of better than 3 cm in order to meet the accuracy requirements of meteorological and climatological applications of GPS-derived precipitable water vapor. Received: 16 July 2001 / Accepted: 25 April 2002 Acknowledgments. The authors are grateful to H.G. Scherneck for fruitful discussions and for his help with the ocean loading calculations. They thank H. Vedel for making the HIRLAM data available; D. Jerett for helpful discussions; and the city of Rostrenen, the Laboratoire d'Océanographie of Concarneau, and the Institut de Protection et de S?reté Nucléaire (BERSSIN) for their support during the GPS measurement campaign. Reviews by C.K. Shum and two anonymous referees significantly improved this paper. This work was carried out in the framework of the MAGIC project (http://www.acri.fr/magic), funded by the European Commission, Environment and Climate Program (EC Contract ENV4-CT98–0745). Correspondence to: E. Calais, Department of Earth and Atmospheric Sciences, Purdue University, West Lafayette, IN 47907-1397, USA. e-mail: ecalais@purdue.edu Tel. : +1-765-496-2915; Fax:+1-765-496-1210  相似文献   

19.
The multiresolution character of collocation   总被引：3，自引：0，他引：3  
 An interesting theoretical connection between the statistical (non-stochastic) collocation principle and the multiresolution/wavelet framework of signal approximation is presented. The rapid developments in multiresolution analysis theory over the past few years have provided very useful (theoretical and practical) tools for approximation and spectral studies of irregularly varying signals, thus opening new possibilities for `non-stationary' gravity field modeling. It is demonstrated that the classic multiresolution formalism according to Mallat's pioneering work lies at the very core of some of the general approximation principles traditionally used in physical geodesy problems. In particular, it is shown that the use of a spatio-statistical (non-probabilistic) minimum mean-square-error criterion for optimal linear estimation of deterministic signals, in conjunction with regularly gridded data, always gives rise to a generalized multiresolution analysis in the Hilbert space L 2(R), under some mild constraints on the spatial covariance function and the power spectrum of the unknown field under consideration. Using the theory and the actual approximation algorithms associated with statistical collocation, a new constructive framework for building generalized multiresolution analyses in L 2(R) is presented, without the need for the usual dyadic restriction that exists in classic wavelet theory. The multiresolution and `non-stationary' aspects of the statistical collocation approximation procedure are also discussed, and finally some conclusions and recommendations for future work are given. Received: 26 January 1999 / Accepted: 16 August 1999  相似文献   

20.
Fast transform from geocentric to geodetic coordinates   总被引：3，自引：0，他引：3  
 A new iterative procedure to transform geocentric rectangular coordinates to geodetic coordinates is derived. The procedure solves a modification of Borkowski's quartic equation by the Newton method from a set of stable starters. The new method runs a little faster than the single application of Bowring's formula, which has been known as the most efficient procedure. The new method is sufficiently precise because the resulting relative error is less than 10−15, and this method is stable in the sense that the iteration converges for all coordinates including the near-geocenter region where Bowring's iterative method diverges and the near-polar axis region where Borkowski's non-iterative method suffers a loss of precision. Received: 13 November 1998 / Accepted: 27 August 1999  相似文献   

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