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1.
 Two iterative vector methods for computing geodetic coordinates (φ, h) from rectangular coordinates (x, y, z) are presented. The methods are conceptually simple, work without modification at any latitude and are easy to program. Geodetic latitude and height can be calculated to acceptable precision in one iteration over the height range from −106 to +109 m. Received: 13 December 2000 / Accepted: 13 July 2001  相似文献   

2.
 A potential-type Molodensky telluroid based upon a minimum-distance mapping is derived. With respect to a reference potential of Somigliana–Pizzetti type which relates to the World Geodetic Datum 2000, it is shown that a point-wise minimum-distance mapping of the topographical surface of the Earth onto the telluroid surface, constrained to the gauge W(P)=u(p), leads to a system of four nonlinear normal equations. These normal equations are solved by a fast Newton–Raphson iteration. Received: 7 February 2000 / Accepted: 23 October 2001  相似文献   

3.
 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   

4.
 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   

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.
 The analytical continuation of the surface gravity anomaly to sea level is a necessary correction in the application of Stokes' formula for geoid estimation. This process is frequently performed by the inversion of Poisson's integral formula for a sphere. Unfortunately, this integral equation corresponds to an improperly posed problem, and the solution is both numerically unstable, unless it is well smoothed, and tedious to compute. A solution that avoids the intermediate step of downward continuation of the gravity anomaly is presented. Instead the effect on the geoid as provided by Stokes' formula is studied directly. The practical solution is partly presented in terms of a truncated Taylor series and partly as a truncated series of spherical harmonics. Some simple numerical estimates show that the solution mostly meets the requests of a 1-cm geoid model, but the truncation error of the far zone must be studied more precisely for high altitudes of the computation point. In addition, it should be emphasized that the derived solution is more computer efficient than the detour by Poisson's integral. Received: 6 February 2002 / Accepted: 18 November 2002 Acknowledgements. Jonas ?gren carried out the numerical calculations and gave some critical and constructive remarks on a draft version of the paper. This support is cordially acknowledged. Also, the thorough work performed by one unknown reviewer is very much appreciated.  相似文献   

7.
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   

8.
 The recovery of a full set of gravity field parameters from satellite gravity gradiometry (SGG) is a huge numerical and computational task. In practice, parallel computing has to be applied to estimate the more than 90 000 harmonic coefficients parameterizing the Earth's gravity field up to a maximum spherical harmonic degree of 300. Three independent solution strategies (preconditioned conjugate gradient method, semi-analytic approach, and distributed non-approximative adjustment), which are based on different concepts, are assessed and compared both theoretically and on the basis of a realistic-as-possible numerical simulation regarding the accuracy of the results, as well as the computational effort. Special concern is given to the correct treatment of the coloured noise characteristics of the gradiometer. The numerical simulations show that the three methods deliver nearly identical results—even in the case of large data gaps in the observation time series. The newly proposed distributed non-approximative adjustment approach, which is the only one of the three methods that solves the inverse problem in a strict sense, also turns out to be a feasible method for practical applications. Received: 17 December 2001 / Accepted: 17 July 2002 Acknowledgments. We would like to thank Prof. W.-D. Schuh, Institute of Theoretical Geodesy, University of Bonn, for providing us with the serial version of the PCGMA algorithm, which forms the basis for the parallel PCGMA package developed at our institute. This study was partially performed in the course of the GOCE project `From E?tv?s to mGal+', funded by the European Space Agency (ESA) under contract No. 14287/00/NL/DC. Correspondence to: R. Pail  相似文献   

9.
GPS vector configuration design for monitoring deformation networks   总被引：1，自引：0，他引：1  
 The performance of geodetic monitoring networks is heavily influenced by the configuration of the measured GPS vectors. As an effective design of the GPS measurements will decrease GPS campaign costs and increase the accuracy and reliability of the entire network, the identification of the preferred GPS vectors for measurement has been highlighted as a core problem in the process of deformation monitoring. An algorithm based on a sensitivity analysis of the network, as dependent upon a postulated velocity field, is suggested for the selection of the optimal GPS vectors. Relevant mathematical and statistical concepts are presented as the basis for an improved method of vector configuration design. A sensitivity analysis of the geodetic geodynamic network in the north of Israel is presented, where the method is examined against two deformation models, the Simple Transform Fault and the Locked Fault. The proposed method is suggested as a means for the improvement of the design of monitoring networks, a common practice worldwide. Received: 30 July 2001 / Accepted: 3 June 2002 Acknowledgments. It is my pleasant duty to thank the Survey of Israel and Dr. E. Ostrovsky for providing the variance–covariance matrix of the G1 network in northern Israel. I would like to thank the reviewers of this paper for their constructive and helpful remarks.  相似文献   

10.
 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   

11.
 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   

12.
 The identification of mean semi-major axes (suitably defined) for satellite orbits to satisfy a variety of requirements for geodesy, geophysics and oceanography, in terms of repeat orbits (with orbital resonances), is investigated. Various options for the definition of semi-major axis, from the viewpoint of satellite dynamics, are described. Simple simulations of the expected resonant changes in inclination are presented, and tools for the analysis of orbit resonances to extract certain lumped harmonic coefficients of the geopotential (e.g. from the very precise CHAMP orbit) are resurrected. Finally, a preliminary example of the 46th-order resonance analysis possible for CHAMP, based on the mean orbital elements produced by GFZ (GeoForschungs Zentrum) for ephemeris prediction, is presented. Received: 10 July 2001 / Accepted: 17 July 2002 Correspondence to: J. Klokočník at Ondřejov Observatory Acknowledgements. We thank Prof. Dr. Ch. Reigber, Dr. P. Schwintzer, Dr. T. Gruber and Dr. R. K?nig from GFZ Potsdam for various consultations and discussions, and for the CHAMP two-line mean elements. This investigation was performed under the aegis of CEDR (Center for Earth's Dynamics Research, Prague-Ondřejov); it has been supported by project LN00A005 (provided by the Ministry of Education of the Czech Republic) and by grant A 3004 of the Grant Agency of the Academy of Sciences of the Czech Republic.  相似文献   

13.
 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   

14.
 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   

15.
 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   

16.
 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   

17.
 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   

18.
 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   

19.
 The latest gravimetric geoid model for Japan, JGEOID2000, was successfully combined with the nationwide net of GPS at benchmarks, yielding a new hybrid geoid model for Japan, GSIGEO2000. The least-squares collocation (LSC) method was applied as an interpolation for fitting JGEOID2000 to the GPS/leveling geoid undulations. The GPS/leveling geoid undulation data were reanalyzed in advance, in terms of three-dimensional positions from GPS and orthometric heights from leveling. The new hybrid geoid model is, therefore, compatible with the new Japanese geodetic reference frame. GSIGEO2000 was evaluated internally and independently and the precision was estimated at 4 cm throughout nearly the whole region. Received: 15 October 2001 / Accepted: 27 March 2002 Acknowledgments. Messrs. Toshio Kunimi and Tadashi Saito at the Third Geodetic Division of the Geographical Survey Institute (GSI) mainly carried out the computations of most of the updated leveled heights. With regard to the reanalysis of GPS data, the discussions with Messrs. Yuki Hatanaka and Shoichi Matsumura of GSI were of great help in building the analysis strategy. Messrs. Kazuyuki Tanaka and Hiromi Shigematsu collaborated in the preparatory stages of GPS data computation. The authors' thanks are extended to these colleagues. Some plots were made by GMT software (Wessel and Smith 1991). Correspondence to: Y. Kuroishi  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   

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