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  • 1
    Monograph available for loan
    Monograph available for loan
    Observing our changing earth : proceedings of the 2007 IAG General Assembly, Perugia, Italy, July 2-13, 2007 (2009)
    New York [u.a.] : Springer
    Associated volumes
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    Call number: 6/M 08.0391
    In: International Association of Geodesy symposia
    Description / Table of Contents: Contents: Symposium GSS001: Reference Frames.- Symposium GSS002: Gravity Field.- Symposium GSS003: Earth Rotation and Geodynamics.- Symposium GSS004: Positioning and Applications.- Symposium GSS005: The Global Geodetic Observing System (GGOS).
    Type of Medium: Monograph available for loan
    Pages: 710 S. : Ill.
    ISBN: 9783540854258
    Series Statement: International Association of Geodesy symposia 133
    Location: Reading room
    Branch Library: GFZ Library
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  • 2
    Monograph available for loan
    Monograph available for loan
    Geoid determination : theory and methods (2013)
    Berlin [u.a.] : Springer
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    Call number: 6/M 15.0285
    In: Lecture notes in earth system sciences, volume 110
    Description / Table of Contents: Based on the material of the lecture notes in several International Schools for the determination and use of the Geoid, organized by the International Geoid Service of the International Association of Geodesy. the book consolidates, unifies, and streamlines this material in a unique way not covered by the few other books that exist on this subject. More specifically, the book presents (for the first time in a single volume) the theory and methodology of the most common technique used for precise determination of the geoid, including the computation of the marine geoid from satellite altimetry data. These are illustrated by specific examples and actual computations of local geoids. In addition, the book provides the fundamentals of estimating orthometric heights without spirit levelling, by properly combining a geoid with heights from GPS. Besides the geodectic and geophysical uses, this last application has made geoid computation methods very popular in recent years because the entire GPS and GIS user communities are interested in estimating geoid undulations in order to convert GPS heights to physically meaningful orthometric heights (elevations above mean sea level). The overall purpose of the book is, therefore, to provide the user community (academics, graduate students, geophysicists, engineers, oceanographers, GIS and GPS users, researchers) with a self-contained textbook, which will supply them with the complete roadmap of estimating geoid undulations, from the theoretical definitions and formulas to the available numerical methods and their implementation and the test in practice.
    Type of Medium: Monograph available for loan
    Pages: xxi, 734 S. : Ill. graph. Darst.
    ISBN: 9783540746997
    Series Statement: Lecture notes in earth system sciences 110
    Classification:
    Geodesy
    Location: Upper compact magazine
    Branch Library: GFZ Library
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  • 3
    Monograph available for loan
    Monograph available for loan
    Gravity, geoid and geodynamics 2000 : IAG international symposium, Banff, Alberta, Canada, Juli 31 - August 4, 2000 (2002)
    Berlin [u.a.] : Springer
    Associated volumes
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    Call number: 6/M 01.0493
    In: International Association of Geodesy symposia
    Type of Medium: Monograph available for loan
    Pages: XIII, 398 S.
    ISBN: 3540424695
    Series Statement: International Association of Geodesy symposia 123
    Classification:
    A.1.1.
    Location: Reading room
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  • 4
    Electronic Resource
    Electronic Resource
    Gravity field convolutions without windowing and edge effects (1993)
    Springer
    Journal of geodesy 67 (1993), S. 107-118 
    Details
    ISSN: 1432-1394
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract A new set of formulas has been developed for the computation of geoid undulations and terrain corrections by FFT when the input gravity anomalies and heights are mean gridded values. The effects of the analytical and the discrete spectra of kernel functions and that of zero-padding on the computation of geoid undulations and terrain corrections are studied in detail. Numerical examples show that the discrete spectrum is superior to the analytically-defined one. By using the discrete spectrum and 100% zero-padding, the RMS differences are 0.000 m for the FFT geoid undulations and 0.200 to 0.000 mGal for the FFT terrain corrections compared with results obtained by numerical integration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01371374
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  • 5
    Electronic Resource
    Electronic Resource
    Minimization and estimation of geoid undulation errors (1994)
    Springer
    Journal of geodesy 68 (1994), S. 201-219 
    Details
    ISSN: 1432-1394
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract The objective of this paper is to minimize the geoid undulation errors by focusing on the contribution of the global geopotential model and regional gravity anomalies, and to estimate the accuracy of the predicted gravimetric geoid. The geopotential model's contribution is improved by (a) tailoring it using the regional gravity anomalies and (b) introducing a weighting function to the geopotential coefficients. The tailoring and the weighting function reduced the difference (1σ) between the geopotential model and the GPS/levelling-derived geoid undulations in British Columbia by about 55% and more than 10%, respectively. Geoid undulations computed in an area of 40° by 120° by Stokes' integral with different kernel functions are analyzed. The use of the approximated kernels results in about 25 cm (σ) and 190 cm (maximum) geoid errors. As compared with the geoid derived by GPS/levelling, the gravimetric geoid gives relative differences of about 0.3 to 1.4 ppm in flat areas, and 1 to 2.5 ppm in mountainous areas for distances of 30 to 200 km, while the absolute difference (1σ) is about 5 cm and 20 cm, respectively. A optimal Wiener filter is introduced for filtering of the gravity anomaly noise, and the performance is investigated by numerical examples. The internal accuracy of the gravimetric geoid is studied by propagating the errors of the gravity anomalies and the geopotential coefficients into the geoid undulations. Numerical computations indicate that the propagated geoid errors can reasonably reflect the differences between the gravimetric and GPS/levelling-derived geoid undulations in flat areas, such as Alberta, and is over optimistic in the Rocky Mountains of British Columbia.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00808101
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  • 6
    Electronic Resource
    Electronic Resource
    A new, high-resolution geoid for Canada and part of the U.S. by the 1D-FFT method (1995)
    Springer
    Journal of geodesy 69 (1995), S. 92-108 
    Details
    ISSN: 1432-1394
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract A new, high-resolution and high-precision geoid has been computed for the whole of Canada and part of the U.S., ranging from 35°N to about 90°N in latitude and 210°E to 320°E in longitude. The OSU91A geopotential model complete to degree and order 360 was combined with a 5′ × 5′ mean gravity anomaly grid and 1km × 1km topographical information to generate the geoid file. The remove-restore technique was adopted for the computation of terrain effects by Helmert's condensation reduction. The contribution of the local gravity data to the geoid was computed strictly by the 1D-FFT technique, which allows for the evaluation of the discrete spherical Stokes integral without any approximation, parallel by parallel. The indirect effects of up to second order were considered. The internal precision of the geoid, i.e. the contribution of the gravity data and the model coefficients noise, was also evaluated through error propagation by FFT. In a relative sense, these errors seem to agree quite well with the external errors and show clearly the weak areas of the geoid which are mostly due to insufficient gravity data coverage. Comparison of the gravimetric geoid with the GPS/levelling-derived geoidal heights of eight local GPS networks with a total of about 900 stations shows that the absolute agreement with respect to the GPS/levelling datum is generally better than 10 cm RMS and the relative agreement ranges, in most cases, from 4 to 1 ppm over short distances of about 20 to 100km, 1 to 0.5 ppm over distances of about 100 to 200 km, and 0.5 to 0.1 ppm for baselines of 200 to over 1000 km. Other existing geoids, such as UNB90, GEOID90 and GSD91, were also included in the comparison, showing that the new geoid achieves the best agreement with the GPS/levelling data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00819555
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  • 7
    Electronic Resource
    Electronic Resource
    A numerical investigation on height anomaly prediction in mountainous areas (1995)
    Springer
    Journal of geodesy 69 (1995), S. 143-156 
    Details
    ISSN: 1432-1394
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract This paper provides numerical examples for the prediction of height anomalies by the solution of Molodensky's boundary value problem. Computations are done within two areas in the Canadian Rockies. The data used are on a grid with various grid spacings from 100 m to 5 arc-minutes. Numerical results indicate that the Bouguer or the topographicisostatic gravity anomalies should be used in gravity interpolation. It is feasible to predict height anomalies in mountainous areas with an accuracy of 10 cm (1σ) if sufficiently dense data grids are used. After removing the systematic bias, the differences between the geoid undulations converted from height anomalies and those derived from GPS/levelling on 50 benchmarks is 12 cm (1σ) when the grid spacing is 1km, and 50 cm (1σ) when the grid spacing is 5′. It is not necessary, in most cases, to require a grid spacing finer than 1 km, because the height anomaly changes only by 3 cm (1σ) when the grid spacing is increased from 100 m to 1000 m. Numerical results also indicate that, only the first two terms of the Molodensky series have to be evaluated in all but the extreme cases, since the contributions of the higher order terms are negligible compared to the objective accuracy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00815483
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  • 8
    Electronic Resource
    Electronic Resource
    Fourier geoid determination with irregular data (1995)
    Springer
    Journal of geodesy 70 (1995), S. 2-12 
    Details
    ISSN: 1432-1394
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract The fast Fourier transform (FFT) and, recently, the fast Hartley transform (FHT) have been extensively used by geodesists for efficient geoid determination. For this kind of efficiency, data must be given on a regular grid and, consequently, a pre-processing step of interpolation is required when only point measurements are available. This paper presents a way of computing a grid of geoid undulations N without explicitly gridding the data. The method is applicable to all FFT or FHT techniques of geoid or terrain effects determination, and it works with planar as well as spherical formulas. This method can be used not only for, e.g., computing a grid of undulations from irregular gravity anomalies Δg but it also lends itself to other applications, such as the gridding of gravity anomalies and, since the contribution of each data point is computed individually, the update of N- or Δg-grids as soon as new point measurements become available. In the case that there are grid cells which contain no measurements, the results of gravity interpolation or geoid estimation can be drastically improved by incorporating into the procedure a frequency-domain interpolating function. In addition to numerical results obtained using a few simple interpolating functions, the paper presents briefly the mathematical formulas for recovering missing grid values and for transforming values from one grid to another which might be rotated and/or scaled with respect to the first one. The geodetic problems where these techniques may find applications are pointed out throughout the paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00863415
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  • 9
    Electronic Resource
    Electronic Resource
    Evaluation of deflections of the vertical on the sphere and the plane: a comparison of FFT techniques (1997)
    Springer
    Journal of geodesy 71 (1997), S. 461-468 
    Details
    ISSN: 1432-1394
    Keywords: Key words. Fast Fourier transform ; Vertical deflections ; Terrain corrections
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. This paper presents a set of efficient formulas to evaluate the deflections of the vertical on the sphere using gridded data. The Vening-Meinesz formula, the topographic indirect effect on the deflections of the vertical as well as the terrain corrections are expressed as both 2D and 1D convolutions on the sphere, and consequently can be evaluated by the 2D and the 1D fast Fourier transform (FFT). When compared with the results obtained from pointwise integration, the use of the 1D FFT gives identical results, and therefore these results were used as control values in this paper. The use of the spherical 2D FFT improves significantly the computational efficiency with little sacrifice of accuracy (0.6″ rms difference from the 1D FFT results). The planar 2D FFT, which is as efficient as the spherical 2D FFT, gives worse results (1.2″ rms difference from the 1D FFT results) because of the extra approximations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001900050114
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  • 10
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    Vertical datum unification for the International Height Reference System (IHRS) (2017)
    Oxford University Press
    Details
    Publication Date: 2017-01-21
    Description: The International Association of Geodesy released in July 2015 a resolution for the definition and realisation of an International Height Reference System (IHRS). According to this resolution, the IHRS coordinates are potential differences referring to the equipotential surface of the Earth's gravity field realised by the conventional value W0 = 62 636 853.4 m2s−2. A main component of the IHRS realisation is the integration of the existing height systems into the global one; that is existing vertical coordinates should be referred to one and the same reference level realised by the conventional W0. This procedure is known as vertical datum unification and its main result are the vertical datum parameters, that is the potential differences between the local and the global reference levels. In this paper, we rigorously derive the observation equations for the vertical datum unification in terms of potential quantities based on the geodetic boundary value problem (GBVP) approach. Those observation equations are then empirically evaluated for the vertical datum unification of the North American and South American height systems. In the first case, simulations performed in North America provide numerical estimates about the impact of omission errors and direct and indirect effects on the vertical datum parameters. In the second case, a combination of local geopotential numbers, ITRF coordinates, satellite altimetry observations, tide gauge registrations and high-resolution gravity field models is performed to estimate the level differences between the South American height systems and the global level W0. Results show that indirect effects vanish when a satellite-only gravity field model with a degree higher than n ≥ 180 is used for the solution of the GBVP. However, the component derived from satellite-only global gravity models has to be refined with terrestrial gravity data to minimise the omission error and its effect on the vertical datum parameter estimation. The empirical evaluations demonstrate that the vertical datum unification should be based on geodetic stations of highest quality and standardised geodetic data; for example, geometric coordinates should refer to the same ITRF and be given in the same tide system and reference epoch as the geopotential numbers and gravity field model. After a standardisation of the input data used in the unification of the South American height systems and a rigorous error propagation analysis, we demonstrate that the vertical datum parameters can be estimated with accuracy better than ±5 cm in well-surveyed regions and some decimetres (±40 cm) in sparsely surveyed regions. This paper concludes with detailed guidelines for the appropriate data treatment when the integration of a local vertical datum into the IHRS is desired. These guidelines may be applicable in any region of the world.
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Royal Astronomical Society.
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