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  • 1
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    Accuracy of the determination of mean anomalies and mean geoid undulations from a satellite gravity field mapping mission (1980)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: Improved knowledge of the Earth's gravity field was obtained from new and improved satellite measurements such as satellite to satellite tracking and gradiometry. This improvement was examined by estimating the accuracy of the determination of mean anomalies and mean undulations in various size blocks based on an assumed mission. In this report the accuracy is considered through a commission error due to measurement noise propagation and a truncation error due to unobservable higher degree terms in the geopotential. To do this the spectrum of the measurement was related to the spectrum of the disturbing potential of the Earth's gravity field. Equations were derived for a low-low (radial or horizontal separation) mission and a gradiometer mission. For a low-low mission of six month's duration, at an altitude of 160 km, with a data noise of plus or minus 1 micrometers sec for a four second integration time, we would expect to determine 1 deg x 1 deg mean anomalies to an accuracy of plus or minus 2.3 mgals and 1 deg x 1 deg mean geoid undulations to plus or minus 4.3 cm. A very fast Fortran program is available to study various mission configurations and block sizes.
    Keywords: GEOPHYSICS
    Type: REPT-307
    Format: application/pdf
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  • 2
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    A comparison of altimeter and gravimetric geoids in the Tonga Trench and Indian Ocean areas (1980)
    In:  Other Sources
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    Publication Date: 2019-06-27
    Description: Geoids computed from GEOS-3 altimeter data are compared with gravimetric geoids computed by various techniques for 30 x 30 deg areas in the Tonga Trench and the Indian Ocean. The gravimetric geoids were calculated using the standard Stokes integration with the Molodenskii truncation procedure, the modified Stokes integration suggested by Ostach (1970) and Meissl (1971) with modified Molodenskii truncation functions, and three sets of potential coefficients including one complete to degree 180. It is found that the modified Stokes procedure with a cap size of 10 deg provides better results when used with a combined altimeter terrestrial anomaly field data set. Excellent agreement at the plus or minus 1 m level is obtained between the altimeter and gravimetric geoid using the combined data set, with the modified Stokes procedure having a greater accuracy. Coefficients derived from the 180 x 180 solution are found to be of an accuracy comparable to that of the modified Stokes method, however to require six times less computational effort.
    Keywords: GEOPHYSICS
    Type: Bulletin Geodesique; 54; 2, 19; 1980
    Format: text
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  • 3
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    Ellipsoidal corrections for geoid undulation computations using gravity anomalies in a cap (1981)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: Ellipsoidal correction terms have been derived for geoid undulation computations when the Stokes equation using gravity anomalies in a cap is combined with potential coefficient information. The correction terms are long wavelength and depend on the cap size in which its gravity anomalies are given. Using the regular Stokes equation, the maximum correction for a cap size of 20 deg is -33 cm, which reduces to -27 cm when the Stokes function is modified by subtracting the value of the Stokes function at the cap radius. Ellipsoidal correction terms were also derived for the well-known Marsh/Chang geoids. When no gravity was used, the correction could reach 101 cm, while for a cap size of 20 deg the maximum correction was -45 cm. Global correction maps are given for a number of different cases. For work requiring accurate geoid computations these correction terms should be applied.
    Keywords: GEOPHYSICS
    Type: Journal of Geophysical Research; 86; Nov. 10
    Format: text
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  • 4
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    Ellipsoidal corrections for geoid undulation computations (1981)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: The computation of accurate geoid undulations is usually done combining potential coefficient information and terrestrial gravity data in a cap surrounding the computation point. In doing this a spherical approximation is made that can cause the errors that were investigated. The equations dealing with ellipsoidal corrections developed by Lelgemann and by Moritz were used to develop a computational procedure considering the ellipsoid as a reference surface. Terms in the resulting expression for the geoid undulation are identified as ellipsoidal correction terms. These equations were developed for the case where the Stokes function is used, and for the case where the modified Stokes function is used. For a cap of 20 deg the correction can reach -33 cm.
    Keywords: GEOPHYSICS
    Type: NASA-CR-164440 , REPT-308
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  • 5
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    A comparison of satellite Doppler and gravimetric geoid undulations considering terrain-corrected gravity data (1984)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: Geoid undulations derived from Doppler satellite positioning are compared with corresponding values derived from terrestrial and satellite information using three different procedures. Doppler undulations are compared with uncorrected gravimetric undulations, and systematic differences of 1.6 m and 0.4 m are found for western and eastern U.S. stations, respectively. The systematic difference of 1.6 m was reduced to 0.1 m when terrain-related corrections were applied. Undulations computed from a spherical harmonic expansion to degree 180 yielded standard deviations only slightly poorer than the combined data. A more systematic difference in the western than in the eastern stations remained.
    Keywords: GEOPHYSICS
    Type: Journal of Geophysical Research (ISSN 0148-0227); 89; 1105-111
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  • 6
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    The precise computation of geoid undulation differences with comparison to results obtained from the global positioning system (1984)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: Ellipsoidal height differences have been determined for 13 station pairs in the central Ohio region using measurements made with the Global Positioning System. This information was used to compute geoid undulation differences based on known orthometric heights. These differences were compared to gravimetrically-computed undulations (using a Stokes integration procedure, and least squares collocation having an internal r.m.s. agreement of plus or minus 1 cm in undulation differences). The two sets of undulation differences have an r.m.s. discrepancy of plus or minus 5 cm while the average station separation is of the order of 14 km. This good agreement suggests that gravimetric data can be used to compute accurate geoid undulation differences that can be used to convert ellipsoidal height differences obtained from GPS to orthometric height differences.
    Keywords: GEOPHYSICS
    Type: Geophysical Research Letters (ISSN 0094-8276); 11; 821-824
    Format: text
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  • 7
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    Degree variances of the earth's potential, topography and its isostatic compensation (1982)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: A spherical harmonic expansion of the earth's gravitational potential and equivalent rock topography to degree and order 180 is described. The potential implied by the topography considered as uncompensated and with isostatic compensation has been computed. Good agreement with the observed potential field is found when the depth of compensation in the Airy theory is assumed to be 50 km. At the higher degrees the correlation coefficient between the potential expansion and the equivalent rock topography is about 0.5. The Lachapelle equations for the topographic isostatic potential were tested using 1 x 1 deg equivalent rock topography. The degree variances agree at the lower degrees but at degree 36 the Lachapelle results using 5 deg data underestimate the potential degree variances by about one-third.
    Keywords: GEOPHYSICS
    Type: Bulletin Geodesique; 56; 2, 19; 1982
    Format: text
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