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  • Isostasy  (1)
  • Key words. Atmospheric correction  (1)
  • Key words: Least squares – Modified Stokes' kernel – Truncated Stokes' formula  (1)
  • Unification  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    The exterior Airy/Heiskanen topographic–isostatic gravity potential, anomaly and the effect of analytical continuation in Stokes' formula (1998)
    Springer
    Journal of geodesy 72 (1998), S. 654-662 
    Details
    ISSN: 1432-1394
    Keywords: Key words. Analytical continuation ; Isostasy ; Stokes' formula
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. This study deals with the external type of topographic–isostatic potential and gravity anomaly and its vertical derivatives, derived from the Airy/Heiskanen model for isostatic compensation. From the first and the second radial derivatives of the gravity anomaly the effect on the geoid is estimated for the downward continuation of gravity to sea level in the application of Stokes' formula. The major and regional effect is shown to be of order H 3 of the topography, and it is estimated to be negligible at sea level and modest for most mountains, but of the order of several metres for the highest and most extended mountain belts. Another, global, effect is of order H but much less significant
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001900050205
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Some modifications of Stokes' formula that account for truncation and potential coefficient errors (2000)
    Springer
    Journal of geodesy 74 (2000), S. 232-238 
    Details
    ISSN: 1432-1394
    Keywords: Key words: Least squares – Modified Stokes' kernel – Truncated Stokes' formula
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract.  Stokes' formula from 1849 is still the basis for the gravimetric determination of the geoid. The modification of the formula, originating with Molodensky, aims at reducing the truncation error outside a spherical cap of integration. This goal is still prevalent among various modifications. In contrast to these approaches, some least-squares types of modification that aim at reducing the truncation error, as well as the error stemming from the potential coefficients, are demonstrated. The least-squares estimators are provided in the two cases that (1) Stokes' kernel is a priori modified (e.g. according to Molodensky's approach) and (2) Stokes' kernel is optimally modified to minimize the global mean square error. Meissl-type modifications are also studied. In addition, the use of a higher than second-degree reference field versus the original (Pizzetti-type) reference field is discussed, and it is concluded that the former choice of reference field implies increased computer labour to achieve the same result as with the original reference field.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001900050281
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  • 3
    Electronic Resource
    Electronic Resource
    Unification of vertical datums by GPS and gravimetric geoid models with application to Fennoscandia (1998)
    Springer
    Journal of geodesy 72 (1998), S. 64-70 
    Details
    ISSN: 1432-1394
    Keywords: Key words. Vertical datums ; Unification ; GPS ; Geoid ; Fennoscandia
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. The second Baltic Sea Level (BSL) GPS campaign was run for one week in June 1993. Data from 35 tide gauge sites and five fiducial stations were analysed, for three fiducial stations (Onsala, Metsähovi and Wettzell) fixed at the ITRF93 system. On a time-scale of 5 days, precision was several parts in 109 for the horizontal and vertical components. Accuracies were about 1 cm in comparison with the International GPS Geodynamical Service (IGS) coordinates in three directions. To connect the Swedish and the Finnish height systems, our numerical application utilises three approaches: a rigorous approach, a bias fit and a three-parameter fit. The results between the Swedish RH70 and the Finnish N 60 systems are estimated to −19.3 ± 6.5, −17 ± 6 and −15 ± 6 cm, respectively, by the three approaches. The results of the three indirect methods are in an agreement with those of a direct approach from levelling and gravity measurements.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001900050149
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  • 4
    Electronic Resource
    Electronic Resource
    The IAG approach to the atmospheric geoid correction in Stokes' formula and a new strategy (1999)
    Springer
    Journal of geodesy 73 (1999), S. 362-366 
    Details
    ISSN: 1432-1394
    Keywords: Key words. Atmospheric correction ; Atmospheric gravity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. The well-known International Association of Geodesy (IAG) approach to the atmospheric geoid correction in connection with Stokes' integral formula leads to a very significant bias, of the order of 3.2 m, if Stokes' integral is truncated to a limited region around the computation point. The derived truncation error can be used to correct old results. For future applications a new strategy is recommended, where the total atmospheric geoid correction is estimated as the sum of the direct and indirect effects. This strategy implies computational gains as it avoids the correction of direct effect for each gravity observation, and it does not suffer from the truncation bias mentioned above. It can also easily be used to add the atmospheric correction to old geoid estimates, where this correction was omitted. In contrast to the terrain correction, it is shown that the atmospheric geoid correction is mainly of order H of terrain elevation, while the term of order H 2 is within a few millimetres.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001900050254
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