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  • 1
    Electronic Resource
    Electronic Resource
    Terrain corrections to power 3 in gravimetric geoid determination (1998)
    Springer
    Journal of geodesy 72 (1998), S. 124-135 
    Details
    ISSN: 1432-1394
    Keywords: Key words. Geoid ; Terrain correction ; Remove-restore ; Stokes' formula
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. In precise geoid determination by Stokes formula, direct and primary and secondary indirect terrain effects are applied for removing and restoring the terrain masses. We use Helmert's second condensation method to derive the sum of these effects, together called the total terrain effect for geoid. We develop the total terrain effect to third power of elevation H in the original Stokes formula, Earth gravity model and modified Stokes formula. It is shown that the original Stokes formula, Earth gravity model and modified Stokes formula all theoretically experience different total terrain effects. Numerical results indicate that the total terrain effect is very significant for moderate topographies and mountainous regions. Absolute global mean values of 5–10 cm can be reached for harmonic expansions of the terrain to degree and order 360. In another experiment, we conclude that the most important part of the total terrain effect is the contribution from the second power of H, while the contribution from the third power term is within 9 cm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001900050154
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  • 2
    Electronic Resource
    Electronic Resource
    On the indirect effect in the Stokes–Helmert method of geoid determination (1999)
    Springer
    Journal of geodesy 73 (1999), S. 87-93 
    Details
    ISSN: 1432-1394
    Keywords: Key words. Geoid ; Helmert condensation ; Indirect effect ; Remove ; restore
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. The classical integral formula for determining the indirect effect in connection with the Stokes–Helmert method is related to a planar approximation of the sea level. A strict integral formula, as well as some approximations to it, are derived. It is concluded that the cap- size truncated integral formulas will suffer from the omission of some long-wavelength contributions, of the order of 50 cm in high mountains for the classical formula. This long-wavelength information can be represented by a set of spherical harmonic coefficients of the topography to, say, degree and order 360. Hence, for practical use, a combination of the classical formula and a set of spherical harmonics is recommended.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001900050222
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    Paper (German National Licenses)
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