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  • Helmert condensation  (1)
  • Key words: Direct effect – Helmert reduction – Stokes' formula – Topographic effect  (1)
  • 1
    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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  • 2
    Electronic Resource
    Electronic Resource
    Topographic effects by the Stokes–Helmert method of geoid and quasi-geoid determinations (2000)
    Springer
    Journal of geodesy 74 (2000), S. 255-268 
    Details
    ISSN: 1432-1394
    Keywords: Key words: Direct effect – Helmert reduction – Stokes' formula – Topographic effect
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. The topographic potential and the direct topographic effect on the geoid are presented as surface integrals, and the direct gravity effect is derived as a rigorous surface integral on the unit sphere. By Taylor-expanding the integrals at sea level with respect to topographic elevation (H) the power series of the effects is derived to arbitrary orders. This study is primarily limited to terms of order H 2. The limitations of the various effects in the frequently used planar approximations are demonstrated. In contrast, it is shown that the spherical approximation to power H 2 leads to a combined topographic effect on the geoid (direct plus indirect effect) proportional to H˜2 (where terms of degrees 0 and 1 are missing) of the order of several metres, while the combined topographic effect on the height anomaly vanishes, implying that current frequent efforts to determine the direct effect to this order are not needed. The last result is in total agreement with Bjerhammar's method in physical geodesy. It is shown that the most frequently applied remove–restore technique of topographic masses in the application of Stokes' formula suffers from significant errors both in the terrain correction C (representing the sum of the direct topographic effect on gravity anomaly and the effect of continuing the anomaly to sea level) and in the term t (mainly representing the indirect effect on the geoidal or quasi-geoidal height).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001900050284
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    Paper (German National Licenses)
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