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  • Indirect effect  (1)
  • Key words: Direct effect – Helmert condensation – Spherical harmonics – Geoid  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of geodesy 73 (1999), S. 87-93 
    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
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of geodesy 74 (2000), S. 488-496 
    ISSN: 1432-1394
    Keywords: Key words: Direct effect – Helmert condensation – Spherical harmonics – Geoid
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract.  The direct topographical correction is composed of both local effects and long-wavelength contributions. This implies that the classical integral formula for determining the direct effect may have some numerical problems in representing these different signals. On the other hand, a representation by a set of harmonic coefficients of the topography to, say, degree and order 360 will omit significant short-wavelength signals. A new formula is derived by combining the classical formula and a set of spherical harmonics. Finally, the results of this solution are compared with the Moritz topographical correction in a test area.
    Type of Medium: Electronic Resource
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