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Abstrakty
If the gravitational potential or the disturbing potential of the Earth be downward continued by harmonic continuation inside the Earth’s topography, it will be biased, the bias being the difference between the downward continued fictitious, harmonic potential and the real potential inside the masses. We use initial value problem techniques to solve for the bias. First, the solution is derived for a constant topographic density, in which case the bias can be expressed by a very simple formula related with the topographic height above the computation point. Second, for an arbitrary density distribution the bias becomes an integral along the vertical from the computation point to the Earth’s surface. No topographic masses, except those along the vertical through the computation point, affect the bias. (To be exact, only the direct and indirect effects of an arbitrarily small but finite volume of mass around the surface point along the radius must be considered.) This implies that the frequently computed terrain effect is not needed (except, possibly, for an arbitrarily small innerzone around the computation point) for computing the geoid by the method of analytical continuation.
Słowa kluczowe
Rocznik
Tom
Strony
75--84
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
autor
- Royal Institute of Technology, Division of Geodesy, SE-100 44 Stockholm, Sweden
Bibliografia
- Ågren J. (2004) Regional geoid determination methods for the era of satellite gravimetry, Doctoral dissertation in Geodesy, Royal Institute of Technology, TRITA-INFRA 04-033, Stockholm. www.infra.kth.se/geo/).
- Bjerhammar A. (1962) Gravity reduction to a spherical surface. Royal Institute of Technology, Division of Geodesy, Stockholm.
- Bjerhammar A (1974) Discrete approaches to the solution of the boundary value problem of physical geodesy. Paper presented at the International School of Geodesy, Erice, Italy.
- Cook A. H. (1967) The determination of the external gravity field of the Earth from observation of artificial satellites. Geophysical Journal of Royal Astronomy Society, Vol. 13.
- Heiskanen W.A. and H. Moritz (1967). Physical geodesy. W H Freeman and Co., San Francisco and London.
- Holota P. (1994) Two branches of the Newton potential and geoid. In H Suenkel and I Marson (eds.): Gravity and Geoid. IAG Symposia No. 113, Graz, Springer, 205-214.
- Holota P. (1996) Geoid, Cauchy’s problem and displacement. In J Segawa, H Fujimoto and S Okubo (eds.): Gravity, Geoid and Marin Geodesy. IAG Symposia No. 117, Tokyo, Springer, 368-375.
- Kellog O.D.(1953) Foundations of potential theory, Dover Publ., Inc., New York.
- Krarup T. (1969) A contribution to the mathematical foundation of physical geodesy. Geodaetisk Institut, Meddelelse no. 48, Copenhagen.
- Landkof N.S. (1972) Foundations of modern potential theory, Springer, Berlin, Heidelberg, New York.
- Moritz H. (1980) Advanced physical geodesy. Herbert Wichmann Verlag, Karlsruhe.
- Rapp R.H. (1997) Use of potential coefficient models for geoid undulation determinations using a spherical harmonic representation of the height anomaly/geoid undulation difference, Journal of Geodesy, Vol. 71, 282-289.
- Sjöberg L. E. (1977) On the errors of spherical harmonic developments of gravity at the surface of the earth, Depth Geod Sci Rep No. 257, The OSU, Columbus, OH.
- Sjöberg L.E. (2003a) A solution to the downward continuation effect on the geoid determined by Stokes’s formula, Journal of Geodesy, Vol. 77, 94-100.
- Sjöberg L.E. (2003b) A computational scheme to model the geoid by the modified Stokes’s formula without gravity reductions, Journal of Geodesy, Vol. 77, 423-432.
- Sjöberg L.E. (2007) The topographic bias by analytical continuation in physical geodesy, Journal of Geodesy, Vol. 81, 345-350.
- Sjöberg L. E.(2008) Answers to the comments by M. Vermeer on L.E. Sjöberg (2007) ”The topographic bias by analytical continuation in physical geodesy” J Geod 81:345-350, Journal of Geodesy, Vol. 82, 451-452.
- Sjöberg L.E. (2009a) The terrain correction in gravimetric geoid computation - is it needed? Geophysical Journal International, Vol. 176, 14-18.
- Sjöberg L.E. (2009b) On the topographic bias in geoid determination by the external gravity field, Journal of Geodesy, Vol. 83, 967-972.
- Vermeer M. (2008) Comment on Sjöberg (2007 ) ”The topographic bias by analytical continuation in physical geodesy ”J Geod 81(5),345-350, Journal of Geodesy, Vol. 82, 445-450.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
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