A Study on Two-boundary Problems in Airborne Gravimetry and Satellite Gradiometry

  • P. Holota
  • M. Kern
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 129)


Current gravity data, which are used for refined studies of the Earth’s gravity field, result from cutting-edge technologies and advanced measuring techniques. They often refer to some exceptional surfaces or manifolds and can lead to interesting mathematical problems. In this paper, three cases are considered where airborne gravimetry is combined with terrestrial gravity data, airborne measurements are collected at two flight levels, and satellite gradiometry is combined with terrestrial gravity data. The three cases are studied mathematically and the disturbing potential is expressed explicitly. The spectral representation based on spherical harmonics is used. Subsequently, an optimum procedure is discussed in order to treat the overdetermined problems and to keep the typical regularity of harmonic functions at infinity. Some practical aspects are also mentioned.


Earth’s gravity field geodetic boundary-value problems overdetermined problems optimization 


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  1. Grafarend E and Sansò F (1984) The multibody space-time geodetic boundary value problem and the Honkasalo term. Geophys. J.R. astr. Soc. 255–275Google Scholar
  2. Holota P (1995) Boundary and Initial Value Problems in Airborne Gravimetry. In: Proc. IAG Symp. on Airborne Gravity Field Determination, IUGG XXI Gen. Assembly, Boulder, CO, USA, Jul 2–14, 1995, (Conv.: Schwarz K-P, Brozena JM, Hein GW). Special rep. No. 60010, Dept. of Geomatics Eng., The Univ. of Calgary, Calgary, 67–71Google Scholar
  3. Holota P (2004) Some topics related to the solution of boundary-value problems in geodesy. Intl. Assoc. of Geodesy Symposia, Vol. 127, Springer, Berlin etc., 189–200Google Scholar
  4. Kellogg OD (1953) Foundations of potential theory. Dover Publications, Inc., New YorkGoogle Scholar
  5. Necas J and HIavacek I (1981) Mathematical theory of elastic and elasto-plastic bodies: An introduction. Elsevier Sci. Publ. Company, Amsterdam-Oxford-New YorkGoogle Scholar
  6. Rektorys K (1977) Variational methods. Reidel Co., Dordrecht-BostonGoogle Scholar
  7. Rummel R, Teunissen P and Van Gelderen M (1989) Uniquely and over-determined geodetic boundary value problem by least squares. Bull. Géodésique, Vol. 63, 1–33Google Scholar
  8. Sacerdote F and Sansò F (1985) Overdetermined boundary value problems in physical geodesy. Manuscripta Geodaetica, Vol. 10, No. 3, 195–207Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • P. Holota
    • 1
  • M. Kern
    • 2
  1. 1.Topography and CartographyResearch Institute of GeodesyZdiby 98, Praha-vychodCzech Republic
  2. 2.Institute of Navigation and Satellite GeodesyGraz University of TechnologyGrazAustria

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