Advertisement

Bulletin Géodésique

, Volume 54, Issue 1, pp 73–79 | Cite as

The geopotential from gravity measurements, levelling data and satellite results

  • W. Bosch
  • K. R. Koch
Article
  • 26 Downloads

Abstract

The geodetic boundary value problem is formulated which uses as boundary values the differences between the geopotential of points at the surface of the continents and the potential of the geoid. These differences are computed by gravity measurements and levelling data. In addition, the shape of the geoid over the oceans is assumed to be known from satellite altimetry and the shape of the continents from satellite results together with three-dimensional triangulation. The boundary value problem thus formulated is equivalent to Dirichlet's exterior problem except for the unknown potential of the geoid. This constant is determined by an integral equation for the normal derivative of the gravitational potential which results from the first derivative of Green's fundamental formula. The general solution, which exists, of the integral equation gives besides the potential of the geoid the solution of the geodetic boundary value problem. In addition approximate solutions for a spherical surface of the earth are derived.

Keywords

Integral Equation Gravity Field Spherical Surface Normal Gravity Satellite Altimetry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. W. BOSCH: Untersuchungen zu schiefachsigen und gemischeten Randwertaufgaben der Geodäsie. Deutsche Geodätische Kommission, Reihe C. Nr., 258, München 1979.Google Scholar
  2. M. HOTINE: Mathematical Geodesy. ESSA Monograph 2, U.S. Department of Commerce, Washington 1969.Google Scholar
  3. K.R. KOCH: Die Berechnung des Störpotentials und seiner Ableitungen aus den Integral-und Integrodifferentialgleichungen der Greenschen Fundamentalformel mit Hilfe schrittweiser Annäherung. Deutsche Geodätische Kommission, Reihe C, Nr. 105, München 1967 a.Google Scholar
  4. K.R. KOCH: Determination of the First Derivatives of the Disturbing Potential by Green's Fundamental Formula. Department of Geodetic Science Rep. No. 90, The Ohio State University, Columbus 1967 b.Google Scholar
  5. K.R. KOCH: Reformulation of the Geodetic Boundary Value Problem in View of the Results of Geometric Satellite Geodesy. In “Advances in Dynamic Gravimetry”, edited by W.T. Kattner, p. 111–114. Instrument Society of America, Pittsburgh 1970.Google Scholar
  6. K.R. KOCH: Die geodätische Randwertaufgabe bei bekannter Erdoberfläche. Zeitschrift für Vermessungswesen, 96, Jg., p. 218–224, 1971.Google Scholar
  7. K.R. KOCH: Parameterschätzung und Hypothesentests in linearen Modellen. Dümmiers Verlag, Bonn 1980.Google Scholar
  8. K.R. KOCH and A.J. POPE: Uniqueness and Existence for the Geodetic Boundary Value Problem Using the Known Surface of the Earth. Bulletin Géodésique, No. 106, p. 467–476, 1972.CrossRefGoogle Scholar
  9. S.G. MICHLIN: Vorlesungen über lineare Integralgleichungen. Verlag der Wissenschaften, Berlin 1962.Google Scholar
  10. C. MIRANDA: Partial Differential Equations of Elliptic Type. Springer-Verlag, Berlin 1970.CrossRefGoogle Scholar
  11. M.S. MOLODENSKII, V.F. EREMEEV and M.I. YURKINA: Methods for Study of the External Gravitational Field and Figure of the Earth. U.S. Department of Commerce, Washington 1962.Google Scholar

Copyright information

© Bureau Central de L’Association Internationale de Géodésie 1980

Authors and Affiliations

  • W. Bosch
    • 1
  • K. R. Koch
    • 1
  1. 1.Institut für Theoretische GeodäsieBonn 1Fed. Rep. of Germany

Personalised recommendations