Satellite Gradiometry — A New Approach

  • Willi Freeden
  • Michael Schreiner
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 114)


The determination of the gravitational field of the earth by satellite gradiometry has been investigated in many publications (cf. e.g. (Rummel, 1986; Rummel et al., 1993) and the literature cited therein). These contributions mostly deal with the gravitational field as finite series in terms of spherical harmonics and assume that the data are given in discrete points. In this paper, we study two different aspects of satellite gradiometry. At first, we consider the data to be given as continuous function on a surface in the harmonicity domain of the potential. This enables us to classify which types of data guarantee the uniqueness of the solution. Needless to say that those investigations turn also out to be of importance for the discrete problem. Then we propose a method for the determination of the gravitational field by use of locally supported trial functions in satellite gradiometry. We expect that such methods will significantly improve the knowledge of the microstructure of the earth’s gravitational field in the future.


Vector Field Gravitational Field Spline Interpolation Trial Function Tensor Field 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Backus, G.E. (1966). Potentials for Tangent Tensor Fields on Spheroids, Arch. Rational Mech. Anal 22, 210–252Google Scholar
  2. Backus, G.E. (1967). Converting Vector and Tensor Equations to Scalar Equations in Spherical Coordinates, Geophys. J.R. Astr. Soc. 13, 71–101CrossRefGoogle Scholar
  3. Freeden, W. (1978). Eine Klasse von Integralformeln der Mathematischen Geodäsie, Veröff. Geod. Inst. RWTH Aachen 27 Google Scholar
  4. Freeden, W. (1981). On Spherical Spline Interpolation and Approximation, Math. Meth. in the Appl. Sci. 3, 551–575CrossRefGoogle Scholar
  5. Freeden, W. (1990). Spherical Spline Approximation and its Application in Physical Geodesy, Geophysical Data Inversion Methods and Applications, A. Vogel et al. (eds), Vieweg, Braunschweig, 79–104CrossRefGoogle Scholar
  6. Freeden, W., Gervens, T., Schreiner, M. (1994). Tensor Spherical Harmonics and Tensor Spherical Splines, Manuscr. Geod. 19, 70–100Google Scholar
  7. Freeden, W. and Schreiner, M. (1993). Nonorthogonal Expansions on the Sphere, AGTM- Report 97, University of Kaiserslautern, Geomathematics Group, accepted for publication in Math. Meth. in the Appl. Sci.Google Scholar
  8. Rummel, R. (1986). Satellite Gradiometry, Mathematical and Numerical Techniques in Physical Geodesy, Lecture Notes in Earth Sciences 7, H. Sünkel (ed.), Springer, Berlin, 318–363Google Scholar
  9. Rummel, R., van Gelderen, M., Koop, R., Schrama, E., Sansò, F., Brovelli, M., Miggliaccio, F., Sacerdote, F. (1993). Spherical Harmonic Analysis of Satellite Gradiometry, Publications on Geodesy, New Series 39, DelftGoogle Scholar
  10. Schreiner, M. (1994). Tensor Spherical Harmonics and Their Application in Satellite Gradiometry, PhD-Thesis, University of Kaiserslautern, Geomathematics Group, KaiserslauternGoogle Scholar
  11. Spivak, M. (1975). A Comprehensive Introduction to Differential Geometry, Vols. I–III, Publish or Perish, BostonGoogle Scholar
  12. Svensson, S.L. (1983). Pseudodifferential Operators — a New Approach to the Boundary Value Problems of Physical Geodesy, Manuscr. Geod. 8, 1–40Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Willi Freeden
    • 1
  • Michael Schreiner
    • 1
  1. 1.Laboratory of Technomathematics, Geomathematics GroupUniversity of KaiserslauternKaiserslauternGermany

Personalised recommendations