Skip to main content
SpringerLink
Log in

Least-squares geopotential approximation by windowed fourier transform and wavelet transform

  • Chapter
  • First Online:
Wavelets in the Geosciences

Part of the book series: Lecture Notes in Earth Sciences ((LNEARTH,volume 90))

  • 866 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Driscoll J.R., Healy D.M.: Computing Fourier Transforms and Convolutions on the 2-Sphere. Adv. Appl. Math., 15, (1996), 202–250.

    Google Scholar 

  2. Freeden, W.: Über eine Klasse von Integralformeln der Mathematischen Geodäsie. Veröff. Geod. Inst. RWTH Aachen, Heft 27, 1979.

    Google Scholar 

  3. Freeden, W.: On the Approximation of External Gravitational Potential With Closed Systems of (Trial) Functions., Bull. Geod., 54, (1980), 1–20.

    Google Scholar 

  4. Freeden, W.: Least Squares Approximation by Linear Combinations of (Multi-) Poles. Dept. Geod. Sci., 344, The Ohio State University, Columbus, 1983

    Google Scholar 

  5. Freeden, W.: A Spline Interpolation Method for Solving Boundary-value Problems of Potential Theory from Discretely Given Data. Numer. Meth. Part. Diff. Eqs., 3, (1987), 375–398.

    Google Scholar 

  6. Freeden, W.: Multiscale Modelling of Spaceborne Geodata, Teubner-Verlag, Stuttgart Leipzig, 1999.

    Google Scholar 

  7. Freeden, W., Gervens, T., Schreiner, M.: Constructive Approximation on the Sphere (with Applications to Geomathematics), Oxford Science Publications, Clarendon Press, Oxford, 1998.

    Google Scholar 

  8. Freeden, W., Glockner, O., Schreiner, M.: Spherical Panel Clustering and Its Numerical Aspects. J. of Geod., 72, (1998), 586–599.

    Google Scholar 

  9. Freeden, W., Kersten, H.: A Constructive Approximation Theorem for the Oblique Derivative Problem in Potential Theory. Math. Meth. in the Appl. Sci., 3, (1981), 104–114.

    Google Scholar 

  10. Freeden, W., Michel, V.: Constructive Approximation and Numerical Methods in Geodetic Research Today — An Attempt at a Categorization Based on an Uncertainty Principle., J. of Geod. (accepted for publication).

    Google Scholar 

  11. Freeden, W., Schneider, F.: An Integrated Wavelet Concept of Physical Geodesy. J. of Geod., 72, (1998), 259–281.

    Google Scholar 

  12. Freeden, W., Schneider, F.: Wavelet Approximation on Closed Surfaces and Their Application to Bounday-value Problems of Potential Theory. Math. Meth. Appl. Sci., 21, (1998), 129–165.

    Google Scholar 

  13. Freeden, W., Windheuser, U.: Spherical Wavelet Transform and its Discretization. Adv. Comp. Math., 5, (1996), 51–94.

    Google Scholar 

  14. Gabor, D.: Theory of Communications. J. Inst. Elec. Eng. (London), 93, (1946), 429–457.

    Google Scholar 

  15. Heil, C.E., Walnut, D.F.: Continuous and Discrete Wavelet Transforms. SIAM Review, 31, (1989), 628–666.

    Google Scholar 

  16. Kaiser, G.: A Friendly Guide to Wavelets. Birkhäuser-Verlag, Boston, 1994.

    Google Scholar 

  17. Kellogg, O.D.: Foundations of Potential Theory. Frederick Ungar Publishing Company, 1929.

    Google Scholar 

  18. Lemoine, F.G., Smith, D.E., Kunz, L., Smith, R., Pavlis, E.C., Pavlis, N.K., Klosko, S.M., Chinn, D.S., Torrence, M.H., Williamson, R.G., Cox, C.M., Rachlin, K.E., Wang, Y.M., Kenyon, S.C., Salman, R., Trimmer, R., Rapp, R.H., Nerem, R.S.: The Development of the NASA, GSFC, and NIMA Joint Geopotential Model. International Symposium on Gravity, Geoid, and Marine Geodesy, The University of Tokyo, Japan, Springer, IAG Symposia, 117, 1996, 461–469.

    Google Scholar 

  19. Michel, V.: A Multiscale Method for the Gravimetry Problem — Theoretical and Numerical Aspects of Harmonic and Anharmonic Modelling, PhD University of Kaiserslautern, Geomathematics Group, Shaker-Verlag, Aachen, 1999.

    Google Scholar 

  20. Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. W.H. Freeman and Company, New York, 1970.

    Google Scholar 

  21. Müller, C.: Spherical Harmonics, Lecture Notes in Mathematics, no. 17, Springer-Verlag, Heidelberg, 1966.

    Google Scholar 

  22. Rapp, R.H., Wang, M., Pavlis, N.: The Ohio State 1991 Geopotential and Sea Surface Topography Harmonic Coefficient Model. Dept. Geod. Sci., 410, The Ohio State University, Columbus, 1991.

    Google Scholar 

  23. Schwintzer, P., Reigber, C., Bode, A., Kang, Z., Zhu, S.Y., Massmann, F.H., Raimondo, J.C., Biancale, R., Balmino, G., Lemoine, J.M., Moynot, B., Marty, J.C., Barlier, F., Boudon, Y.: Long Wavelength Global Gravity Field Models: GRIM4-S4, GRIM4-C4. J. of Geod., 71, (1997), 189–208.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Technomathematics, Geomathematics Group, University of Kaiserslautern, P.O. Box 3049, 67653, Kaiserslautern, Germany

    Willi Freeden & Volker Michel

Authors
  1. Willi Freeden
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Volker Michel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Roland Klees Roger Haagmans

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag

About this chapter

Cite this chapter

Freeden, W., Michel, V. (2000). Least-squares geopotential approximation by windowed fourier transform and wavelet transform. In: Klees, R., Haagmans, R. (eds) Wavelets in the Geosciences. Lecture Notes in Earth Sciences, vol 90. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0011097

Download citation

  • DOI: https://doi.org/10.1007/BFb0011097

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66951-7

  • Online ISBN: 978-3-540-46590-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation