Advertisement

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

  • Willi Freeden
  • Volker Michel
Chapter
  • 847 Downloads
Part of the Lecture Notes in Earth Sciences book series (LNEARTH, volume 90)

Keywords

Discrete Wavelet Transform Scaling Function Multiresolution Analysis Admissibility Condition Regular Surface 
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. 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. 2.
    Freeden, W.: Über eine Klasse von Integralformeln der Mathematischen Geodäsie. Veröff. Geod. Inst. RWTH Aachen, Heft 27, 1979.Google Scholar
  3. 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. 4.
    Freeden, W.: Least Squares Approximation by Linear Combinations of (Multi-) Poles. Dept. Geod. Sci., 344, The Ohio State University, Columbus, 1983Google Scholar
  5. 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. 6.
    Freeden, W.: Multiscale Modelling of Spaceborne Geodata, Teubner-Verlag, Stuttgart Leipzig, 1999.Google Scholar
  7. 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. 8.
    Freeden, W., Glockner, O., Schreiner, M.: Spherical Panel Clustering and Its Numerical Aspects. J. of Geod., 72, (1998), 586–599.Google Scholar
  9. 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. 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. 11.
    Freeden, W., Schneider, F.: An Integrated Wavelet Concept of Physical Geodesy. J. of Geod., 72, (1998), 259–281.Google Scholar
  12. 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. 13.
    Freeden, W., Windheuser, U.: Spherical Wavelet Transform and its Discretization. Adv. Comp. Math., 5, (1996), 51–94.Google Scholar
  14. 14.
    Gabor, D.: Theory of Communications. J. Inst. Elec. Eng. (London), 93, (1946), 429–457.Google Scholar
  15. 15.
    Heil, C.E., Walnut, D.F.: Continuous and Discrete Wavelet Transforms. SIAM Review, 31, (1989), 628–666.Google Scholar
  16. 16.
    Kaiser, G.: A Friendly Guide to Wavelets. Birkhäuser-Verlag, Boston, 1994.Google Scholar
  17. 17.
    Kellogg, O.D.: Foundations of Potential Theory. Frederick Ungar Publishing Company, 1929.Google Scholar
  18. 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. 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. 20.
    Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. W.H. Freeman and Company, New York, 1970.Google Scholar
  21. 21.
    Müller, C.: Spherical Harmonics, Lecture Notes in Mathematics, no. 17, Springer-Verlag, Heidelberg, 1966.Google Scholar
  22. 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. 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

Copyright information

© Springer-Verlag 2000

Authors and Affiliations

  • Willi Freeden
    • 1
  • Volker Michel
    • 1
  1. 1.Laboratory of Technomathematics, Geomathematics GroupUniversity of KaiserslauternKaiserslauternGermany

Personalised recommendations