Skip to main content
Log in

A quadrature formula over the sphere with application to high resolution spherical harmonic analysis

  • Published:
View saved research
Bulletin géodésique Aims and scope Submit manuscript

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

Access this article

Subscribe and save

Springer+
from €37.37 /Month
  • Starting from 10 chapters or articles per month
  • Access and download chapters and articles from more than 300k books and 2,500 journals
  • Cancel anytime
View plans

Buy Now

Price includes VAT (Netherlands)

Instant access to the full article PDF.

References

  • L.B. ALLDREDGE, 1980: “Local functions to represent regional and local fields”. Geophys. 45 (1980), pp. 244–254.

    Article  Google Scholar 

  • J. BALMINO, K. LAMBECK, W.M. KAULA, 1973: “A spherical harmonic analysis of the Earth’s topography”. J. Geophys. Res. 78 (1973), pp. 478–481.

    Article  Google Scholar 

  • R.B. BLACKMAN, J.W. TUCKEY, 1959: “The measurement of power spectra”. Dover Publications Inc., New York, 1959.

    Google Scholar 

  • S. CHAPMAN, J. BARTELS, 1940: “Geomagnetism”. Oxford at the Clarendon Press 1940, Vol. II, pp. 634–637.

    Google Scholar 

  • O.L. COLOMBO, 1981: “Numerical methods for harmonic analysis on the sphere”. Reports of the Dept. of Geodetic Science, The Ohio State University, Report 350.

  • R.E. EDWARDS, 1965: “Functional analysis—theory and applications”. Holt, Rinehar & Winston, New York, 1965.

    Google Scholar 

  • W. FREEDEN, 1978: “An application of a summation formula to numerical computation of integrals over the space”. Bull. Géod. 52 (1978), pp. 165–175.

    Article  Google Scholar 

  • P.F. FOUGERE, 1966: “A defense of the Gram-Schmidt orthogonalization procedure applied to spherical harmonic analysis”. J. Geophys. Res. 67 (1966), pp. 5171–5173.

    Google Scholar 

  • G.E.O. GIACAGLIA, C.A. LUNDQUIST, 1972: “Sampiing functions for geophysics”. Smithsonian Astrophysical Observatory—Special Report 344.

  • G.E.O. GIACAGLIA, 1980: “Transformations of spherical harmonics and applications to geodesy and satellite theory”. Studia Geoph. et Geod. 24 (1980), pp. 1–11.

    Article  Google Scholar 

  • E. GROTEN, 1981: “Local and global gravity field representation”. Rev. Geophys. Space Phys. 19 (1981), pp. 407–414.

    Article  Google Scholar 

  • R.W. HAMMING, 1962: “Numerical methods for scientists and engineers”. McGraw-Hill New York, 1962, pp. 520–522.

    Google Scholar 

  • H. JEFFREYS, B.S. Jeffreys, 1946: “Methods of mathematical physics”. Cambridge University Press Cambridge 1946.

    Google Scholar 

  • W.E. MILNE, 1949: “Numerical Calculus”, Princeton University Press, Princeton, N.J.

    Google Scholar 

  • M.H. PAYNE, 1971: “Truncation effects in geopotential modelling”. Analytical Mechanics Associates, Seabrook Maryland 1971.

    Google Scholar 

  • L.J. RICARDI, M.L. BURROWS, 1972: “A recurrence technique for expanding a function in spherical harmonics”.IEEE Trans. on Computers 21 (1972), pp. 583–585.

    Article  Google Scholar 

  • R.H. RAPP, 1977: “The relationship between mean anomaly block sizes and spherical harmonic representations”: J. Geophys. Res. 82 (1977), pp. 5360–5364.

    Article  Google Scholar 

  • H.E. SCHMIDT, 1981: “Sampling function and finite element method representation of the gravity field”. Rev. Geophys. Space Phys.. 19 (1981), pp. 421–436.

    Article  Google Scholar 

  • D.R. SCHMITZ, J.C. CAIN, 1983: “Geomagnetic spherical harmonic analyses 1. Techniques”. J. Geophys. Res. 88 (1983), pp. 1222–1228.

    Article  Google Scholar 

Download references

Rights and permissions

Reprints and permissions

About this article

Cite this article

A quadrature formula over the sphere with application to high resolution spherical harmonic analysis. Bull. Géodésique 60, 1–14 (1986). https://doi.org/10.1007/BF02519350

Download citation

  • Received:

  • Accepted:

  • Issue date:

  • DOI: https://doi.org/10.1007/BF02519350

Keywords