Numerical realization of a new iteration procedure for the recovery of potential coefficients

  • M. S. Petrovskaya
  • A. N. Vershkov
  • N. K. Pavlis
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 121)


The application of the standard iteration procedure, developed by Pellinen, Rapp and Cruz for recovering the spherical harmonic coefficients \({\bar C_{nm}}\) of the earth’s potential, reveals their «exotic», behavior, as a consequence of the unbounded increment of the ellipsoidal correction terms with increasing the degree n. The new iteratior procedure, proposed by Petrovskaya (1999), is more appropriate for evaluating high degree potential coefficients. In the present paper the efficiency of this procedure is studied numerically for n≤5 358, As the input data, the same surface gravity anomal is used as was applied for constructing EGM9E geopotential model. From the coefficients \({\bar C_{nm}}\) derived by the standard and new iteration procedures the corresponding gravity anomaly degree variances are evaluated. The similar variances are also estimated for \({\bar C_{nm}}\) obtained b) applying Jekeli’s ellipsoidal harmonic approach fog deriving the spherical harmonic potentia: coefficients. It appears that the variance: corresponding to the new iteration procedure are close to the ones derived by Jekeli’s approach, a opposed to the standard iteration procedure. Severa possible applications of the derived solution for \({\bar C_{nm}}\) are discussed.


Gravitational potential coefficients gravimetric boundary value problem solution iteration procedure 


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  1. Jekeli C . (1981). The downward continuation to the earth’s surface of truncated spherical and ellipsoidal harmonic series of the gravity and height anomaly. Dept. Geod. Sci. Ohio State Univ.Rep. 323 Google Scholar
  2. Jekeli, C. (1988). The exact transformation between ellipsoidal and spherical harmonic expansions Manuscripta GeodaeticaVol. 13 No 2, pp. 106–113.Google Scholar
  3. Lemoine FG., SC. Kenyon, JK. Factor, RG. Trimmer, NK. Pavlis, DS. Chinn, CM. Cox, SM. Klosko, SB. Luthcke, MH. Torrence, YM. Wang, RG. Williamson, EC. Pavlis, RH. Rapp, TR. Olson (1998). Geopotential Model EGM96. NASAITP-1998-206861. Goddard Space Flight Center GreenbeltGoogle Scholar
  4. Pellinen, L.P. (1982). Effects of the earth’s ellipticity on solving geodetic boundary value problem. Bollettino di Geodesia Scienze Affini, Vol. 41, No 1, pp. 89–103.Google Scholar
  5. PetrovskaYa, M.S. (1999). Iteration procedure for evaluating high degree potential coefficients from gravity data. In:Proc. of International Association of Geodesy Symposia (IV Hotine-Marussi Symposium on Mathematical Geodesy, Trento, Italy, 1988),in printGoogle Scholar
  6. RaPP, R.H. and J.Y. Cruz (1986). Spherical harmonic expansions of the earth’s gravitational potential to degree 360 using 30′ mean anomalies. Dept. Geod Sci., Ohio State Univ., Rep. 376.Google Scholar
  7. RaPP, R.H. and N.K. Pavlis (1990). The development and analysis of geopotential coefficient models to spherical harmonic degree 360. Journal of Geophysical Research, Vol. 95, B13, pp. 21885–21911CrossRefGoogle Scholar

Copyright information

© SPringer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • M. S. Petrovskaya
    • 1
  • A. N. Vershkov
    • 1
  • N. K. Pavlis
    • 2
  1. 1.Main (Pulkovo) Astronomical Observatory of Russian Academy of SciencesSt. PetersburgRussia
  2. 2.Raytheon STX CorporationGreenbeltUSA

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