The Anomalous Potential and Its Determination

  • Fernando SansòEmail author
  • Mirko Reguzzoni
  • Riccardo Barzaghi
Part of the Springer Geophysics book series (SPRINGERGEOPHYS)


The knowledge of the normal potential and related ellipsoidal quantities are not enough to properly treat the problem of relating different types of geodetic heights.


  1. Brockmann J.M., Zehentner N., Höck E., Pail R., Loth I., Mayer-Gürr T., Schuh W.-D. (2014). EGM TIM RL05: An independent geoid with centimeter accuracy purely based on the GOCE mission. Geophysical Research Letters, 41(22):8089–8099.CrossRefGoogle Scholar
  2. Förste C., Bruinsma S.L., Abrikosov O., Lemoine J.M., Schaller T., Götze H.J., Ebbing J., Marty J.C., Flechtner F., Balmino G., Biancale R. (2014). EIGEN-6C4: The latest combined global gravity field model including GOCE data up to degree and order 2190 of GFZ Potsdam and GRGS Toulouse. In: 5th GOCE User Workshop, Paris. 25–28 November 2014.
  3. Heck B. (1991). On the linearized Boundary Value Problem of physical geodesy. Report No. 407, Department of Geodetic Science and Survey, The Ohio State University, Columbus.Google Scholar
  4. Heiskanen W.A. and Moritz H. (1967). Physical geodesy. Freeman, San Francisco.CrossRefGoogle Scholar
  5. Kaula W.M. (1966). Tests and combination of satellite determinations of the gravity eld with gravimetry. Journal of Geophysical Research, 71:5303–5314.CrossRefGoogle Scholar
  6. Kaula W.M. (2000). Theory of satellite geodesy. Dover, New York.Google Scholar
  7. Krarup T. (2006). Letters on Molodenskiy’s problem, III. In: Borre K. (Ed.) Mathematical Foundation of Geodesy. Springer Verlag, Berlin, Heidelberg.Google Scholar
  8. MacMillan W.D. (1958). The theory of the potential. In: Theoretical mechanics, Vol 2. Dover Publications, New York.Google Scholar
  9. Marussi A. (1985). Intrinsic geodesy. Springer, Berlin.CrossRefGoogle Scholar
  10. Molodensky M.S., Eremeev V.F., Jurkina M.I. (1962). Methods for study of the external gravitational field and figure of the Earth. Translated from Russian, Israel Program for Scientific Translations, Jerusalem.Google Scholar
  11. Moritz H. (1980). Advanced physical geodesy, 2nd edn. Wichmann, Karlsruhe.Google Scholar
  12. Pavlis N.K., Holmes S.A., Kenyon S.C., Factor J.K. (2012). The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). Journal of Geophysical Research: Solid Earth, 117(B4):B04406.CrossRefGoogle Scholar
  13. Pavlis N.K., Holmes S.A., Kenyon S.C., Factor J.K. (2013). Correction to “The development and evaluation of the Earth Gravitational Model 2008 (EGM2008)”. Journal of Geophysical Research: Solid Earth, 118(5):2633.Google Scholar
  14. Rapp, R.H. (1993). Use of altimeter data in estimating global gravity models. In: Sansò F., Rummel R. (Eds.), Satellite Altimetry in Geodesy and Oceanography, Lecture Notes in Earth Sciences, 50. Springer-Verlag, Berlin, Heidelberg, pp. 374–417.Google Scholar
  15. Sansò F., Sideris M.G. (2013). Geoid determination: Theory and methods. Lecture Notes in Earth System Sciences, Vol. 110. Springer-Verlag, Berlin, Heidelberg.Google Scholar
  16. Sansò F., Venuti G. (2010). The convergence problem of collocation solutions in the framework of the stochastic interpretation. Journal of Geodesy, 85(1):51–63.CrossRefGoogle Scholar
  17. Shako R., Förste C., Abrykosov O., Bruinsma S., Marty J.-C., Lemoine J.-M., Flechtner F., Neumayer K.-H., Dahle C. (2014). EIGEN-6C: A High-Resolution Global Gravity Combination Model Including GOCE Data. In: Flechtner F., Sneeuw N., Schuh W.-D. (Eds.), Observation of the System Earth from Space - CHAMP, GRACE, GOCE and future missions, Advanced Technologies in Earth Sciences. Springer, Berlin, Heidelberg, pp. 155–161.Google Scholar
  18. Stokes G.G. (1849). On the variation of gravity on the surface of the Earth. Transactions of the Cambridge Philosophical Society, 8:672–695.Google Scholar
  19. Tscherning C.C. and Rapp R.H. (1974). Closed covariance expressions for gravity anomalies, geoid undulations, and deections of the vertical implied by anomaly degree variances. Report No. 208, Department of Geodetic Science and Surveying, The Ohio State University, Columbus.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Fernando Sansò
    • 1
    Email author
  • Mirko Reguzzoni
    • 1
  • Riccardo Barzaghi
    • 1
  1. 1.Department of Civil and Environmental Engineering (DICA)Politecnico di MilanoMilanItaly

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