Explicit formula for the geoid-quasigeoid separation

Studia Geophysica et Geodaetica

Volumn 50, Issue 4, 2006, Pages 607-618

  Tenzer, Robert ^a,e   Novak P ^b   Moore, P ^a   Kuhn, M ^c   Vanicek P ^d  

^a NEWCASTLE UNIVERSITY   (United Kingdom)

^b RESEARCH INSTITUTE OF GEODESY   (Czech Republic)

^c CURTIN UNIVERSITY   (Australia)

^d UNIVERSITY OF NEW BRUNSWICK   (Canada)

^e DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Geoid; Height; Mean gravity; Telluroid

Indexed keywords

GEOID; GRAVITY ANOMALY; GRAVITY FIELD; NUMERICAL METHOD; STOKES FORMULA;

EID: 33751011872     PISSN: 00393169     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11200-006-0038-4     Document Type: Article

References (27)

1. Bjerhammar A., 1962. Gravity Reductions to a Spherical Surface. Royal Institute of Technology, Division of Geodesy, Stockholm, Sweden.
2. Bruns H., 1878. Die Figur der Erde. Publ. Preuss. Geod. Inst., Berlin, Germany.
3. Hageman L. and Young D., 1981. Applied Iterative Methods. Academic Press, New York, USA.
4. Helmert F.R., 1890. Die Schwerkraft im Hochgebirge, insbesondere in den Tyroler Alpen. Veröff. Königl. Preuss. Geod. Inst., No. 1., Berlin.
5. Heiskanen W.H. and Moritz H., 1967. Physical Geodesy. W.H. Freeman and Co., San Francisco, USA.
6. Hobson E.W., 1931. The Theory of Spherical and Ellipsoidal Harmonics. Cambridge University Press, Cambridge, U.K.
7. Holota P., 1997. Variational methods for geodetic boundary-value problems. In: F. Sansò and R. Rummel (Eds.), Geodetic Boundary Value Problems in View of the One Centimetre Geoid. Lecture Notes in Earth Sciences, 65. Springer Verlag, Berlin, Heidelberg, New York, 468-481.
8. Hörmander L., 1976. The boundary problems of physical geodesy. Arch. Ration. Mech. Anal., 62, 1-52.
9. Kingdon R., Vaníček P., Santos M., Ellmann A. and Tenzer R., 2005. Toward an improved height system for Canada. Geomatica, 59/3, 241-250.
10. Martinec Z., 1996. Stability investigations of a discrete downward continuation problem for geoid determination in the Canadian Rocky Mountains. J. Geodesy, 70, 805-828.
11. Molodensky M.S., 1945. Fundamental problems of geodetic gravimetry. TRUDY Ts NIIGAIK, 42, Geodezizdat, Moscow, Russia (in Russian).
12. Molodensky M.S., 1948. External gravity field and the shape of the Earth surface. Izv. AN SSR Geol., 12, 193 (in Russian).
13. Molodensky M.S., Yeremeev V.F. and Yurkina M.I, 1960. Methods for Study of the External Gravitational Field and Figure of the Earth. TRUDY Ts NIIGAiK, 131, Geodezizdat, Moscow (English translat.: Israel Program for Scientific Translation, Jerusalem 1962).
14. Novák P., Kern M., Schwarz K.P. and Heck B., 2001. The Determination of the Geoid from Airborne Gravity Data. UCGE Report 30013, University of Calgary, Calgary, Canada.
15. Pick M., Pícha J. and Vyskočil V., 1973. Theory of the Earth's Gravity Field. Elsevier, Amsterdam, The Netherlands.
16. Pizzetti P., 1911. Sopra il calcolo teorico delle deviazioni del geoide dall' ellissoide. Atti R. Accad. Sci., V.46, Torino, Italy.
17. Sjöberg L.E., 1995. On the quasigeoid to geoid separation. Manuscripta Geodaetica, 20(3), 182-192.
18. Stokes G.G., 1849. On the variation of gravity on the surface of the Earth. Transactions of the Cambridge Philosophical Society, No.8.
19. Sun W. Vaníček P. 1998 On some problems of the downward continuation of the 5′ × 5′ mean Helmert gravity disturbance. J. Geodesy, 72, 411-420.
20. Tenzer R., 2004. Discussion of mean gravity along the plumbline. Stud. Geophys. Geod, 48, 309-330.
21. Tenzer R. Vaníček P., Santos M., Featherstone W.E. and Kuhn M., 2005. The rigorous determination of orthometric heights. J. Geodesy, 79, 82-92.
22. Vaníček P. and Sjöberg L.E., 1991. Reformulation of Stokes' theory for higher than second-degree reference field and modification of integration kernels. J. Geophys. Res., 96(B4), 6529-6540.
23. Vaníček P., Sun W., Ong P., Martinec Z., Najafi M., Vajda P. and Horst B., 1996. Downward continuation of Helmert's gravity. J. Geodesy, 71, 21-34.
24. Vaníček P., Tenzer R., Sjöberg L.E., Martinec Z. and Featherstone E.W., 2004. New views of the spherical Bouguer gravity anomaly. Geophys. J. Int., 159, 460-472.
25. Varga D., 1962. Matrix Iterative Analysis. Prentice-Hall, Englewood Cliffs, NJ, USA.
26. Vening Meinesz F.A, 1928. A formula expressing the deflection of the plumb-line in the gravity anomalies and some formulae for the gravity field and the gravity potential outside the geoid. Proc. Koninkl. Ned. Akad., 31(3), 315-331.
27. Young D., 1972. Iterative Solutions of Large Linear Systems. Academic Press, New York, USA.