On Helmert's methods of condensation

Journal of Geodesy

Volumn 77, Issue 3, 2003, Pages 155-170

  Heck, B ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Condensation models; Geoid; Helmert's condensation reduction; Isostatic compensation; Quasigeoid; Topographical correction

Indexed keywords

CONDENSATION; GEOID; GRAVIMETRY; GRAVITY FIELD; STOKES FORMULA; TOPOGRAPHY;

EID: 0042268056     PISSN: 09497714     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00190-003-0318-5     Document Type: Article

References (29)

1. Engels J. Grafarend EW, Sorcik P (1995) The gravitational field of topographic-isostatic masses and the hypothesis of mass condensation - Part I and II. Schriftenreihe der Institute des Fachbereichs Vermessungswesen. Tech rep 1995.1, Department of Geodesy, Stuttgart
2. Engels J, Grafarend EW, Sorcik P (1996) The gravitational field of topographic-isostatic masses and the hypothesis of mass condensation II - the topographic-isostatic geoid. Surv Geophys 17:41-66
3. Forsberg R (1984) A study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modelling. Rep 355, Department of Geodetic Science. The Ohio State University, Columbus
4. Forsberg R, Sideris M (1989) On topographic effects in gravity field approximation. Festschrift to T. Krarup, Geodaetisk Institut Meddelelse no. 58, Kopenhagen, pp 129-148
5. Grafarend EW, Engels J (1993) The gravitational field of topographic-isostatic masses and the hypothesis of mass condensation. Surv Geophys 140:495-524
6. Heck B (1993) A revision of Helmert's second method of condensation in geoid and quasigeoid determination. In: Montag H. Reigber C (eds) Geodesy and Physics of the Earth. IAG Symp no. 112. Springer, Berlin Heidelberg New York, pp 246-251
7. Heiskanen WH, Moritz H (1967) Physical geodesy. W.H. Freeman, San Francisco
8. Helmert FR (1884) Die mathematischen und physikalischen Theorieen der Höheren Geodäsie. II. Teil: Die physikalischen Theorieen. Teubner, Leipzig (reprinted 1962)
9. Kuhn M (2000) Geoidbestimmung unter Verwendung verschiedener Dichtehypothesen. Deutsche Geodätische Kommission, Rh. C, Heft Nr 520, Munich
10. Martinec Z (1995) Boundary-value problems for gravimetric determination of a precise geoid. Faculty of Mathematics and Physics, Charles University in Prague
11. Moritz H (1968) On the use of the terrain correction in solving Molodensky's problem. Rep 108, Department of Geodetic Science, The Ohio State University, Columbus
12. Moritz H (1980) Advanced physical geodesy. H. Wichmann, Karlsruhe
13. Novak P (2000) Evaluation of gravity data for the Stokes-Helmert solution to the geodetic boundary value problem. Tech rep 207, Department of Geodesy and Geomatics Engineering, University of New Brunswick, Fredericton
14. Novak P. Heck B (2002) Downward continuation and geoid determination based on band-limited airborne gravity data. J Geod 76:269-278
15. Novak P, Vanicek P. Martinec Z, Veronneau M (2001) Effects of the spherical terrain on gravity and the geoid. J Geod 75:491-504
16. Novak R, Bruton AM, Bayoud FA, Kern M, Schwarz KP (in press) Topographical effects on airborne gravity. J Geodesy
17. Sideris M (1990) Rigorous gravimetric terrain modelling using Molodensky's operator. Manuscr Geod 15:97-106
18. Sideris M, Forsberg R (1991) Review of geoid prediction methods in mountainous regions. In: Rapp RH, Sansò F (eds) Determination of the geoid: present and future. IAG Symp no. 106. Springer, Berlin Heidelberg New York, pp 51-62
19. Sjöberg LE (2000) Topographic effects by the Stokes-Helmert method of geoid and quasi-geoid determinations. J Geod 74:255-268
20. Sjöberg LE, Nahavandchi H (1999) The indirect effect in geoid determination by the Stokes-Helmert method. J Geod 73:87-93
21. Smith DA, Robertson DS, Milbert DG (2001) Gravitational attraction of local crustal masses in spherical coordinates. J Geod 74:783-795
22. Stokes GG (1849) On the variation of gravity on the surface of the Earth. Trans Camb Phil Soc 8:672-695
23. Sun W, Vanicek P (1998) On some problems for the downward continuation of 5' × 5' mean Helmert's gravity disturbance. J Geod 72:411-420
24. Vanicek P, Kleusberg A (1987) The Canadian geoid - Stokesian approach. Manuscr Geod 12:86-98
25. Vanicek P, Martinec Z (1994) The Stokes-Helmert scheme for the evaluation of a precise geoid. Manuscr Geod 19:119-128
26. Vanicek P, Sun W, Ong P, Martinec Z, Vajda P, ter Horst B (1996) Downward continuation of Helmert's gravity. J Geod 71:21-34
27. Vanicek P, Huang J, Novak P, Pagiatakis S, Véronneau M, Martinec Z, Featherstone WE (1999) Determination of the boundary values for the Stokes-Helmert problem. J Geod 73:180-192
28. Vanicek P, Novak P, Martinec Z (2001) Geoid, topography and the Bouguer plate or shell. J Geod 75:210-215
29. Wichiencharoen C (1982) The indirect effects on the computation of geoid undulations. Rep 336, Department of Geodetic Science, The Ohio State University, Columbus