Advertisement

Geodetic Boundary-Value Problems and the Height Datum Problem

  • Fausto Sacerdote
  • Fernando Sanso’
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 127)

Abstract

The analysis of boundary-value problems has always been used in geodesy as a frame to understand the nature of the problem of determining the gravity disturbing potential, with respect to well-posedness (existence, uniqueness, continuous dependence of the solution on boundary data). The first historical problem of this kind is Stokes’s, followed by Molodensky’s and other more and more sophisticated versions of boundary-value problems of mixed type, in an attempt of approaching more realistic (Closer to measurements) conditions. Formulations for realistic problems have invariably displayed “nice” mathematical properties. As shown in this paper, also a realistic boundary-value problem for gravity and geopotential numbers as boundary data on continental areas and marine geoid, as derived from altimetry and stationary sea surface heights, on the oceans, can be demonstrated to have such properties for solutions lying in suitable function spaces. In order to establish realistic boundary conditions for this problem it is necessary to take into account that 1) for different continental areas that are not connected by levelling lines one must assume different reference geopotential values, and even on very large individual continents, because of error propagation in levelling, it is not possible to impose a unique reference value with the required accuracy; 2) ocean circulation models enable us to compute the sea surface topography but for an additive constant; furthermore, such models cannot be applied close to coasts, so the marine geoid cannot be used to connect different continental geoids; 3) moreover, there are oceanic regions (for example, equatorial areas) where stationary SST models do not hold, so that the marine geoid too has to be computed separately for a number of different patches that cannot be directly connected. Consequently, a number of different unknown constants must be introduced in the boundary conditions, and correspondingly suitable constraints have to be imposed. The type of unknowns to account for different height datums and the correspondent conditions to be imposed to the solutions are thoroughly discussed.

Keywords

Height Data Ellipsoidal Height Geodetic Boundary Suitable Function Space Geopotential Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Balasubramania, N. (1994) - Definition and Realisation of a Global Vertical Datum,OSU Report 427.Google Scholar
  2. Heck, B. and R.Rummel (1990) - Strategies for solving the vertical datum problem using terrestrial and satellite geodetic data,in Sea Surface Topography and the Geoid, IAG Symposia 104, 116–128, Springer Verlag.Google Scholar
  3. Heiskanen, W. and H.Moritz (1967) - Physical Geodesy,Freeman and Co.Google Scholar
  4. Lehmann, R. (2000)–Altimetry-Gravimetry Problems with Free Vertical Datum, Journal of Geodesy, 74, 327–334.Google Scholar
  5. van Onselen, K. (1997) - Quality investigation of vertical datum connection, DEOS Rep. 97.3, TU Delft.Google Scholar
  6. Pedlosky, J. (1998) - Ocean Circulation Theory,Springer.Google Scholar
  7. Rummel, R. and P.Teunissen (1988)–Height datum definition, height datum connection and the role of geodetic boundary value problem, Bull. Géod., 62, 477–498.Google Scholar
  8. Sacerdote, F. and F.Sansò (1987)–Further Remarks on the Altimetry-Gravimetry Problems, Bull.Géod., 61, 65–82.Google Scholar
  9. Sacerdote, E. and ESansò (2001)–Wo: A story of the height datum problem, in Festschrift W.Torge, Wissenschaftliche Arbeiten der Fachrichtung Vermes- sungswesen der Universität Hannover, 241, 49–56.Google Scholar
  10. Sacerdote, F. and F.Sansò (2002) - Remarks on the role of height datum in altimetry-gravimetry boundary-value problems,to appear in Proceedings of the Workshop “Earth Gravity from Space - from Sensors to Earth Sciences”, Bern.Google Scholar
  11. Sansò, F. and S.Usai (1995)–Height datum and local geodetic datums in the theory of geodetic boundary value problems, AVN, 102, 343–355.Google Scholar
  12. Svensson, L. (1985)–Some Remarks on the AltimetryGravimetry Problem, in Proc. of the I Hotine-Marussi Symposium on Math. Geodesy, Rome, 559–582.Google Scholar
  13. Wunsch, C. (1993) - Physics of the Ocean Circulation, in Satellite Altimetry in Geodesy and Oceanography,R.Rummel and F.Sansò eds., Lecture Notes in Earth Sciences, 50, Springer-Verlag, 9–98.Google Scholar
  14. Xu, P. and R.Rummel (1991) - A Quality Investigation of Global Vertical Datum Connection,Netherland Geodetic Commission, Publications on Geodesy, New Series, 34. Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Fausto Sacerdote
    • 1
  • Fernando Sanso’
    • 2
  1. 1.Dipartimento di Ingegneria CivileUniversitá di FirenzeGermany
  2. 2.DIIAR - Facoltá di Ingegneria di ComoPolitecnico di MilanoGermany

Personalised recommendations