| Abstract: What is a horizontal surface and who needs it? Whoever is
determining or using heights uses it, implicitly or explicitly: one particular horizontal surface,
the geoid, is the reference surface for heights, the “heights above the sea level”. These heights
are used exclusively in engineering practice as well as in other applications. A horizontal surface
is realized, more or less, by a surface of a water body, but how about dry land; what is needed for
tracing a horizontal surface on land? What is needed, are gravity data observed on the surface of
the earth, earth topography, some idea about topo-density, some idea about long-wavelength features
of gravity field (derived from satellite tracking), and a conventional reference system with respect
to which the tracing and the display should be done. The tracing is done through solving a
non-linear boundary value problem for gravity potential with the boundary (the geoid) being
itself a function of the potential. The solution is obtained by finite element or finite
difference techniques, after transforming the boundary value problem into Green’s form.
The solution uses a vast amount of data irregularly distributed on the surface of the earth.
Abstract:
Petr Vaníc,ˇek, P.Eng., Ph.D., Dr.Sc, is Professor Emeritus of geodesy in the Department of
Geodesy and Geomatics Engineering at UNB. He retired in 1999, after 28 years of teaching and
is now involved only in post-graduate student supervision and in research. His research interests
cover the whole spectrum of geodesy, geophysics and applied mathematics. He is a fellow of AGU,
IAG, Senior Distinguished Scientist Humboldt awardee (1989), and recipient of CGU 1996 Tuzo J.
Wilson medal. He is also author and co-author of about 450 publications including the comprehensive
textbook “Geodesy: the concepts” used world-wide.
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