## Geodetic Networks, Gravity and the Geoid

by

C.Chr.Tscherning
Department of Geophysics &
International Association of Geodesy
Juliane Maries Vej 30
DK-2100 Copenhagen Ø, Denmark

**Abstract:** Ellipsoidal or Cartesian coordinates of points at the surface of the Earth are today
determined using a combination of space techniques and traditional observations. The
calculated associated ellipsoidal heights may be converted to heights above mean sea-level
(orthometric or normal heights) using the knowledge of the geoid.

The height of the geoid may be calculated from available spherical harmonic series, regular
grids of pre-calculated geoid heights or by using the heights of the points in a levelling
network with known ellipsoidal heights.

Gravity values may be obtained by interpolation in the points of a gravity network or
observed with a gravimeter. These gravity values may be used locally to determine geoid
height differences or improve values calculated from a spherical harmonic expansion. This is
due to the very strong (70 % - 90 %) correlation between residual gravity anomalies and
residual geoid heights obtained by subtracting the contribution from a spherical harmonic
expansion and the residual topography from the original gravity and geoid height values.

Using a few simple examples it is shown how gravity information may be used to support the
calculation of geoid height differences and thereby the transfer of physical heights between
points in a geodetic network.

It is finally pointed out, that geoid and gravity data may be used to calculate the deflections
of the vertical which are needed in order to rigorously combine points in a network
determined with space techniques and "ex-centric" points determined by traditional types of
geodetic measurements. Differences between deflections of the vertical determined by
gravity data will generally be superior to values obtained by astronomical methods.

Presented at "WHERE ARE WE GOING ?", A symposium to mark the retirement of
Professor Vidal Ashkenazi, Nottingham, UK, October 1998.

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