FIG Working Week 2000, 21-26 May, Prague
Abstracts 



The Carmel Mountain Precise Geoid

by Dan Sharni & Haim B. Papo

Key words: Israel geoid, Stokes, gravity anomalies. 


Abstract

This paper presents the final results of a pilot-project, for mapping an accurate geoid of the State of Israel. The purpose of the project was to develop a feasible methodology, assemble all necessary data, design and test field procedures and finally to work out a suitable analysis algorithm, including the respective computer programs. The project was funded and supported by the Survey of Israel over a period of five years between 1994 and 1999. An area of about 600 sq. km. on and around the Carmel Mountain served as a field laboratory and proving ground. The ultimate goal was to render a geoid map of the pilot area with a one-sigma accuracy of 4 cm.

The geoid map was compiled from three complementary data sources:

  • Measured geoid undulations (indirectly - by GPS and trigonometric leveling) at a network of anchor points. The network density was set high by a factor of three to four in order to provide means for testing the quality of the map.
  • A global gravity model of the highest order available. Over the years 1994-1999 a succession of gravity models was used, beginning with OSU91, then - EGM96 and finally - the 1800 order GPM98B model.
  • A dense grid of free-air gravity anomalies (3') extending up to a distance of 2o from the pilot area. Within the state boundaries we used directly measured anomalies. At sea and beyond the state boundaries we had to depend on free-air gravity anomalies, reconstructed from a dense Bouguer anomalies grid and a DTM of surface and sea-floor topography.

The computational procedure was based on the "remove-restore" approach as follows:

  • Transform the free-air-anomalies grid into a grid of residual anomalies, by removing model (GPM98B) anomalies.
  • At every anchor point compute model geoid undulations (including a number of corrections such as "zero order" undulation, the effect of global elevation, indirect effect, etc.) and add Stokes's integration of the residual f.a. anomalies field.
  • Subtract the above (b) "crude prediction" from the "measured" undulations and create an anchor-point correction field. Interpolate the correction field into a contour map or - a grid. At any point within the grid boundaries, geoid undulation can be predicted now by adding the interpolated correction grid value to a "GPM98B plus Stokes" crude prediction.

Three factors dominate the accuracy of the final geoid map:

  • Density of the anchor points.
  • Over-all fit of the gravity model to the geoid.
  • Radius of Stokes's integration of the residual f.a. anomalies field.

With anchor points spaced 5-20 km apart; employing the GPM98B model and finally extending Stokes's integration up to 2 degrees we obtained an accuracy (one-sigma) of 2 cm or better. Although our accuracy estimates are based on sound analysis principles they may seem a bit too optimistic. Analysis of additional test fields should confirm our "optimistic" results or else - define more realistic accuracy estimates.


Dr. Dan Sharni
Geodesy
Technion
32000 Haifa
ISRAEL
Tel. + 972 4 829 2482
Fax + 972 4 823 4757
E-mail: sharni@techunix.technion.ac.il

Haim B. Papo
Geodesy
Technion
32000 Haifa
ISRAEL
Fax + 972 4 823 4757
E-mail: haimp@tx.technion.ac.il



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