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Modelling the fine-structure of the geoid: Methods, data requirements and some results

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Abstract

The requirements for precise geoid models on local and regional scales have increased in recent years, primarily due to the ongoing developments in height determination by GPS on land, but also due to oceanographic requirements in using satellite altimetry for recovering dynamic sea-surface topography. Suitable methods for geoid computations from gravity data include Stokes integration, FFT methods, and least-squares collocation. Especially the FFT methods are efficient in handling large amounts of gravity data, and new variants of the methods taking earth curvature rigorously into account provide attractive methods for obtaining continental-scale, high-resolution geoid models. The accuracy of such models may be from 2–5 cm locally, to 50–100 cm on regional scales, depending on gravity data coverage, long wave-length gravity field errors, and datum problems. When approaching the cm-level geoid basic geoid definition questions (geoid or quasigeoid?) become very significant, especially in rugged areas.

In the paper the geoid modelling methods and problems are reviewed, and some investigations on local data requirements for cm-level geoid prediction are presented. Some actual results are presented from Scandinavia, where a recent regional high-resolution geoid model yields apparent accuracies of 2–10 cm over GPS baselines of 50 to 2000 km.

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References

  • Denker, H.: 1990, ‘GPS Control of the 1989 Gravimetric Quasigeoid for the Federal Republic of Germany’,Proceedings, 1st International Geoid Commission Symposium, Milano, June 1990, 152–159.

  • Forsberg, R.: 1984a, ‘A Study of Terrain Reductions, Density Anomalies and Geophysical Inversion Methods in Gravity Field Modelling’, Dept. of Geodetic Science, Ohio State University, Report 355.

  • Forsberg, R.: 1984b, ‘Local Covariance Functions and Density Distributions’, Dept. of Geodetic Science, Ohio State University, Report 356.

  • Forsberg, R.: 1990, ‘A New High-resolution Geoid of the Nordic Area’,Proceedings, 1st International Geoid Commission Symposium, Milano, June 1990, 241–250.

  • Forsberg, R. and Tscherning, C. C.: 1981, ‘The use of Height Data in Gravity Field Modelling by Collocation’,Journ. Geoph. Res. 86, 7843–7854.

    Google Scholar 

  • Heiskanen, W.A. and Moritz, H.: ‘Physical Geodesy’, W. H. Freeman.

  • Kaula, W.: 1966, ‘Theory of Satellite Geodesy’, Blaisdell, Waltham, Mass. USA.

    Google Scholar 

  • Knudsen, Per: 1990, ‘Some Accuracy Estimates of Local Geoids’,Proc., 1st International Geoid Commission Symposium, Milano, June 1990, 422–431.

  • Madsen, F. and Aarrestrup, M.: 1990, ‘The Determination of Height Differences by GPS Across the Fehmarn Belt and the Great Belt’,Proc. Nordic Geodetic Commission Meeting, Copenhagen, May 1990, 199–207.

  • Rapp, R. H. and Pavlis, N. K.: 1990, ‘The OSU89 Geopotential Models’,Proc. 1st International Geoid Commission Symposium, Milano, June 1990, 7–9.

  • Schutz, B. E., Tapley, B. D., Ho, C. S., Rim, H. J., and Ambusali, C.: 1989, ‘GPS Orbit Determination: Experiments and Results’,Proc. 5th Int. Geodetic Symp. on Satellite Positioning, Las Cruces, New Mexico, March 1989.

  • Schwarz, K. P., Sideris, M. G., and Forsberg, R.: 1990, ‘The Use of FFT Techniques in Physical Geodesy’,Geophys. J. Int. 100, 485–514.

    Google Scholar 

  • Sideris, M. and Forsberg, R.: 1991, ‘Testing the Spherical FFT Formula for the Geoid over Large Regions’, AGU spring meeting, Baltimore.

    Google Scholar 

  • Strang van Hees, G.: 1990, ‘Stokes Formula Using Fast Fourier Techniques’,Manuscripta Geodaetica 15, 235–239.

    Google Scholar 

  • Torge, W., Basic, T., Denker, H., Doliff, J., and Wenzel, H.-G.: 1989, ‘Long Range Geoid Control Through the European GPS Traverse’, Deutsche Geodaetische Commission, Reihe B, Heft 290, Munchen.

    Google Scholar 

  • Tscherning, C. C. and Rapp, R. H.: 1974, ‘Closed Covariance Expressions for Gravity Anomalies, Geoid Undulations, and Deflections of the Vertical Implied by Anomaly Degree Variance Models’, Dept of Geodetic Science, Ohio State University, Rep. 208.

  • Tscherning, C. C. and Forsberg, R.: 1987, ‘Geoid Determination in the Nordic Countries from Gravity and Height Data’,Boll. Geod. Sci. Aff. 46, 21–43.

    Google Scholar 

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Forsberg, R. Modelling the fine-structure of the geoid: Methods, data requirements and some results. Surv Geophys 14, 403–418 (1993). https://doi.org/10.1007/BF00690568

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