Comparison of interpolation and collocation techniques using torsion balance data

• Autorzy: Tóth G. , Völgyesi L.
• Konferencja: Geodetic and Geodynamic Programmes of the CEI (10; EGS Symposium; 21-26.04.2002; Nice, France)
• Języki publikacji: EN

Abstrakty

EN

First the relewant theory of the interpolation and collocation methods, both used here for the recovery of deflections of the vertical and geoid heights from torsion balance data is discussed. We have selected a mostly flat area in Hungary where all kind of torsion balance measurements are available at 249 points. There were 3 astrogeodetic points providing initial data for the interpolation, and there were geoid heights at 10 checkpoints interpolated from an independent gravimetric geoid solution. The size of our test area is about 800 km sq.m. and the average site distance of torsion balance data is 1.5-2 km. The interpolation method provided a least squares solution for deflections of the vertical and geoid heights at all points of the test network. By collocation two independent solutions were computed from W(zx), W(zy) and W(yy)-W(xx), 2W(xy) gradients for all the above, using astrogeodetic data to achieve a complete agreement at these site with the interpolation method. These two solutions agreed at the cm level for geoid heights. The standard deviation of geoid height differences at checkpoints were about +-1-3 cm. The W(yy)-W(xx) , 2W(xy) combination (i.e. pure horizontal gradients) yielded better results since the maximum geoid height difference was only 3.6 cm. The differences in the deflection components were generally below 1", slightly better for the (pi) component. The above results confirm the fact that torsion balance measurements give good possibility to compute very precise local geoid heights at least for flat areas.

Słowa kluczowe

EN

measurements; satellite geodesy

PL

geodezja satelitarna; pomiary

• Wydawca: Wydział Geodezji i Kartografii Politechniki Warszawskiej
• Czasopismo: Reports on Geodesy
• Rocznik: 2002
• Tom: z. 1/61
• Strony: 171--182
• Opis fizyczny: Bibliogr. 11 poz., wykr., schem.

Twórcy

autor

Tóth G.

• Dept. of Geodesy and Surveying, Budapest University of Technology and Economics, Budapest, Hungary

autor

Völgyesi L.

• Dept. of Geodesy and Surveying, Budapest University of Technology and Economics, Budapest, Hungary

Bibliografia

• [1] Hein, G. and Jochcmczyk, H. (1979): Reflections on Covariances and Collocation with Special Emphasis on Gravity Gradient Covariances. Manuscripta Geodaetica, 4, pp 45-86.
• [2] Moritz, H. (1980): Advanced Physical Geodesy. Herbert Wichmann Verlag, Karlsruhe.
• [3] Tóth Gy. Rózsa Sz, (2000): New Datasets and Techniques - an improvement in the Hungarian Geoid Solution. Paper presented at Gravity, Geoid and Gcodynamics Conference, Banff, Alberta, Canada July 31-Aug 4, 2000.
• [4] Tóth Gy Rózsa Sz, Ádám J. and Tziavos, I.N. (2002a): Gravity Field Recovery from Torsion Balance Data Using Collocation and Spectral Methods. Paper presented at the XXVI General Assembly, Nice, France, March 25-30, Session G7, 2001. Accepted for publication in the IGeS Bulletin, 2002.
• [5] Tóth Gy Rózsa Sz, Ádám J. and Tziavos, I.N. (2002b): Gravity Field Modelling by Torsion Balance Data - a Case Study in Hungary. Vistas for Geodesy in the New Millennium, IAG Symposia Vol 125, pp 193-198, Springer-Verlag, 2002 (in press).
• [6] Tscherning, C. (1994): Geoid Determination by Least-squares Collocation using GRAVSOFT, in International School for the Detemnination and Use of the Geoid, Milan, October 10-15, 1994, pp. 135-164.
• [7] Völgyesi L. 1993: Interpolation of Deflection of the Vertical Based on Gravity Gradients. Periodica Polytechnica Ser. Civil Eng. Vol.37. No.2, 137-166.
• [8] Völgyesi L. 1995: Test Interpolation of Deflection of the Vertical in Hungary Based on Gravity Gradients. Periodica Polytechnica Ser. Civil Eng. Vol.39. No.1, 37-75.
• [9] Völgyesi L. 1998: Geoid Computations Based on Torsion Balance Measurements. Reports of the Finnish Geodetic Inst. 98:4, 145-151.
• [10] Völgyesi L. 2001: Local geoid determination based on gravity gradients. Acta Geodaetica et Geophysica Hungarica Vol.36 (2), pp. 153-162.
• [11] Völgycsi L. 2001: Geodetic applications of torsion balance measurements in Hungary. Reports on Geodesy, Warsaw University of Technology, No.2 (57), pp. 203-212.