Abstract
Mean gravity anomalies, deflections of the vertical, and a geopotential model complete to degree and order180 are combined in order to determine geoidal heights in the area bounded by [34°≦ϕ≤42°, 18°≦λ≦28°]. Moreover, employing point gravity anomalies simultaneously with the above data, an attempt is made to predict deflections of the vertical in the same area. The method used in the computations is least squares collocation. Using empirical covariance functions for the data, the suitable errors for the different sources of observations, and the optimum cap radius around each point of evaluation, an accuracy better than±0.60m for geoidal heights and±1″.5 for deflections of the vertical is obtained taking into account existing systematic effects. This accuracy refers to the comparison between observed and predicted values.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. ARABELOS: Untersuchungen zur gravimetrischen Geoidbestimmung dargestellt am Testgebiet Griechenland. Wiss. Arb. Univ. Hann., Nr. 98, Dissertation, 1980.
D. ARABELOS, L.N. MAVRIDIS and I.N. TZIAVOS: Gravimetric geoid determination for the area of Greece. Proc. IAU Symp. “Sun and Planetary System (eds. Fricke W. and G. Teleki)”. D. Reidel Publishing Co., pp. 203–204, 1982.
D. ARABELOS and I.N. TZIAVOS: Determination of deflections of the vertical using a combination of spherical harmonics and gravity anomalies for the area of Greece. Bull. Géod., 57, pp. 240–256, 1983.
D. ARABELOS: Evaluation of deflections of the vertical using topographic-isostatic and astrogeodetic data for the area of Greece. Bull. Géod., 59, pp. 109–123, 1985.
D. BALODIMOS: Geoidal studies in Greece. Ph.D. thesis, Oxford, 1972.
D. BALODIMOS: The Hellenic geoid on ED50. Paper presented at the Ist Int. Symp. “Geoid in Europe and Mediterranean Area”, pp. 39–49, Ancona, Italy, 1978.
O.L. COLOMBO: Numerical methods for harmonic analysis on the sphere. Dept. of Geodetic Science. Rep. No. 310, Ohio State Univ., 1981.
A. DERMANIS: Theory and application of collocation in surveying. Paper presented at seminario “Tecniche moderne di analysi dei dati geodetici con particolare riguardo alla collocazione”, pp. 37–67, Universita Di Bologna, 1983.
A. DERMANIS. Signals in geodetic network. Paper presented at the Int. School of advanced geodesy “Design and Optimization of Geodetic Networks”, pp. 221–256, Erici, Trapani, Sicily, Italy, 1984.
M. DOUFEXOPOULOU-PATSADA: Study to the local gravity field in the Hellenic area for geoid approximation. Ph. D. thesis (in Greek), Athens, 1985.
T. EENGELIS, C.C. TSCHERNING and R.H. RAPP: The precise computation of geoid undulation differences with comparison to results obtained from GPS. Manuscripta Geodaetica, 10, pp. 187–194, 1985.
R. FORSBERG. Local covariance functions and density distributions. Dept. of Geodetic Science, Rep. No. 356, Ohio State Univ., 1984.
R. FORSBERG and C.C. TSCHERNING: Deflection and gravity anomaly prediction using collocation. Proceedings 2nd Int. Symp. “Inertial Techniques for Surveying and Geodesy”, pp. 89–105, Banff, Canada, 1981.
A. FOTIOU, E. LIVIERATOS and I.N. TZIAVOS. Comparisons of the various representations of the geoid for the Hellenic area. IAG Int. Symp. “The Definition of the Geoid”, Florence, Italy, 1986.
C.C. GOAD, C.C. TSCHERNING and M.M. CHIN: Gravity empirical covariance values for the continental United States. J. Geophys. Res., 89, pp. 1962–1968, 1984.
W. HEISKANEN and H. MORITZ Physical Geodesy W.H. Freeman, San Francisco, 1967.
A.H.W. KEARSLEY. Non-stationary estimation in gravity prediction. Dept. of Geodetic Science, Rep. No. 165. Ohio State Univ., 1977.
A.H.W. KEARSLEY, M.G. SIDERIS, Jan KRYNSKI, R. FORSBERG and K.P. SCHWARZ. White Sands revisited—A comparison of techniques to predict deflections of the vertical. UCSE Report #30007, Division of Surveying Engineering, The University of Calgary, Calgary, Alberta, 1985.
T. KRARUP: A contribution to the mathematical foundation of physical geodesy. The Danish Geodetic Institute, Meddelelse, Nr. 44, 1969.
G. LACHAPELLE and A. MAINVILLE: Evaluation of deflections of the vertical in mountainous areas using a combination of topographic-isostatic and astrogeodetic data. Collected papers, pp. 99–122, Geod. Survey, Dept. of Energy, Mines and Resources, Surveys and Mapping Branch, 1979.
G. LACHAPELLE and C.C. TSCHERNING: Use of collocation for predicting geoid undulations and related quantities over large areas. Proc. of the 1st Int. Symp. “Geoid in Europe and the Mediterranean Area”, pp. 165–182, Ancona, Italy, 1978.
S.L. LAURITZEN: The probabilistic background of some statistical methods in physical geodesy. The Danish Geodetic Institute, Meddelelse, No. 48, 1973.
H. MORITZ: Least Square collocation. DGK, Reihe A, Nr. 75, 1973.
H. MORITZ: Advanced physical geodesy. Herbert Wichmann Verlag, Karlsruhe, 1980.
R.H. RAPP. The earth's gravity field to degree and order 180 using SEASAT altimeter data terrestrial gravity data, and other data. Dept. of Geodetic Science and Surveying Rep. No. 202, Ohio State Univ., 1981.
R.H. RAPP. A Fortran program for the computation of gravimetric quantities from high degree spherical harmonic expansions. Dept. of Geodetic Science and Surveying, Rep. No. 334, Ohio State Univ., 1982.
C. RIZOS. An efficient computer technique for the evaluation of the geopotential from spherical harmonic models. Aust. J. Geod. Photo. Surv., No. 30, pp. 161–169, 1979.
R. RUMMEL: A model comparison in least squares collocation. Dept. of Geodetic Science, Rep. No. 238, Ohio State Univ., 1976.
F. SANSÒ. The minimum mean square estimation error principle in physical geodesy. (Stochastic and nonstrochastic interpretation). Boll. Geod. Sci. Aff., No. 2, pp. 111–129, 1980.
W. SCHLÜTER, P. WILSON and H. SEEGER: Final results of the EROS-Doppler observation campaign. Paper presented at XVII. IUGG Gen Ass., Canberra, Australia, 1979.
K.P. SCHWARZ. Capabilities of airborne gradiometry for gravity estimation. Boll. Geod. Sci. Aff., No. 2, pp. 195–214, 1977.
K.P. SCHWARZ and G. LACHAPELLE: Local characteristics of the gravity anomaly covariance function. Bull. Géod., 54, pp. 21–36, 1980.
K.P. SCHWARZ and M.G. SIDERIS: Precise geoid heights and their use in GPS-interferometry. Contract Report No. 85-004, Geodetic Survey of Canada, Department of Energy, Mines and Resources, Ottawa, Ontario, 1985.
M.G. SIDERIS and K.P. SCHWARZ: Improvements of medium and short wavelength features of geopotential solutions by local data. Paper presented at the Int. Symp. on “The Definition of the Geoid”, Florence, 1986.
H. SÜNKEL: The geoid in the Styrian test network. Proc. of the 2nd Int. Symp. “Geoid in Europe and the Mediterranean Area”, pp. 362–382, Rome, 1982.
W. TORGE, G. WEBER and H.G. WENZEL: Determination of 12′×20′ mean free air gravity anomalies for the North Sea region. DGK, Reihe B, Nr. 247, 1980.
C.C. TSCHERNING: Covariance expressions for second and lower order derivatives of the anomalous potential. Dept. of Geodetic Science, Rep. No. 225, Ohio State Univ., 1976a.
C.C. TSCHERNING: Determination of datum shift parameters using least squares collocation. Boll. Geod. Sci. Aff., No. 2, pp. 173–183, 1976b.
C.C. TSCHERNING: A note of the choice of norm when using collocation for the computation of approximation to the anomalous potential. Bull. Géod. 51, pp. 137–147, 1977.
C.C. TSCHERNING: Comparison of some methods for the detailed representation of the earth's gravity field. Rev. Geophys. Sp. Phys., 19, pp. 213–221, 1981.
C.C. TSCHERNING: Geoid determination for the Nordic countries using collocation. Proc. of the IAG Gen. Meeting, pp. 472–483, Tokyo, 1982.
C.C. TSCHERNING: The role of the high degree spherical harmonic expansions in solving geodetic problems. Proc. of the IAG Symposium, pp. 431–444, Hamburg, 1983a.
C.C. TSCHERNING Effects of the lack of adequate height and gravity data on the use of positions determined by space techniques in developing countries. Proc. of the IAG Symposium, pp. 658–670, Hamburg, 1983b.
C.C. TSCHERNING and R.H. RAPP Closed covariance expressions for gravity anomalies, geoid undulations and deflections of the vertical implied by anomaly degree variance models. Dept. of Geod. Science, Rep. No. 108, Ohio State Univ., 1974.
C.C. TSCHERNING and R. FORSBERG: Prediction of deflections of the vertical. Proc. of the 2nd Int. Symp. “Problems related to the Redefinition of North American Geodetic Networks”, pp. 117–134, Washington, 1978.
C.C. TSCHERNING, R.H. RAPP and C.C. GOAD: A comparison of methods for computing gravimetric quantities from high degree spherical harmonic expansions. Manuscripta Geodaetica, 8, pp. 249–272, 1984.
I.N. TZIAVOS: Study of the optimal combination of heterogeneous data on geoid determination with applications for the area of Greece. Ph. D. thesis (in Greek), Thessaloniki, 1984.
I.N. TZIAVOS: Fehler-Kovarianzfunktionen und Modelle für Schwereanomalien und Kugelfunktionsentwicklungen. ZfV, Heft 9, pp. 417–429, 1986.
H.G. WENZEL and D. ARABELOS: Zur Schätzung von Anomalie-Gradvarianzen aus lokalen empirischen Kovarianzfunktionen. ZfV, 106, pp. 234–243, 1981.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tziavos, I.N. Determination of geoidal heights and deflections of the vertical for the hellenic area using heterogeneous data. Bull. Geodesique 61, 177–197 (1987). https://doi.org/10.1007/BF02521266
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02521266