Abstract
Terrestrial free-air gravity anomalies form a most essential data source in the framework of gravity field determination. Gravity anomalies depend on the datums of the gravity, vertical, and horizontal networks as well as on the definition of a normal gravity field; thus gravity anomaly data are affected in a systematic way by inconsistencies of the local datums with respect to a global datum, by the use of a simplified free-air reduction procedure and of different kinds of height system. These systematic errors in free-air gravity anomaly data cause systematic effects in gravity field related quantities like e.g. absolute and relative geoidal heights or height anomalies calculated from gravity anomaly data.
In detail it is shown that the effects of horizontal datum inconsistencies have been underestimated in the past. The corresponding systematic errors in gravity anomalies are maximum in mid-latitudes and can be as large as the errors induced by gravity and vertical datum and height system inconsistencies. As an example the situation in Australia is evaluated in more detail: The deviations between the national Australian horizontal datum and a global datum produce a systematic error in the free-air gravity anomalies of about −0.10 mgal which value is nearly constant over the continent
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K. ARNOLD: Numerische Beispiele zur strengen Theorie der Figur der Erde. Veroff Geod. Inst. Potsdam, No. 16, 1960.
J.D. BOSSLER: New Adjustment of North American Datum. J. Surveying and Mapping Division 108 (1982), pp. 47–52.
J.D. BOULANGER, G.P. ARNAUTOV and S.N. SCHEGLOV: Check of IGSN–71 System, BGI Bull. d'lnformation No. 53, 1983, pp. 138–141.
J. BRENNECKE, E. GROTEN, R. RUMMEL and H. SCHAAG: Variationen zum Geoid in Deutschland. Deutsche Geodäitische Kommission, Rep. A 83, Munich 1976.
K. BRETREGER: Tidal Effects on Geodetic Levelling. Austr. J. Geoid.,Photogram.,Surv. 45 (1986), pp. 37–54.
D.C. CHRISTODOULIDIS: On the Realization of a 10 cm Relative Oceanic Geoid. Report Dept. Geodetic Science, No. 247, The Ohio State University, 1976.
DMA: Supplement to Department of Defense World Geodetic System 1984, Techn. Report, Part I, 1987.
T. ENGELIS, R.H. RAPP and Y. BOCK: Measuring Orthometric Height Differences with GPS and Gravity Data. Manuscripta geodaetica 10 (1985), pp. 187–194.
E. GRAFAREND: The Definition of the Telluroid. Bull. Géod. 52 (1978), pp. 25–37.
E. GROTEN: Geodesy and the Earth's Gravity Field. Vol. I, Dümmler, Bonn 19
E. GROTEN: Model Refinements in the Solutions of the Boundary Value Problems of Physical Geodesy. In; K.P. Schwarz (ed.), Proc. Beijing Int. Summer School on Local Gravity Field Approximation, Beijing 1984. Publ. 60003, Division of Surveying Engineering, Univ. of Calgary 1985, pp. 217–274.
B. HECK: Zur Bestimmung vertikaler rezenter Erdkrustenbewegungen und zeitlicher,Änderungen des Schwerefeldes aus wiederholten Schweremessungen und Nivellements. Deutsche Geodätische Kommission, Rep. C 302, Munich 1984.
B. HECK: A Numerical Comparison of Some Telluroid Mappings. In: F. Sansò (ed.), Proc. I. Hotine- Marussi Symposium on Mathematical Geodesy, Roma 1985. Milano 1986, Vol. 1, pp. 19–38.
B. HECK: Rechenverfahren und Auswertemodelle der Landesvermessung. H. Wichmann Verlag, Karlsruhe 1987.
B. HECK: A Contribution to the Scalar Free Boundary Value Problem of Physical Geodesy. Manuscripta geodaetica, 14 (1989), pp. 87–99.
W.A. HEISKANEN and H. MORITZ: Physical Geodesy. W.H. Freeman and Co., San Francisco/London 1967.
F.R. HELMERT: Die Schwerkraft im Hochgebirge, insbesondere in den Tyroler Alpen. Veröff. Königl. Preuss. Geod. Inst. No. 1, 1890.
R.A. HIRVONEN: New Theory of Gravimetric Geodesy. Publ. Isostat. Inst. IAG No. 32, Hetsinki 1960.
G.J. HUSTI: The Final Results of the NEDOC Project. Rep. Dept. of Geodesy, Math. and Phys. Geodesy, No. 83.1, Delft University of Technology, March 1983.
IAG: Geodetic Reference System 1967. lAG Special Publ. No. 3, Paris 1971.
IAG; The Geodesist's Handbook 1984. Bull. Gdod. 58, No. 3, 1984.
R. KELM: Vertical Datum Definitions Discussed in View of European Vertical and Horizontal Networks. Proc. 3rd Int. Symp. on the North American Vertical Datum. National Geodetic Information Center, NOAA, Rockville 1985, pp. 95–103.
J. KOK, W. EHRNSPERGER and H. RIETVELD: The 1979 Adjustment of the United European Levelling Network (UELN) and its Analysis of Precision and Reliability. Proc, 2 nd Int. Symp. on Problems Related to the Redefinition of the North American Vertical Geodetic Networks. Ottawa 1980, pp. 455–483.
P. LASKOWSKI: The Effect of Vertical Datum Inconsistencies on the Determination of Gravity Related Quantities. Rep. Dept. Geodetic Science and Surveying No. 349, The Ohio State University 1983.
K. LEDERSTEGER: Handbuch der Vermessungskunde, Bd. V, Astronomische und Physikalische Geodäsie (Erdmessung). 10. Ausgabe Jordan/Eggert/Kneissl. J.B. Metzlersche Verlagsbuchhandlung, Stuttgart 1969.
S. LEVITUS: Climatological Atlas of the World Ocean, NOAA Professional Paper 13, 1982.
E. LISITZIN: The Mean Sea Level of the World Ocean. Comment. Phys.-Math. Helsingf, 30 (1965).
E. LISITZIN: Sea Level Changes. Elsevier Science Publ. Comp., Amsterdam/New York, 1974.
R.S. MATHER: On the Solution of the Geodetic Boundary Value Problem for the Definition of Sea Surface Topography. Geophys. J.R. astr. Soc. 39, 1974, pp. 87–109.
R.S. MATHER, C. RIZOS, B. HIRSCH and B.C. BARLOW: An Australian Gravity Data Bank for Sea Surface Topography Determinations (Ausgad 76). Unisurv G 2525, 1976, pp. 54–84.
M.S. MOLODENSKII, V.F. EREMEEV and M.I. YURKINA: Methods for Study of the External Gravitational Field and Figure of the Earth. Transl. from Russian (1960), Israel Program for Scientific Translations, Jerusalem 1962.
C. MORELLI, C. GANTAR, T. HONKASALO, R.K. MCCONNELL, J.G. TANNER, B. SZABO, U. UOTILA and C.T. WHALEN: The International Gravity Standardization Net 1971 (I.G.S.N. 71). IAG Special Publ. No. 4, Paris 1974.
C. MORELLI: The International Gravity Standardization Net 1971 (IGSN 71): A Still Valid, Fundamental Cornerstone in Science. Deutsche Geodätische Kommission, Rep. B 287, Munich 1988, pp. 142–148.
T. NIETHAMMER: Nivellement und Schwere als Mittel zur Berechnung wahrer Meereshöhen. Kartenverlag der Schweizerischen Landestopographie, Bern 1932.
M. OGLER: Integration du Réseau Gravimetrique Francais RGF 83 dans le Réseau International IGSN 71. BGI Bull. d'Information No. 53, 1983, pp. 142–149.
N.K. PAVLIS: Modeling and Estimation of a Low Degree Geopotential Model from Terrestrial Gravity Data. Rep. Dept. Geodetic Science and Surveying, No. 386, The Ohio State University 1988.
K. RAMSAYER: Vergleich verschiedener Schwerareduktionen von Nivellements. Zeitschrift für Vermessungswesen 79 (1954), pp. 140–150.
K. RAMSAYER: Über den zulässigen Abstand der Schwerepunkte bei der Bestimmung geopotentieller Koten im Hochgebirge, Mittelgebirge und Flachland. Deutsche Geodätische Kommission, Rep. A 44, Munich 1963.
R.H. RAPP: Tidal Gravity Computations Based on Recommendations of The Standard Earth Tide Committee. Bull. d'Information, Commission Permanente des Marees Terrestres, No. 89. pp. 5814–5819, 1983.
O. REMMER: RefractiOn and Other Systematic Effects in Levelling. In: H. Pelzer W. Niemeier (eds.), Precise Levelling, Dümmler, Bonn 1983}, pp. 181
R. RUMMEL and P. TEUNISSEN: Height Datum Definition, Height Datum Connection and the Role of the Geodetic Boundary Value Problem. Bull. Géod. 62 (1988), pp. 477–498.
W. SCHLLITER: Vergleiche der DÖDOC-Ergebnisse (Deutscher Anteil) mit terrestrischen Koordinaten. Deutsche Geodätische Kommission, Rep. B 260, Munich 1982, pp. 91–111.
R. SIGL: Neuberechnung der geopotentiellen Kotenunterschiede mit Hilfe der Normalschwere für den westdeutschen Anteil am REUN. Deutsche Geodäitische Kommission, Rep. B 78, Munich 1961.
R. SIGL, W. TORGE, H. BEETZ and K. STUBER: Das Schweregrundnetz 1976 der Bundesrepublik Deutschland (DSGN 76). Tell I. Deutsche Geodätische Kommission, Rep. B 254, Munich 1981, pp. 7–16.
W.E. STRANGE: An Evaluation of Orthometric Height Accuracy Using Bore Hole Gravimetry. Bull. Géod. 56 (1982), pp. 300–311.
W. TORGE: Geodesy. An Introduction. W. de Gruyter, Berlin/New York 1980.
W. TORGE: Zum Aufbau von Schwerebezugssystemen. Deutsche Geodätische Kommission, Rep. B 287, Munich 1988, pp. 207–217.
U.A. UOTILA: Some Analyses of Absolute and Relative Gravity Measurements in the U.S.A. BGI Bull. d'Information No. 51, 1982, pp. 69–76.
P. VANI>CEK and E. KRAKIWSKY: Geodesy. The Concepts. North Holland Publ. Co., 2nd edition 1986.
E.B. WADE: Impact of North American Datum of 1983. J. Surveying Engineering, Surv. and Mapping Division, Vol. 112 (1986), pp. 49–62.
J. ZEGER: Aufbau eines neuen Höhensystems in Österreich. Allgemeine Vermessungs-Nachrichten 92 (1985), pp. 299–310.
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Heck, B. An evaluation of some systematic error sources affecting terrestrial gravity anomalies. Bull. Geodesique 64, 88–108 (1990). https://doi.org/10.1007/BF02530617
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DOI: https://doi.org/10.1007/BF02530617