Abstract
Geodesy, with its three core areas positioning and reference systems, Earth rotation determination, and gravity field modeling, is striving for a relative accuracy of at least 10−9 for all relevant quantities, and to a great extent this goal has already been reached (10−9 corresponds to about 6 mm relative to the Earth’s radius and \( 10^{ - 8} \,{\text{ms}}^{ - 2} = 1\,\upmu {\text{Gal}} \) in terms of gravity). Regarding gravity field modeling, the highest accuracy demands are from geodesy, especially Global Navigation Satellite System (GNNS) positioning, oceanography, and geophysics. In this context, the geoid and quasigeoid are of major interest; e.g., these quantities are required for the transformation between the purely geometric GNSS (ellipsoidal) heights and gravity field related heights as well as for the modeling of the (mean) dynamic ocean topography (DOT), requiring accuracies at the level of about 1 cm or even below. In this way, the importance of geoid and quasigeoid modelling has increased considerably—also for economic reasons—and as early as 1982 Torge (1982) postulated a “renaissance of the geoid.”
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Ågren J, Svensson R (2007) Postglacial land uplift model and system definition for the new Swedish height system RH 2000. Reports in geodesy and geographical information systems, Lantmateriet, Gävle
Andersen EG (1976) The effect of the topography on solution of Stokes’ problem. Unisurv S-14, Sydney
Andersen EG, Rizos C, Mather RS (1975) Atmospheric effects in physical geodesy. Unisurv G-23, Sydney, pp 23–41
Andersen OB, Knudsen P, Berry PAM (2010) The DNSC08GRA global marine gravity field from double retracked satellite altimetry. J Geod 84:191–199
Andersen OB, Knudsen P, Trimmer R (2005) Improved high resolution altimetric gravity field mapping (KMS2002 global marine gravity field). In: Sansò F (ed) A window on the future of geodesy, IAG symposia, vol 128. Springer-Verlag, Berlin, Heidelberg, pp 326–331
Angermann D, Seitz M, Drewes H (2012) Global terrestrial reference systems and their realizations. Sciences of geodesy—II, this volume. Springer-Verlag, Berlin, Heidelberg
Bäumker M (1984) Zur dreidimensionalen Ausgleichung von terrestrischen und Satellitenbeobachtungen. Wiss. Arb. d. Fachr. Verm.wesen d. Univ. Hannover, Nr. 130, Hannover
Behrend D (1999) Untersuchungen zur Schwerefeldbestimmung in den europäischen Randmeeren. Wiss. Arb. d. Fachr. Verm.wesen d. Univ. Hannover, Nr. 229, Hannover
Bian S (1997) Some cubature formulas for singular integrals in physical geodesy. J Geod 71:443–453
BIPM (2006) Le Système international d’unités—The International System of Units (SI), 8th edn. Bureau international des poids et measures, Sèvres, France
Bosch W, Savcenko R (2010) On estimating the dynamic ocean topography—a profile based approach. In: Mertikas SP (ed) Gravity, geoid and earth observation, IAG symposia, vol 135. Springer-Verlag, Berlin, Heidelberg, pp 263–269
Bürki B, Müller A, Kahle H-G (2004) DIADEM: the new digital astronomical deflection measuring system for high-precision measurements of deflections of the vertical at ETH Zurich. In: Proceedings of gravity, geoid and space missions, GGSM 2004, IAG symposia, Porto, Portugal, 30 Aug–3 Sept (CD)
Bursa M, Groten E, Kenyon S, Kouba J, Radej K, Vatrt V, Voytiskova M (2002) Earth’s dimension specified by geoidal potential. Stud Geophys Geod 46:1–8
Bursa M, Kenyon S, Kouba J, Radej K, Vatrt V, Voytiskova M (2001) In: Drewes H, Dodson A, Fortes LPS, Sanchez L, Sandoval P (eds) Vertical reference system, IAG symposia, vol 124. Springer-Verlag, Berlin, Heidelberg, pp 291–296
Campbell J (1971) Eine Erweiterung der Theorie des astronomischen Nivellements bei Einbeziehung von Schweremessungen. Wiss. Arb. d. Lehrstühle f. Geodäsie, Photogrammetrie und Kartographie a. d. Techn. Univ. Hannover, Nr. 49, Hannover
Cazenave A, Chen J (2010) Time-variable gravity from space and present-day mass redistribution in the earth system. Earth Planet Sci Lett 298:263–274
Christie RR (1994) A new geodetic heighting strategy for Great Britain. Surv Rev 32:328–343
Christodoulidis DC (1979) Influence of the atmospheric masses on the gravitational field of the Earth. Bull Géod 53:61–77
Condi F, Wunsch C (2004) Gravity field variability, the geoid, and ocean dynamics. In: Sansò F (ed) V Hotine-Marussi symposium on mathematical geodesy, IAG symposia, vol 127. Springer-Verlag, Berlin, Heidelberg, pp 285–292
Demianov GV, Majorov AN (2004) On the definition of a common world normal height system. In: Physical geodesy, scientific and technical reports on geodesy, photogrammetry and cartography, Federal Office of Geodesy and Cartography (Roskartographia), ZNIIGAiK, Moscow, pp 168–182 (in Russian)
Denker H (1988) Hochauflösende regionale Schwerefeldbestimmung mit gravimetrischen und topographischen Daten. Wiss. Arb. d. Fachr. Verm.wesen d. Univ. Hannover, Nr. 156, Hannover
Denker H (1989) A new gravimetric quasigeoid for the Federal Republic of Germany. Deutsche Geodät. Komm., Reihe B, Nr. 291, München
Denker H (1998) Evaluation and improvement of the EGG97 quasigeoid model for Europe by GPS and leveling data. In: Vermeer M, Ádám J (eds) Second continental workshop on the geoid in Europe, Proceedings Rep. Finnish Geod. Inst., vol 98, issue 4, Masala, pp 53–61
Denker H (2001) On the effect of datum inconsistencies in gravity and position on Europen geoid computations. Poster, IAG 2001 scientific assembly, 2–7 Sept 2001, Budapest
Denker H (2003) Computation of gravity gradients over Europe for calibration/validation of GOCE data. In: Tziavos IN (ed) Gravity and geoid 2002, 3rd Meeting of the Internat. Gravity and Geoid Commission, Ziti Editions, Thessaloniki, pp 287–292
Denker H (2005) Evaluation of SRTM3 and GTOPO30 terrain data in Germany. In: Jekeli C, Bastos L, Fernandes J (eds) Gravity, geoid and space missions, IAG symposia, vol 129. Springer-Verlag, Berlin, Heidelberg, pp 218–223
Denker H, Barriot J-P, Barzaghi R, Fairhead D, Forsberg R, Ihde J, Kenyeres A, Marti U, Sarrailh M, Tziavos IN (2009) The development of the European gravimetric geoid model EGG07. In: Sideris MG (ed) Observing our changing earth, IAG symposia, vol 133. Springer-Verlag, Berlin, Heidelberg, pp 177–186
Denker H, Barriot J-P, Barzaghi R, Forsberg R, Ihde J, Kenyeres A, Marti U, Tziavos IN (2005) Status of the European gravity and geoid project EGGP. In: Jekeli C, Bastos L, Fernandes J (eds) Gravity, geoid and space missions, IAG symposia, vol 129. Springer-Verlag, Berlin, Heidelberg, pp 125–130
Denker H, Roland M (2005) Compilation and evaluation of a consistent marine gravity data set surrounding Europe. In: Sansò F (ed) A window on the future of geodesy, IAG symposia, vol 128. Springer-Verlag, Berlin, Heidelberg, pp 248–253
Denker H, Torge W (1998) The European gravimetric quasigeoid EGG97—An IAG supported continental enterprise. In: Forsberg R, Feissel M, Dietrich R (eds) Geodesy on the move—Gravity, geoid, geodynamics and Antarctica, IAG symposia, vol 119. Springer-Verlag, Berlin, Heidelberg, pp 249–254
Denker H, Tziavos IN (1999) Investigation of the Molodensky series terms for terrain reduced gravity field data. Boll Geof Teor Appl 40:195–203
Denker H, Wenzel H-G (1987) Local geoid determination and comparison with GPS results. Bull Géod 61:349–366
Duquenne H, Duquenne F, Rebischung P (2007) New scientific levelling network NIREF. Data set and internal report, prepared for European gravity and geoid project (EGGP)
Ecker E, Mittermayer E (1969) Gravity corrections for the influence of the atmosphere. Boll Geof Teor Appl 11:70–80
Eeg J, Krarup T (1973) Integrated geodesy. The Danish Geodetic Institute, Internal Rep. No. 7, Copenhagen
Ekman M (1989a) The impact of geodynamic phenomena on systems for height and gravity. In: Andersen OB (ed) Modern techniques in geodesy and surveying, National Survey and Cadastre, KMS, Denmark, Publ. 4. Series vol. 1. Copenhagen, Denmark, pp 109–167
Ekman M (1989b) Impacts of geodynamic phenomena on systems for height and gravity. Bull Géod 63:281–296
Ekman M (1996) The permanent problem of the permanent tide: what to do with it in geodetic reference systems? Marées Terrestres. Bull d’Inf 125:9508–9513 (Bruxelles)
Elhabiby M, Sampietro D, Sansò F, Sideris MG (2009) BVP, global models and residual terrain correction. In: Sideris MG (ed) Observing our changing earth, IAG symposia, vol 133. Springer-Verlag, Berlin, Heidelberg, pp 211–217
ESA (1999) Gravity field and steady-state ocean circulation mission. Reports for mission selection, the four candidate earth explorer core missions, ESA SP-1233(1)
Featherstone WE, Kirby JF, Hirt C, Filmer MS, Claessens SJ, Brown NJ, Hu G, Johnston GM (2011) The AUSGeoid09 model of the Australian height datum. J Geod 85:133–150
Flechtner F, Thomas M, Dobslaw H (2010) Improved non-tidal atmospheric and oceanic de-aliasing for GRACE and SLR satellites. In: Flechtner F, Gruber Th, Güntner A, Mandea M, Rothacher M, Schöne T, Wickert J (eds) System earth via geodetic-geophysical space techniques, advanced technologies in earth sciences. Springer-Verlag, Berlin, pp 131–142
Flury J, Rummel R (2009) On the geoid-quasigeoid separation in mountain areas. J Geod 83:829–847
Forsberg R (1984) A study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modeling. Report Department of Geodetic Science, no 355, The Ohio State University, Columbus, Ohio, USA
Forsberg R (1987) A new covariance model for inertial gravimetry and gradiometry. J Geophys Res B 92:1305–1310
Forsberg R (1993) Modelling of the fine-structure of the geoid: methods, data requirements and some results. Surv Geophys 14:403–418
Forsberg R (2010) Geoid determination in the mountains using ultra-high resolution spherical harmonic models—the Auvergne case. In: Contadakis ME, Kaltsikis C, Spatalas S, Tokmakidis K, Tziavos IN (eds) The apple of the knowledge, In Honor of Professor Emeritus Demetrius N. Arabelos, pp 101–111. Ziti Editions (ISBN: 978-960-243-674-5), Thessaloniki
Forsberg R, Kenyon S (2004) Gravity and geoid in the Arctic region—the northern GOCE polar gap filled. In: Proceedings of 2nd international GOCE workshop, Esrin, 8–10 March 2004, CD-ROM
Forsberg R, Tscherning CC (1981) The use of height data in gravity field approximation. J Geophys Res B 86:7843–7854
Forsberg R, Tscherning CC (1997) Topographic effects in gravity field modelling for BVP. In: Sansò F, Rummel R (eds) Geodetic boundary value problems in view of the one centimeter geoid, Lecture notes in earth sciences, vol 65. Springer-Verlag, Berlin, Heidelberg, pp 241–272
Förste C, and 12 others (2008a) The GeoForschungsZentrum Potsdam/Groupe de Recherche de Gèodésie Spatiale satellite-only and combined gravity field models: EIGEN-GL04S1 and EIGEN-GL04C. J Geod 82:331–346
Förste C, and 12 others (2008b) EIGEN-GL05C—a new global combined high-resolution GRACE-based gravity field model of the GFZ-GRGS cooperation. In: General assembly European Geosciences Union (Vienna, Austria 2008), Geophysical research abstracts, vol 10, Abstract No. EGU2008-A-06944
Gitlein O, Timmen L (2006) Atmospheric mass flow reduction for terrestrial absolute gravimetry in the Fennoscandian land uplift network. In: Tregoning P, Rizos C (eds) Dynamic planet, IAG symposia, vol 130. Springer-Verlag, Berlin, Heidelberg, pp 461–466
Goad CC, Tscherning CC, Chin MM (1984) Gravity empirical covariance values for the continental United States. J Geophys Res B 89:7962–7968
Grafarend EW (1978a) The definition of the telluroid. Bull Géod 52:25–37
Grafarend EW (1978b) Operational geodesy. In: Moritz H, Sünkel H (eds) Approximation methods in geodesy, Sammlung Wichmann, Neue Folge, Bd. 10, H. Wichmann Verlag, Karlsruhe, pp 235–284
Grafarend EW (1988) The geometry of the Earth’s surface and the corresponding function space of the terrestrial gravitational field. In: Festschrift Rudolf Sigl zum 60. Geburtstag, Deutsche Geod. Komm., Reihe B, Heft Nr. 287, pp 76–94 (München)
Grote T (1996) Regionale Quasigeoidmodellierung aus heterogenen Daten mit “cm”-Genauigkeit. Wiss. Arb. d. Fachr. Verm.wesen d. Univ. Hannover, Nr. 212, Hannover
Haagmans R, de Min E, von Gelderen M (1993) Fast evaluation of convolution integrals on the sphere using 1D FFT, and a comparison with existing methods for Stokes’ integral. Manuscripta geodaetica 18:227–241
Haagmans R, Prijatna K, Omang O (2003) An alternative concept for validation of GOCE gradiometry results based on regional gravity. In: Tziavos IN (ed) Gravity and geoid 2002, 3rd meeting of the Internat. Gravity and Geoid commission, pp 281–286, Ziti Editions, Thessaloniki
Heck B (1986) A numerical comparison of some telluroid mappings. In: Proceedings of I Hotine-Marussi symposium on mathematical geodesy (Roma, 3–6 June 1985), vol. 1. Milano, pp 19–38
Heck B (1990) An evaluation of some systematic error sources affecting terrestrial gravity anomalies. Bull Géod 64:88–108
Heck B (1991) On the linearized boundary value problems of physical geodesy. Report Department of Geodetic Science and Surveying, no 407, The Ohio State University, Columbus, Ohio, USA
Heck B (1997) Formulation and linearization of boundary value problems: from observables to a mathematical model. In: Sansò F, Rummel R (eds) Geodetic boundary value problems in view of the one centimeter geoid, Lecture notes in earth sciences, vol 65. Springer-Verlag, Berlin, Heidelberg, pp 121–160
Heck B (2003) Rechenverfahren und Auswertemodelle der Landesvermessung—Klassische und moderne Methoden, 3rd edn. Wichmann Verlag, Heidelberg
Heck B (2004) Problems in the definition of vertical reference frames. In: Sansò F (ed) V Hotine-Marussi symposium on mathematical geodesy, IAG symposia, vol 127. Springer-Verlag, Berlin, Heidelberg, pp 164–173
Heck B, Rummel R (1990) Strategies for solving the vertical datum problem using terrestrial and satellite geodetic data. In: Sünkel H, Baker T (eds) Sea surface topography and the geoid, IAG symposia, vol 104. Springer-Verlag, Berlin, Heidelberg, pp 116–128
Heck B, Seitz K (2007) A comparison of the tesseroid, prism and point-mass approaches for mass reductions in gravity field modeling. J Geod 81:121–136
Hein GW (1986) Integrated geodesy—state-of-the-art 1986 reference text. In: Sünkel H (ed) Mathematical and numerical techniques in physical geodesy, lecture notes in earth sciences, vol 7. Springer-Verlag, Berlin, Heidelberg, pp 505–548
Heiskanen WA, Moritz H (1967) Physical geodesy. W.H. Freeman and Company, San Francisco
Hipkin RG (2004) Ellipsoidal geoid computation. J Geod 78:167–179
Hipkin R, Haines K, Beggan C, Bingley R, Hernandez F, Holt J, Baker T (2004) The geoid EDIN2000 and mean sea surface topography around the British Isles. Geophys J Int 157:565–577
Hirt C (2004) Entwicklung und Erprobung eines digitalen Zenitkamerasystems für die hochpräzise Lotabweichungsbestimmung. Wiss. Arb. d. Fachr. Verm.wesen d. Univ. Hannover, Nr. 253, Hannover
Hirt C, Feldmann-Westendorff U, Denker H, Flury J, Jahn C-H, Lindau A, Seeber G, Voigt C (2008) Hochpräzise Bestimmung eines astrogeodätischen Quasigeoidprofils im Harz für die Validierung des Quasigeoidmodells GCG05. Zeitschrift f. Verm.wesen (zfv) 133:108–119
Hirt C, Flury J (2008) Astronomical-topographic levelling using high-precision astrogeodetic vertical deflections and digital terrain model data. J Geod 82:231–248
Hirt C, Seeber G (2008) Accuracy analysis of vertical deflection data observed with the Hannover digital zenith camera system TZK2-D. J Geod 82:347–356
Hirt C, Schmitz M, Feldmann-Westendorff U, Wübbena G, Jahn C-H, Seeber G (2010) Mutual validation of GNSS height measurements from high-precision geometric-astronomical levelling. GPS Solutions 15:149–159
Hotine M (1969) Mathematical geodesy. ESSA Monograph 2, U.S. Department of Commerce, Washington
IAG (1970) Geodetic reference system 1967. Publ. Spéciale du Bull Géod, Paris
IAG (1984) Resolutions of the XVIII general assembly of the International Association of Geodesy, Hamburg, Germany, 15–27 Aug 1983. J Geod 58:309–323
IERS (2010) IERS conventions (2010). In: Petit G, Luzum B (eds) IERS technical note no. 36, Verlag des Bundesamtes für Kartographie und Geodäsie, Frankfurt am Main
Ihde J (2009) Inter-commission project 1.2: vertical reference frames. In: Drewes H, Hornik H (eds) International Association of Geodesy, Travaux, vol 36
Ihde J, Adam J, Gurtner W, Harsson BG, Sacher M, Schlüter W, Wöppelmann G (2000) The height solution of the European vertical reference network (EUVN). Veröff. Bayer. Komm. für die Internat. Erdmessung, Astronom. Geod. Arb., Nr. 61, München pp 132–145
Ihde J, Mäkinen J, Sacher M (2008) Conventions for the definition and realization of a European vertical reference system (EVRS)—EVRS conventions 2007. EVRS conventions V5.1, Bundesamt für Kartographie und Geodäsie, Finnish Geodetic Institute, publication date 17 Dec 2008
Ihde J, Sanchez L (2005) A unified global height reference system as a basis for IGGOS. J Geodyn 40:400–413
Ihde J, Wilmes H, Müller J, Denker H, Voigt C, Hosse M (2010) Validation of satellite gravity field models by regional terrestrial data sets. In: Flechtner F, Gruber Th, Güntner A, Mandea M, Rothacher M, Schöne T, Wickert J (eds) System earth via geodetic-geophysical space techniques, advanced technologies in earth sciences. Springer-Verlag, Berlin, pp 277–296
Jekeli C (1983) A numerical study of the divergence of the spherical harmonic series of the gravity and height anomalies at the Earth’s surface. Bull Géod 57:10–28
Jekeli C (2009) Potential theory and static gravity field of the Earth. In: Herring T (vol ed) Treatise on geophysics, vol 3, Geodesy. Elsevier, Amsterdam, pp 11–42
Jekeli C, Yang HJ, Kwon JH (2009) Evaluation of EGM08—globally and locally in South Korea. In: External quality evaluation reports of EGM08, Newton’s Bulletin, vol 4, pp 38–49
JPL (2007) SRTM—The mission to map the world. Jet Propulsion Laboratory, California Institute of Technology. http://www2.jpl.nasa.gov/srtm/index.html
Kaula WM (1966) Theory of satellite geodesy. Blaisdell Publ. Comp., Waltham (Mass.)
Kellog OD (1953) Foundations of potential theory. Dover Publ. Inc., New York
Kelsey J (1972) Geodetic aspects concerning possible subsidence in Southeastern England. Phil Trans R Soc Lond 272:141–149. doi:10.1098/rsta.1972.0040
Kenyeres A, Sacher M, Ihde J, Denker H, Marti U (2010) EUVN Densification action—final report. http://www.bkg.bund.de/nn_166762/geodIS/EVRS/EN/Projects/02EUVN-DA/01Introduction/introduction__node.html__nnn=true
Kern M (2004) A comparison of data weighting methods for the combination of satellite and local gravity data. In: Sansò F (ed) V Hotine-Marussi Symposium on mathematical geodesy, IAG symposia, vol 127. Springer-Verlag, Berlin, Heidelberg, pp 137–144
Kovalevsky J, Seidelmann PK (2004) Fundamentals of astrometry. Cambridge University Press, Cambridge
Krarup T (1969) A contribution to the mathematical foundation of physical geodesy. Geodætisk Institut, Meddelelse No. 44, Copenhagen
Kumar M (2005) When ellipsoidal heights will do the job, why look elsewhere? Surv Land Inf Sci 65:91–94
Kurtenbach E, Mayer-Gürr T, Eicker A (2009) Deriving daily snapshots of the Earth’s gravity field from GRACE L1B data using Kalman filtering. Geophys Res Lett 36:L17102. doi:10.1029/2009GL039564
Lemoine FG, and 14 others (1998) The development of the joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) geopotential model EGM96. NASA/TP-1998-206861, Greenbelt, MD, USA
Li YC, Sideris MG, Schwarz K-P (1995) A numerical investigation on height anomaly prediction in mountainous areas. Bull Géod 69:143–156
Liebsch G, Schirmer U, Ihde J, Denker H, Müller J (2006) Quasigeoidbestimmung für Deutschland. DVW-Schriftenreihe 49:127–146
MacMillan WD (1958) Theoretical mechanics, vol 2., The theory of the potential. Dover Publ. Inc., New York
Mäkinen J, Ihde J (2009) The permanent tide in height systems. In: Sideris MG (ed) Observing our changing earth, IAG symposia, vol 133. Springer-Verlag, Berlin, Heidelberg, pp 81–87
Marti U, Schlatter A (2001) The new height system in Switzerland. In: Drewes H, Dodson A, Fortes LPS, Sanchez L, Sandoval P (eds) Vertical reference system, IAG symposia, vol 124. Springer-Verlag, Berlin, Heidelberg, pp 50–55
Marussi A (1985) Intrinsic geodesy. Springer-Verlag, Berlin
Mayer-Gürr T (2006) Gravitationsfeldbestimmung aus der Analyse kurzer Bahnbögen am Beispiel der Satellitenmissionen CHAMP und GRACE. Dissertation, University of Bonn
Mayer-Gürr T, Kurtenbach E, Eicker A (2010) ITG-Grace2010 gravity field model. URL: www.igg.uni-bonn.de/apmg/index.php
Meschkowski H (1962) Hilbertsche Räume mit Kernfunktionen. Springer-Verlag, Berlin
Mohr PJ, Taylor BN, Newell DB (2008) CODATA recommended values of the fundamental physical constants: 2006. Rev Mod Phys 80:633–730
Molodenskii MS, Eremeev VF, Yurkina MI (1962) Methods for study of the external gravitational field and figure of the Earth. Translation of the Russian Book, Israel Program for Scientific Translations, Jerusalem
Morelli C, Pisani M, Gantar C (1975) Geophysical anomalies and tectonics in the Western Mediterranean. Boll Geof Teor Appl 18(67):211–249 (Trieste)
Moritz H (1962) Interpolation and prediction of gravity and their accuracy. Report Department of Geodetic Science, no. 24, The Ohio State University, Columbus, Ohio, USA
Moritz H (1971) Kinematical geodesy II. Report Department of Geodetic Science, no. 165, The Ohio State University, Columbus, Ohio, USA
Moritz H (1976) Integral formulas and collocation. Manuscripta Geod 1:1–40
Moritz H (1980) Advanced physical geodesy. Wichmann, Karlsruhe
Moritz H (2000) Geodetic reference system 1980. J Geod 74:128–133
Morse PM, Feshbach H (1953) Methods of theoretical physics. McGraw-Hill, New York
Müller J, Soffel M, Klioner SA (2008) Geodesy and relativity. J Geod 82:133–145
NIMA (1997) Department of Defense World Geodetic System 1984—its definition and relationships with local geodetic datums. NIMA National Imagery and Mapping Agency, Technical Report, NIMA TR8350.2, 3rd Edition, 4 July 1997 (Amendment 1, 3 Jan. 2000; Amendment 2, 23 June 2004)
NIMA (2002) Addendum to NIMA TR 8350.2: implementation of the World Geodetic System 1984 (WGS 84) reference frame G1150. http://earth-info.nga.mil/GandG/publications/tr8350.2/tr8350_2.html
Omang OCD, Tscherning CC, Forsberg R (2012) Generalizing the harmonic reduction procedure in residual topographic modeling. In: Sneeuw N, Novák P, Crespi M, Sansò F (eds) VII Hotine-Marussi symposium on mathematical geodesy, IAG symposia, vol 137. Springer-Verlag, Berlin, Heidelberg, pp 233–238
Pail R, Bruinsma S, Migliaccio F, Foerste C, Goiginger H, Schuh W-D, Hoeck E, Reguzzoni M, Brockmann JM, Abrikosov O, Veicherts M, Fecher T, Mayrhofer R, Krasbutter I, Sansò F, Tscherning CC (2011) First GOCE gravity field models derived by three different approaches. J Geod 85:819–843
Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2008) An earth gravitational model to degree 2160: EGM2008. Presentation, 2008 general assembly of the European Geosciences Union, Vienna, Austria, 13–18 Apr 2008
Poutanen M, Vermeer M, Mäkinen J (1996) The permanent tide in GPS positioning. J Geod 70:499–504
Rapp RH (I983a) The need and prospects for a world vertical datum. In: Proceedings lAG symposia, IUGG XVIII General Assembly, Hamburg, FRG, 1983, vol 2. Report Department of Geodetic Science and Surveying. The Ohio State University, Columbus, Ohio, USA, pp 432-445
Rapp RH (1983b) Tidal gravity computations based on recommendations of the standard earth tide committee. Bull. d’Inf., Marées Terrestres 89: 5814–5819 (Bruxelles)
Rapp RH (1995) A world vertical datum proposal. Allg Verm Nachr 102:297–304
Rapp RH (1997) Use of potential coefficient models for geoid undulation determinations using a spherical harmonic representation of the height anomaly/geoid undulation difference. J Geod 71:282–289
Rapp RH, Balasubramania N (1992) A conceptual formulation of a world height system. Report Department of Geodetic Science and Surveying, no. 421. The Ohio State University, Columbus, Ohio, USA
Rapp RH, Nerem RS, Shum CK, Klosko SM, Williamson RG (1991) Consideration of permanent tidal deformation in the orbit determination and data analysis for the Topex/Poseidon mission. NASA Technical Memorandum 100775, Goddard Space Flight Center, Greenbelt, MD, USA
Rebischung P, Duquenne H, Duquenne F (2008) The new French zero-order levelling network—first global results and possible consequences for UELN. EUREF 2008 symposium, Brussels, Belgium, 18–21 June 2008
Rummel R (1988) Zur iterativen Lösung der geodätischen Randwertaufgabe. In: Festschrift Rudolf Sigl zum 60. Geburtstag, Deutsche Geod. Komm., Reihe B, Heft Nr. 287, pp 175–181 (München)
Rummel R (1995) The first degree harmonics of the Stokes problem—what are the practical implications? In: Festschrift E. Groten on the occasion of his 60th anniversary, pp 98–106 (Munich)
Rummel R (1997) Spherical spectral properties of the Earth’s gravitational potential and its first and second derivatives. In: Sansò F, Rummel R (eds) Geodetic boundary value problems in view of the one centimeter geoid, lecture notes in earth sciences, vol 65. Springer-Verlag, Berlin, Heidelberg, pp 359–404
Rummel R, Rapp RH (1976) The influence of the atmosphere on geoid and potential coefficient determinations from gravity data. J Geophys Res 81:5639–5642
Rummel R, Teunissen P (1988) Height datum definition, height datum connection and the role of the geodetic boundary value problem. Bull Géod 62:477–498
Rummel R, van Gelderen M (1995) Meissl scheme—spectral characteristics of physical geodesy. Manuscripta Geod 20:379–385
Rummel R, Weijong Y, Stummer C (2011) GOCE gravitational gradiometry. J Geod 85:777–790
Sanchez L (2008) Approach for the establishment of a global vertical reference level. In: Xu P, Liu J, Dermanis A (eds) VI Hotine-Marussi symposium on theoretical and computational geodesy, IAG symposia, vol 132. Springer-Verlag, Berlin, Heidelberg, pp 119–125
Sandwell DT, Smith WHF (2009) Global marine gravity from retracked Geosat and ERS-1 altimetry: ridge segmentation versus spreading rate. J Geophys Res B 114:B01411. doi:10.1029/2008JB006008
Sansò F (1986) Statistical methods in physical geodesy. In: Sünkel H (ed) Mathematical and numerical techniques in physical geodesy, lecture notes in earth sciences, vol 7. Springer-Verlag, Berlin, Heidelberg, pp 49–155
Sansò F (1995) The long road from measurements to boundary value problems in physical geodesy. Manuscripta Geod 20:326–344
Sansò F, Tscherning CC (2003) Fast spherical collocation: theory and examples. J Geod 77:101–112
Schwarz KP, Sideris MG, Forsberg R (1990) The use of FFT techniques in physical geodesy. Geophys J Int 100:485–514
Seitz K (1997) Ellipsoidische und topographische Effekte im geodätischen Randwertproblem. Deutsche Geod. Komm., Reihe C, Nr. 483, München
Sideris MG (1987) Spectral methods for the numerical solution of Molodensky’s problem. UCSE Reports, No. 20024, Department of Surveying Engineering, The University of Calgary
Sideris MG (1994) Regional geoid determination. In: Vanicek P, Christou NT (eds) Geoid and its geophysical interpretations. CRC Press, Inc, Boca Raton, FL, USA, pp 77–94
Sideris MG (2011a) Geoid determination, theory and principles. In: Gupta HK (ed) Encyclopedia of Solid Earth Geophysics. Springer-Verlag, Berlin, Heidelberg, pp 356–362
Sideris MG (2011b) Geoid, computational method. In: Gupta HK (ed) Encyclopedia of Solid Earth Geophysics. Springer-Verlag, Berlin, Heidelberg, pp 366–371
Sigl R (1985) Introduction to potential theory. Abacus Press in association with H. Wichmann Verlag
Sjöberg L (1980) Least squares combination of satellite harmonics and integral formulas in physical geodesy. Gerlands Beitr. d. Geophysik 89:371–377
Sjöberg L (1981) Least squares spectral combination of satellite and terrestrial data in physical geodesy. Annales de Géophysique 37:25–30
Sjöberg LE (2003) A general model for modifying Stokes’ formula and its least-squares solution. J Geod 77:459–464
Sjöberg LE (2010) A strict formula for geoid-to-quasigeoid separation. J Geod 84:699–702
Sjöberg LE, Nahavandchi H (2000) The atmospheric geoid effects in Stokes’ formula. Geophys J Int 140:95–100
Smith DA, Roman DR (2001) GEOID99 and G99SSS: 1-arc-minute geoid models for the United States. J Geod 75:469–490
Smith D, Véronneau M, Roman D, Huang JL, Wang YM, Sideris M (2010) Towards the unification of the vertical datums over the North American continent. IAG Commission 1 symposium 2010, reference frames for applications in geosciences (REFAG2010), Marne-La-Vallée, France, 4–8 Oct 2010
Steinberg G, Papo H (1998) Ellipsoidal heights: the future of vertical geodetic control. GPS World 9(2):41–43
Strange WE (1982) An evaluation of orthometric height accuracy using bore hole gravimetry. Bull Géod 56:300–311
Sünkel H (1983) The geoid in Austria. In: Proceedings IAG symposia, IUGG XVIII General Assembly, Hamburg, FRG, 1983, vol 1. Report Department of Geodetic Science and Surveying, The Ohio State University, Columbus, Ohio, USA, pp 348–364
Tapley BD, Bettadpur S, Ries JC, Thompson PF, Watkins M (2004a) GRACE measurements of mass variability in the earth system. Science, vol 305, issue 5683, pp 503–505, 23 July 2004
Tapley BD, Bettadpur S, Watkins M, Reigber C (2004b) The gravity recovery and climate experiment: mission overview and early results. Geophys Res Lett 31(9):L09607. doi:10.1029/2004GL019920
Tapley B, Ries J, Bettadpur S, Chambers D, Cheng M, Condi F, Poole S (2007) The GGM03 mean earth gravity model from GRACE. Eos Trans. AGU, vol 88(52), Fall Meeting Supplement, Abstract G42A-03
Tenzer R, Vaníček P, Santos M, Featherstone WE, Kuhn M (2005) The rigorous determination of orthometric heights. J Geod 79:82–92
Timmen L (2010) Absolute and relative gravimetry. In: Xu G (ed) Sciences of geodesy—I, advances and future directions. Springer-Verlag, Berlin, pp 1–48
Torge W (1977) Untersuchungen zur Höhen- und Geoidbestimmung im dreidimensionalen Testnetz Westharz. Zeitschrift f. Verm.wesen (zfv) 102:173–186
Torge W (1982) Zur Geoidbestimmung im Meeresbereich. In: Geodaesia Universalis—Festschrift Karl Rinner zum 70. Geburtstag, Mitt. Geod. Inst. T.U. Graz, Folge 40, pp 346–355
Torge W (1989) Gravimetry. W. de Gruyter, Berlin
Torge W (2001) Geodesy, 3rd edn. W. de Gruyter, Berlin
Torge W, Denker H (1998) The European geoid—development over more than 100 years and present status. In: Vermeer M, Ádám J (eds) Second continental workshop on the geoid in Europe, Proceedings Rep. Finnish Geod. Inst., vol 98, issue 4, Masala, pp 47–52
Torge W, Röder RH, Schnüll M, Wenzel H-G, Faller JE (1987) First results with the transportable absolute gravity meter JILAG-3. Bull Géod 61:161–176
Torge W, Weber G, Wenzel H-G (1982) Computation of a high resolution European geoid (EGG1). In: Proceedings of 2nd international symposium on the geoid in Europe and Mediterranian area, Rome. Istituto Geografico Militare, Italy, Florence, pp 437–460
Tscherning CC (1976a) Computation of second-order derivatives of the normal potential based on the representation by a Legendre series. Manuscripta Geod 1:71–92
Tscherning CC (1976b) On the chain-rule method for computing potential derivatives. Manuscripta Geod 1:125–141
Tscherning CC (1985) Local approximation of the gravity potential by least squares collocation. In: Schwarz KP (ed) Proceedings of international summer school on local gravity field approximation, Beijing, 21 Aug–4 Sept 1984, The University of Calgary, Publ. 60003, pp 277−361
Tscherning CC (1986) Functional methods for gravity field approximation. In: Sünkel H (ed) Mathematical and numerical techniques in physical geodesy. Lecture notes in earth sciences, vol 7. Springer-Verlag, Berlin, Heidelberg, pp 3–47
Tscherning CC (1994) Geoid determination by least-squares collocation using GRAVSOFT. In: International school for the determination and use of the geoid. Lecture notes, Milan, 10–15 Oct 1994, pp 135–164
Tscherning CC (2004) A discussion of the use of spherical approximation or no approximation in gravity field modeling with emphasis on unsolved problems in least-squares collocation. In: Sansò F (ed) V Hotine-Marussi symposium on mathematical geodesy, IAG symposia, vol 127. Springer-Verlag, Berlin, Heidelberg, pp 184–188
Tscherning CC, Rapp RH (1974) Closed covariance expressions for gravity anomalies, geoid undulations, and deflections of the vertical implied by anomaly degree variance models. Report Department of Geodetic Science, no. 208, The Ohio State University, Columbus, Ohio, USA
USGS (2007) Global 30 arc-second elevation data set GTOPO30. U.S. Geological Survey, Center for Earth Resources Observation and Science (EROS). http://edc.usgs.gov/products/elevation/gtopo30/gtopo30.html
Vaníček P (1998) The height of reason (a letter to the editor). GPS World 9(4):14
Véronneau M, Duvai R, Huang J (2006) A gravimetric geoid model as a vertical datum in Canada. Geomatica 60:165–172
Véronneau M, Huang J (2007) The Canadian gravimetric geoid model 2005 (CGG2005). Report, Geodetic Survey Division, Earth Sciences Sector, Natural Resources Canada, Ottawa, Canada
Wahr JM (2009) Time variable gravity from satellites. In: Herring T (vol ed) Treatise on geophysics, vol 3, geodesy. Elsevier, Amsterdam, pp 213–237
Wang YM, Saleh J, Li X, Roman DR (2011) The US Gravimetric geoid of 2009 (USGG2009): model development and evaluation. J Geod. doi:10.1007/s00190-011-0506-7
Weber G (1984) Hochauflösende Freiluftanomalien und gravimetrische Lotabweichungen für Europa. Wiss. Arb. d. Fachr. Verm.wesen d. Univ. Hannover, Nr. 135, Hannover
Wenzel HG (1981) Zur Geoidbestimmung durch Kombination von Schwereanomalien und einem Kugelfunktionsmodell mit Hilfe von Integralformeln. Zeitschrift f. Verm.wesen (zfv) 106:102–111
Wenzel HG (1982) Geoid computation by least squares spectral combination using integral formulas. In: Proceedings of general meeting of the IAG, Tokyo, 7–15 May 1982, pp 438–453
Wenzel H-G (1985) Hochauflösende Kugelfunktionsmodelle für das Gravitationspotential der Erde. Wiss. Arb. d. Fachr. Verm.wesen d. Univ. Hannover, Nr. 137, Hannover
Wenzel H-G (1989) On the definition and numerical computation of free air gravity anomalies. Bull. d’Information 64. Bureau Gravimetrique Internationale, Toulouse, France, pp 23−40
Wichiencharoen C (1982) The indirect effects on the computation of geoid undulations. Report Department of Geodetic Science, no. 336, The Ohio State University, Columbus, Ohio, USA
Wildermann E (1988) Untersuchungen zur lokalen Schwerefeldbestimmung aus heterogenen Daten dargestellt am Beispiel der Geotraverse venezolanische Anden. Wiss. Arb. d. Fachr. Verm.wesen d. Univ. Hannover, Nr. 155, Hannover
Wolf H (1974) Über die Einführung von Normalhöhen. Zeitschrift f. Verm.wesen (zfv) 99:1–5
Wolf KI (2007) Kombination globaler Potentialmodelle mit terrestrischen Schweredaten für die Berechnung der zweiten Ableitungen des Gravitationspotentials in Satellitenbahnhöhe. Wiss. Arb. d. Fachr. Geodäsie u. Geoinformatik d. Leibniz Univ. Hannover, Nr. 264, Hannover
Wolf KI (2008) Evaluation regionaler Quasigeoidlösungen in synthetischer Umgebung. Zeitschrift f. Verm.wesen (zfv) 133:52–63
Wunsch C, Gaposchkin EM (1980) On using satellite altimetry to determine the general circulation of the oceans with application to geoid improvement. Rev Geophys 18:725–745
Zeman A (1987) Definition of the normal gravity field including the constant part of tides. Stud Geophys Geod 31:113–120
Ziebart MK, Iliffe JC, Forsberg R, Strykowski G (2008) Convergence of the UK OSGM05 GRACE-based geoid and the UK fundamental benchmark network. J Geophys Res B 113:B12401. doi:10.1029/2007JB004959
Zilkoski DB, Richards JH, Young GM (1995) A summary of the results of the general adjustment of the North American vertical datum of 1988. Allg Verm Nachr 102:310–321
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Denker, H. (2013). Regional Gravity Field Modeling: Theory and Practical Results. In: Xu, G. (eds) Sciences of Geodesy - II. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28000-9_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-28000-9_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27999-7
Online ISBN: 978-3-642-28000-9
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)