METADATA IN ENGLISH
About the journal
NAUKA I TEKHNOLOGICHESKIE RAZRABOTKI (SCIENCE AND TECHNOLOGICAL DEVELOPMENTS), ISSN: 2079-5165, eISSN: 2410-7948, DOI: 10.21455/std; https://elibrary.ru/title_about.asp?id=32295; http://std.ifz.ru/. The journal was founded in 1992.
HIGH-DEGREE
MODELS OF THE EARTH'S GRAVITATIONAL FIELD: HISTORY OF DEVELOPMENT,
ASSESSMENT
OF PROSPECTS AND RESOLUTION
P.S. Mikhailov1,2, V.N. Koneshov1, V.V. Pogorelov1,2, A.A. Spesivtsev1,2,
V.N. Solovyev1, L.K. Zheleznyak1
1 Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences, Moscow, Russia
2 Sirius University of Science and Technology, Sochi, Russia
Corresponding author: P.S. Mikhailov e-mail: paulmikh@mail.ru
Highlights
– Methods of creating global models of the Earth's gravitational field
– Considered data sources for creating high-degree models
– The statistical characteristics of the main global models
– Analysis of directions for further development and prospects of global models
Abstract. The article provides a generalized retrospective of creating global models of the Earth’s gravitational field using satellite methods, modern global ultra-high-degree models and the most promising new solutions are considered. The main attention is given to the review of techniques that affect the resolution of satellite methods, their development and ways of further improvement. Modern combined models of the Earth's gravity field, which also include altimetry data, instrumental surveys and global topography, are most interesting. The areas of the possible practical application of global models and the applied problems solved with their help depend on an understanding of the nature of model data and methods for their modification. At present, the resolution of models up to 5540 degrees of field expansion in spherical harmonics is achievable; however, high values of their degree and order do not always determine the reliability of the presented model data (not verified by direct measurements). Therefore, along with the most high-degree solutions, this article considers most of the known models of the Earth's gravitational field and their most characteristic modifications.
Keywords: Earth's gravitational field, gravitational field model, spherical harmonics, gravity anomalies, satellite gravimetry, altimetry
Cite this article as: Mikhailov P.S., Koneshov V.N., Pogorelov V.V., Spesivtsev A.A., Solovyev V.N., Zheleznyak L.K. High-degree models of the Earth's gravitational field: history of development, assessment of prospects and resolution, Nauka i Tekhnologicheskie razrabotki (Science and Technological Developments). 2020, vol. 99, no. 4, pp. 5–33. [in Russian]. https://doi.org/10.21455/std2020.4-1
Funding
This study was performed under State Task of Schmidt Institute of Physics of the Earth RAS and supported by the Russian Foundation for Basic Research, project nos. 19-35-51014 and 20-05-00524
Acknowledgments
The authors thank the reviewers for constructive comments and suggestions for improving the material.
Ethics declarations
The authors declare that there is no conflict of interest.
English translation of the article will be published in Seismic Instruments, ISSN: 0747-9239 (Print)
1934-7871 (Online), https://link.springer.com/journal/11990)
References
Andersen, O.B., Knudsen, P., DNSC08 mean sea surface and mean dynamic topography models, J. Geophys. Res., 2009, vol. 114, C11001. https://doi.org/10.1029/2008JC005179
Andersen, O.B., Knudsen, P., The DTU17 Global Marine Gravity Field: First Validation Results, Fiducial Reference Measurements for Altimetry. International Association of Geodesy Symposia, 2019, vol. 150, pp. 83–87. https://doi.org/10.1007/1345_2019_65
Andersen, O., Knudsen, P., Kenyon, S., Holmes, S., Factor, J.K., Evaluation of the Global Altimetric Marine Gravity Field DTU15: Using Marine Gravity and GOCE Satellite Gravity, International Symposium on Advancing Geodesy in a Changing World – Proceedings of the IAG Scientific Assembly, 2019, vol. 149, pp. 77–81. https://doi.org/10.1007/1345_2018_52
Barnes, D.E., 2019 Updates Earth Gravitational Model 2020, American Geophysical Union, Public release number 15-564, Fall Meeting 2019, 2019. Abstract G33B-0669. Bibcode: 2019AGUFM.G33B0668B
Barthelmes, F., Definition of Functionals of the Geopotential and Their Calculation from Spherical Harmonic Models: Theory and Formulas Used by the Calculation Service of the International Centre for Global Earth Models (ICGEM), Scientific Technical Report STR09/02, Revised Edition, January 2013, GeoForschungZentrum Potsdam, 2013. https://doi.org/10.2312/GFZ.b103-0902-26 http://icgem.gfzpotsdam.de/str-0902-revised.pdf
Bekhterev, S.V., Drobyshev, M.N., Zheleznyak, L.K., Koneshov, V.N., Mikhailov, P.S., Solov’ev, V.N., Errors of Earth Gravity Models as depending on seafloor morphology, Izvestiya. Physics of the Solid Earth, 2019, vol. 55, no. 5, pp. 806–810, https://doi.org/10.1134/S1069351319050021
Bouman, J., Bosch, W., Sebera, J., Assessment of Systematic Errors in the Computation of Gravity Gradients from Satellite Altimeter Data, Marine Geodesy, 2011, vol. 34, no. 2, pp. 85–107. https://doi.org/10.1080/01490419.2010.518498
Brockmann, J.M., Zehentner, N., Hock, E., Pail, R., Loth, I., Mayer-Gurr, T., Schuh, W.D., EGM_TIM_RL05: An independent geoid with centimeter accuracy purely based on the GOCE mission, Geophys. Res. Lett., 2014. vol. 41, no. 22, pp. 8089–8099. https://doi.org/ 10.1002/2014gl061904
Buchar, E., Determination of Some Parameters of the Gravity Field of the Earth from Rotation of the Nodal Line of artificial satellites, Bulletin Géodésique, 1962, no. 65, pp. 269–271.
Demianov, G., Sermyagin, R., Tsybankov, I., Global Gravity Field Model GAO2012 [Data set], 2012, Zenodo. http://doi.org/10.5281/zenodo.814573
Demyanov, G.V., Brovar, B.V., Kryukova, A.V., Mayorov, A.N., Nazarova, N.G., Pashina, N.N., Taranov, V.A., Model of the Gravitation Field of the Earth TSNIIGAiK GAO-98, in: Fizicheskaya geodeziya. Nauchno-tekhnicheskiy sbornik po geodezii, aerokosmicheskim s`emkam i kartografii (Physical geodesy. Scientific and technical collection on geodesy, aerospace surveys and cartography), 1999, pp. 88–116. [in Russian].
Demyanov, G.V., Mayorov, A.N., Pobedinsky, G.G., GLONASS and Geodesy, in: Vestnik GLONASS (GLONASS messenger), 2012, no. 1, iss.4. pp. 48–53. [in Russian].
Ditmar, P., Kuznetsov, V., Van der Sluijs, A.A., Schrama, E., Klees, R., DEOS_CHAMP-01C_70: a model of the Earth’s gravity field computed from accelerations of the CHAMP satellite, J. Geodesy, 2006, vol. 79, pp. 586–601.
Fecher, T., Pail, R., Gruber, T., Schuh, W.-D., Kusche, J., Brockmann, J.M., Loth, I., Müller, S., Eicker, A., Schall, J., Mayer-Gürr, T., Kvas, A., Klinger, B., Rieser, D., Zehentner, N., Baur, O., Höck, E., Krauß, S., Jäggi, A., Meyer, U., Prange, L., Maier, A., GOCO05c: A New Combined Gravity Field Model Based on Full Normal Equations and Regionally Varying Weighting, Surveys in Geophysics, 2017, vol. 2017, no. 38, pp. 571–590. https://doi.org/10.1007/s10712-016-9406-y
Forste, C., Bruinsma, S., Abrikosov, O., Lemoine, J.-M., Marty, J. C., Flechtner, F., Balmino, G., Barthelmes, F., Biancale, R., EIGEN-6C4 The latest combined global gravity field model including GOCE data up to degree and order 2190 of GFZ Potsdam and GRGS Toulouse, GFZ Data Services, 2014. https://doi.org/10.5880/ICGEM.2015.1
Gaposchkin, E.M., Lambeck, K., 1969 Smithsonian Standard Earth (II), Smithonian Astrophysical Observatory, 1970, Spec. Rep. 315, 93 p.
Geodesy for the Layman. Report documentation page, DMA-technical Report: DMA TR 80-003, St. Louis AFS: Defense Mapping Agency Aerospace Center, 1983, 96 p.
Gilardoni, M., Reguzzoni, M., Sampietro, D., GECO: a global gravity model by locally combining GOCE data and EGM2008, Studia Geophysica et Geodaetica, 2016, vol. 60, pp. 228–247.
Gorobec, V., Efimov, G., Stolyarov, I., Experience of Russian Federation for Establishing the State Geodetic Coordinate System 2011, in: Geodeziya, kartografiya, kadastr, GIS – problemy i perspektivy razvitiya. Materialy mezhdunarodnoy nauchno-tekhnicheskoy konferentsii (Novopolotsk, 9–10 iyunya 2016 g.). Chast' 1 (Geodesy, Cartography, Cadastre, GIS – Problems and Development Prospects. Materials of the international scientific and technical conference (Novopolotsk, June 9–10, 2016). Part 1), Novopolotsk: PGU, 2016, pp. 48–65. [in Russian]. ISBN: 978-985-531-543-9
Hasanov, I.M., Muravyev, L.A., Comparison of the new gravity field model XGM2019e with other modern global models of the gravitational field for the Magadan region, Geoinformatics: Theoretical and Applied Aspects 2020, Conference Proceedings, 2020, vol. 2020, pp. 1–5. https://doi.org/10.3997/2214-4609.2020geo112
Hauk, M., Pail, R., Treatment of ocean tide aliasing in the context of a next generation gravity field mission, Geophys. J. Int., 2018, vol. 214, iss. 1, pp. 345–365. https://doi.org/10.1093/gji/ggy145
Hirt, C., Featherstone, W.E., Marti, U., Combining EGM2008 and SRTM/DTM2006.0 residual terrain model data to improve quasigeoid computations in mountainous areas devoid of gravity data, J. Geodesy, 2010, vol. 84, iss. 9, pp. 557–567. https://doi.org/10.1007/s00190-010-0395-1
Hobson, E.W., The Theory of Spherical and Ellipsoidal Harmonics, Cambridge: University Press, 1931, 500 p.
Hobson, E.W., Teoriya sfericheskih i ellipsoidalnyh funktsii (The Theory of Spherical and Ellipsoidal functions), Moscow, IL, 1952, 476 p. [in Russian].
Hobson, E.W., The theory of spherical and ellipsoidal harmonics, New York: Chelsea, 1965, 500 p.
Ince, E.S., Barthelmes, F., Reißland, S., Elger, K., Förste, Ch., Flechtner, F., Schuh, H., ICGEM – 15 years of successful collection and distribution of global gravitational models, associated services and future plans, Earth Syst. Sci. Data, 2019, vol. 11, iss. 2, pp. 647–674. https://doi.org/10.5194/essd-11-647-2019
Kvas, A., Brockmann, J. M., Krauss, S., Schubert, T., Gruber, T., Meyer, U., Mayer-Gürr, T., Schuh, W.-D., Jäggi, A., Pail, R., GOCO06s – a satellite-only global gravity field model, Earth Syst. Sci. Data, 2021, vol. 13, iss. 1, pp. 99–118. https://doi.org/10.5194/essd-13-99-2021
King-Hele, D.G., The Earth's gravitational potential, deduced from the orbits of artificial satellites, Geophys. J. Int., 1962, vol. 6, iss. 2, pp. 270–272.
Kohnlein, W., The Earth’s gravitational field as derived from a combination of satellite data with gravity anomalies, Geodetic satellite results during 1967, 1967, pp. 57–72.
Koneshov, V.N., Nepoklonov, V.B., Studying the representation accuracy of the Earth’s gravity field in the polar regions based on the global geopotential models, Izvestiya. Physics of the Solid Earth, 2018, vol. 54, no. 3, pp. 504–512. https://doi.org/10.1134/S1069351318030047
Koneshov, V.N., Zheleznyak, L.K., Mikhailov, P.S., Solovyev, V.N., Use of the Earth’s gravitational model in marine gravity measurements, Izvestiya. Physics of the Solid Earth, 2015, vol. 51, no. 4, pp. 559–565. https://doi.org/10.7868/S0002333715040134
Koneshov, V.N., Nepoklonov, V.B., Solovyev, V.N., Zheleznyak, L.K., Comparison of modern global ultra-high-grade models of the Earth gravitational field, Geofizicheskie Issledovaniya (Geophysical Research), 2019, vol. 20, no. 1, pp. 13–26. https://doi.org/10.21455/gr2019.1-2
Kozai, Y., New determination of zonal harmonics coefficients of the Earth's gravitational potential, Publications of the Astronomical Society of Japan, 1964, vol. 16, 263 p.
Lemoine, F.G., Kenyon, S.C., Factor, J.K., Trimmer, R.G., Pavlis, N.K., Chinn, D.S., Cox, C.M., Klosko, S.M., Luthcke, S.B., Torrence, M.H., Wang, Y.M., Williamson, R.G., Pavlis, E.C., Rapp, R.H., Olson, T.R., The Development of the Joint NASA GSFC and NIMA Geopotential Model EGM96, NASA Goddard Space Flight Center, Greenbelt, Maryland, USA, 1998. Report NAS 1.60:206861 no. Rept-98B00052, Patent Number: NASA/TP-1998-206861, 584 p. https://ntrs.nasa.gov/citations/19980218814
Liang, W., Xu, X., Li, J., Zhu, G., The determination of an ultra-high gravity field model SGG-UGM-1 by combining EGM2008 gravity anomaly and GOCE observation data, Acta Geodaetica et Cartographica Sinica, 2018, vol. 47, no. 4, pp. 425–434. https://doi.org/10.11947/j.AGCS.2018.20170269
Mayer-Gürr, T., Eicker, A., Ilk, K.H., ITG-GRACE02s: a GRACE gravity field derived from short arcs of the satellite’s orbit, Proceedings of the First Symposium of International Gravity Field Service, Istanbul, 2007, pp. 193–198. https://www.harita.gov.tr/images/dergi/df57dbded091b01.pdf
Molodenskiy, M.S., Method of joint processing of gravimetric and geodetic materials for studying the gravitational field of the Earth and its figure, in: M.S. Molodenskiy. Izbrannye trudy (Selected studies), Moscow: OIFZ RAN, 1999, pp. 218–224. [in Russian].
Molodenskiy, M.S., Eremeev, V.F., Jurkina, M.I., Metody izuchenija vneshnego gravitacionnogo polya i figury Zemli (Methods for studying the external gravitational field and the shape of the Earth), Tr. TsNIIGAiK, iss. 131, M.: Geodezizdat, 1960, 250 p. [in Russian].
Nepoklonov, V.B., On the use of new models of the Earth's gravitational field in automated technologies for survey and design, Avtomatizirovannye tehnologii izyskanij i proektirovanija (Automated survey and design technologies), 2009, no. 2 (33), pp. 72–76. [in Russian].
Nepoklonov, V.B, Maximova, M.V, Abakushina, M.V., Analysis of the dynamics of the system of mathematical models of the Earth's gravitational field, Izvestiya vuzov. Geodeziya i aerofotos"yemka (Izvestiya Vuzov. Geodesy and Aerophotosurveying), 2016. vol. 60, no.,3, pp. 8–14. [in Russian].
Pail, R., Bruinsma, S., Migliaccio, F., Förste, C., Goiginger, H., Schuh, W.-D., Höck, E., Reguzzoni, M., Brockmann, J.M., Abrikosov, Ol., Veicherts, M., Fecher, T., Mayrhofer, R., Krasbutter, I., Sansò, F., Tscherning, C.C., First GOCE gravity field models derived by three different approaches, J. Geodesy, 2011, vol. 85, no. 11, pp. 819–843.
Pail, R., Fecher, T., Barnes, D., Factor, J., Holmes, S., Gruber, T., Zingerle, P., The experimental gravity field model XGM2016, GFZ Data Services, 2017. https://doi.org/10.5880/icgem.2017.003
Panteleev, V.L., Fizika Zemli i planet (Physics of Earth and Planets. Lecture course), Moscow: MSU, 2001, 117 p. [in Russian].
Parametry Zemli 1990 (PZ 90.11). Spravochnoe rukovodstvo (Parameters of the Earth 1990 (PZ 90.11). Reference Guide), Moscow: Research Center for Topogeodetic and Navigational Support “27 Central Research Institute” of the Ministry of Defense of Russia, 2014, 52 p.
Pavlis, N.K., Gravity, Global Models, in: Gupta H.K. (ed.), Encyclopedia of Solid Earth Geophysics. Encyclopedia of Earth Sciences Series, Springer, Dordrecht, 2011. https://doi.org/10.1007/978-90-481-8702-7_76
Pavlis, N.K., Factor, J.K., Holmes, S.A., Terrain-related gravimetric quantities computed for the next EGM, Proceedings of the 1st International Symposium of the International Gravity Field Service, 2007, vol. 18, pp. 318–323.
Pavlis, N.K., Holmes, S.A., Kenyon, S.C., Factor, J.K., The development and evaluation of the Earth Gravitational Model 2008 (EGM2008), J. Geophys. Res., 2012, vol. 117, iss. B4, B04406. https://doi.org/10.1029/2011JB008916
Pellinen, L.P., Determination of the parameters of the figure and the gravitational field of the Earth in TsNIIGAiK, Geodeziya i kartografiya (Geodesy and Cartography), 1992, no. 4, pp. 29–35.
Reigber, C., Balmino, G., Schwintzer, P., Biancale, R., Bode, A., Lemoine, J.-M., König, R., Loyer, S., Neumayer, H., Marty, J.-C., Barthelmes, F., Perosanz, F., Zhu, S.Y., A high-quality global gravity field model from CHAMP GPS tracking data and accelerometry (EIGEN1S), Geophys. Res. Lett., 2002, vol. 29, iss. 14, pp. 37-1–37-4.
Reigber, C., Schwintzer, P., Neumayer, K.-H., Barthelmes, F., König, R., Förste, C., Balmino, G., Biancale, R., Lemoine, J.-M., Loyer, S., Bruinsma, S., Perosanz, F., Fayard, T., The CHAMP-only earth gravity field model EIGEN-2, Adv. in Space Res., 2003, vol. 31, iss. 8, pp. 1883–1888.
Sandwell, D.T., Smith, W.H.F., Gille, S., Kappel, E., Jayne, S., Soofi, K., Coakley, B., Geli, L., Bathymetry from space: rationale and requirements for a new, high-resolution altimetric mission, Comptes Rendus. Geosciences, 2006, vol. 338, pp. 1049–1062.
Sandwell, D.T., Smith, W.H.F., Global marine gravity from retracked Geosat and ERS-1 altimetry: ridge segmentation versus spreading rate, J. Geophys. Res., 2009, vol. 114, iss. B1, B0141, pp.1–18. https://doi.org/10.1029/2008JB006008
Zingerle, P., Brockmann, J.M., Pail, R., Gruber, T., Willberg, M., The polar extended gravity field model TIM_R6, GFZ Data Services, 2019a. https://doi.org/10.5880/ICGEM.2019.005
Zingerle, P., Pail, R., Gruber, T., Oikonomidou, X., The experimental gravity field model XGM2019e, GFZ Data Services, 2019b. https://doi.org/10.5880/ICGEM.2019.007
Zingerle, P., Pail, R., Gruber, T., Oikonomidou, X., The combined global gravity field model XGM2019e, J. Geodesy, 2020, vol. 94, art. 66. https://doi.org/10.1007/s00190-020-01398-0
About the authors
MIKHAILOV Pavel Sergeevich – Schmidt Institute of Physics of the Earth of RAS. Russia, 123242, Moscow, ul. Bolshaya Gruzinskaya 10, stroenie 1; Sirius University of Science and Technology. Russia, 354340, Sochi, Olympic Avenue 1. E-mail: paulmikh@mail.ru
KONESHOV Vyacheslav Nikolaevich – Schmidt Institute of Physics of the Earth of RAS. Russia, 123242, Moscow, ul. Bolshaya Gruzinskaya 10, stroenie 1. E-mail: slavakoneshov@hotmail.com
POGORELOV Vitaly Viktorovich – Schmidt Institute of Physics of the Earth of RAS. Russia, 123242, Moscow, ul. Bolshaya Gruzinskaya 10, stroenie 1; Sirius University of Science and Technology. Russia, 354340, Sochi, Olympic Avenue 1. E-mail: vvp@ifz.ru
SPESIVTSEV Aleksandr Aleksandrovich – Schmidt Institute of Physics of the Earth of RAS. Russia, 123242, Moscow, ul. Bolshaya Gruzinskaya 10, stroenie 1; Sirius University of Science and Technology. Russia, 354340, Sochi, Olympic Avenue 1. E-mail: spesivtsev.a.a@gmail.com
SOLOVYEV Vladimir Nikolevich – Schmidt Institute of Physics of the Earth of RAS. Russia, 123242, Moscow, ul. Bolshaya Gruzinskaya 10, stroenie 1. E-mail: solovyev@ifz.ru
ZHELEZNYAK Leonid Kirillovich – Schmidt Institute of Physics of the Earth of RAS. Russia, 123242, Moscow, ul. Bolshaya Gruzinskaya 10, stroenie 1. E-mail: zlkledovo@yandex.ru