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Modeling of Quasigeoid Heights in the Earth’s Local Surface Areas Based on the Results of the Expansion in a Generalized Fourier Series

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Abstract

Two methods of modeling quasigeoid heights specified discretely in the Earth’s local surface areas using generalized Fourier series are considered. The first method involves modeling of the Earth gravitational field characteristics on a plane; it makes use of a two-dimensional Fourier transform in an orthonormal set of trigonometric functions. The second method implies the expansion of quasigeoid heights in a Fourier series in an orthonormal set of spherical functions on the Earth’s local surface area. The errors in the approximation of the discrete values of the quasigeoid heights obtained within a local area are analyzed. It is shown that with the current state of computer technology, expansion of quasigeoid heights in a Fourier series in an orthonormal set of spherical functions is an accurate and technologically simple method for modeling of quasigeoid heights.

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REFERENCES

  1. Dzhandzhgava, G.I., Gerasimov, G.I., and Avgustov, L.I. Navigation and guidance based on spatial geophysical fields, Izvestiya Yuzhnogo federal’nogo universiteta. Tekhnicheskie nauki, 2013, no. 3, pp. 74–84.

  2. Nepoklonov, V.B., Zueva, A.N., and Pleshakov, D.I., On the development and application of computer modeling systems for global studies of the Earth’s gravitational field, Izvestiya vuzov. Geodeziya i aerofotos’’yemka, 2007, no. 2, pp. 79–97.

  3. Neiman, Yu.M. and Sugaipova, L.S., On the adaptation of the global model of the geopotential to regional characteristics (part 1), Izvestiya vuzov. Geodeziya i aerofotos’’yemka, 2014, no. 3, pp. 3–12.

  4. Koneshov, V.N., Nepoklonov, V.B., Spiridonova, E.S. et al., Comparative Assessment of Global Models of the Earth’s Gravity Field, Izv. Phys. Solid Earth, 2020, 56, pp. 249–259. https://doi.org/10.1134/S1069351320020044

    Article  Google Scholar 

  5. Aka Blush Ulfred. On the creation of a preliminary geoid model for the territory of the Republic of Côte d’Ivoire, Izvestiya vuzov. Geodeziya i aerofotos’’yemka 2019, vol. 63, no. 2, pp. 134‒144. https://doi.org/10.30533/0536-101X-2019-63-2-134-144

  6. Erol, B., Işık, M.S., and Erol, S., An Assessment of the GOCE High-Level Processing Facility (HPF) Released Global Geopotential Models with Regional Test Results in Turkey, Remote Sensing in Geology, Geomorphology and Hydrology: Special Issue “Remote Sensing by Satellite Gravimetry”, 2020, 12(3), 586. https://doi.org/10.3390/rs12030586

    Article  Google Scholar 

  7. Foroughi, I., Vaníček, P., Kingdon, R.W., Goli, M., Sheng, M., Afrasteh, Y., Novak, P., and Santos, M.C., Sub-centimetre geoid, J. Geod., 2019, 93, 6, 849–868. .https://doi.org/10.1007/s00190-018-1208-1

    Article  Google Scholar 

  8. Zingerle, P, Pail, R., Gruber, T., and Oikonomidou, X., The experimental gravity field model XGM2019e, GFZ Data Services, 2019. https://doi.org/10.5880/ICGEM.2019.007

  9. Jiang, T., Dang, Y., and Zhang, C., Gravimetric geoid modeling from the combination of satellite gravity model, terrestrial and airborne gravity data: a case study in the mountainous area, Colorado. Earth Planets Space, 2020, 72, 189. https://doi.org/10.1186/s40623-020-01287-y

    Article  Google Scholar 

  10. Abd-Elmotaal, H.A., Kühtreiber, N., Seitz, K., and Heck, B., A Precise Geoid Model for Africa: AFRgeo2019, International Association of Geodesy Symposia, Springer, Berlin, Heidelberg, 2020. https://doi.org/10.1007/1345_2020_122

  11. Borghi, A., Barzaghi, R., Al-Bayari, O., and Al Madani, S., Centimeter Precision Geoid Model for Jeddah Region (Saudi Arabia), Remote Sens., 2020, 12(12), 2066. https://doi.org/10.3390/rs12122066

    Article  Google Scholar 

  12. Garbanzo-Leon, J. et al., A regional Stokes-Helmert geoid determi-nation for Costa Rica (GCR-RSH-2020): computation and evaluation, Contributions to Geophysics and Geodesy, 2020, vol. 50/2, 223–247. https://doi.org/10.31577/congeo.2020.50.2.3

    Article  Google Scholar 

  13. Sovremennye metody i sredstva izmerenya parametrov gravitatsionnogo polya Zemli (Modern Technologies and Methods for Measuring the Earth’s Gravity Field Parameters), Eds., V.G. Peshekhonov, O.A. Stepanov, St. Petersburg, Concern CSRI Elektropribor, 2017.

    Google Scholar 

  14. Koneshov, V.N., Nepoklonov, V.B., Sermyagin, R.A., and Lidovskaya, E.A., Modern global Earth’s gravity field models and their errors, Gyroscopy and Navigation, 2013, vol. 4, no. 3, pp. 147–155.

    Article  Google Scholar 

  15. Nepoklonov, V.B., On the use of new models of the Earth’s gravitational field in automated technologies for survey and design, Avtomatizirovannye tekhnologii izyskanii i proektirovaniya, 2009, no. 2 (33), pp. 72–76.

  16. Aronov, V.I., Metody matematicheskoi obrabotki geologicheskikh dannykh na EVM (Methods for Mathematical Processing of Geological Data on a Computer), Moscow, Nedra, 1977.

  17. Kanushin, V.F., Basic principles of predicting gravity anomalies taking into account additional information, Deponent v ONTI TsNIIGAiK, 1982, no. 90.

  18. Avsyuk, Yu.N. et al., Gravimetriya i geodeziya (Gravimetry and Geodesy), Ed. B.V. Brovar, Moscow: Nauchnyi mir, 2010.

  19. Buzuk, V.V., Vovk, I.G., Kanushin, V.F., Kostyna, Yu.G., and Suzdalev, A.S., Mathematical modeling of scalar fields by a Fourier series in a set of spherical functions, Novosibirsk: Novosibirskii institut inzhenernoi geodezii aerofotos’’yemki i kartografii, 1979, Deponent v VINITI, 10 04 1979, no. 1284–79.

  20. Davis, J.S., Statistika i analiz geologicheskikh dannykh (Statistics and Data Analysis in Geology), Moscow: Mir, 1977. Translated from English into Russian.

  21. Development of algorithms and programs to determine coherent components of the Earth’s physical fields in the representation by Fourier series: Report on research, SGGA; Supervised by V.F. Kanushin, no. GR. 012004.08851, inv. no. 022008.02255. Novosibirsk, 2007. In Russian

  22. Gienko, E.G., Strukov, A.A., and Reshetov, A.P., Studying the accuracy of obtaining normal heights and deflections of the vertical in the Novosibirsk region using the global geoid model EGM2008, Interexpo Geo-Sibir’, 2011, vol. 1, no. 2, pp. 186–191.

    Google Scholar 

  23. Obidenko, V.I., Opritova, O.A., and Reshetov, A.P., Development of a method and techniques for obtaining normal heights on the territory of the Novosibirsk region using the global geoid model EGM2008, Vestnik SGUGiT, 2016, no. 1 (33), pp. 14–26.

  24. Hobson, E.V., Teoriya sfericheskikh i ellipsoidal’nykh funktsii (The theory of spherical and ellipsoidal functions), Moscow: Izdatel’stvo inostr. literatury, 1952. Translated from English into Russian.

  25. Vovk, I.G. and Kostyna, Yu.G., On the approximation of the relief by the Fourier series in a set of orthogonal functions. Izvestya vuzov Geodeziya i aerofotos’’emka, 1981, no. 4, pp. 19–25.

  26. Vovk, I.G., Kanushin, V.F., and Suzdalev, A.S., Local covariance analysis of the physical fields of the Earth, Geodeziya i kartografiya, 1986, no. 3, pp. 16–20.

  27. Kanushin, V.F., Modeling of gravity anomalies taking into account the data on the Earth’s relief in conditions of incomplete gravimetric knowledge, Cand. Sci. Dissertation, Novosibirsk, 1984.

  28. Zhongolovich, I.D., Vneshnee gravitatsionnoe pole Zemli i fundamental’nye postoyannye svyazannye s nimi (The External Gravitational Field of the Earth and the Fundamental Constants Associated with them), Moscow, Leningrad: Izdatel’stvo AN SSSR, 1952, vol. III.

  29. Vovk, I.G., Algorithms and programs for calculating the integral values of spherical functions, Trudy NIIGAiK, 1972, vol. 26, pp. 21–30.

    Google Scholar 

  30. Karpik, A.P., Kanushin, V.F., Ganagina, I.G., Goldobin, D.N., Kosarev, N.S., and Kosareva, A.M., Determination of the deflection-of-the-vertical components on the territory of Western Siberia by the method of numerical differentiation, Vestnik SGUGiT, 2018, vol. 23, no. 3, pp. 15–29.

    Google Scholar 

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Authors and Affiliations

  1. Siberian State University of Geosystems and Technologies, Novosibirsk, Russia

    V. F. Kanushin, I. G. Ganagina & D. N. Goldobin

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  1. V. F. Kanushin
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  2. I. G. Ganagina
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  3. D. N. Goldobin
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Correspondence to V. F. Kanushin.

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Kanushin, V.F., Ganagina, I.G. & Goldobin, D.N. Modeling of Quasigeoid Heights in the Earth’s Local Surface Areas Based on the Results of the Expansion in a Generalized Fourier Series. Gyroscopy Navig. 12, 61–68 (2021). https://doi.org/10.1134/S2075108721010065

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