Evaluation the global dilatation of the Earth using GNSS data (example 2008-2014)
DOI:
https://doi.org/10.31861/Keywords:
spherical functions, metric tensor, deformation, dilatation, GNSS.Abstract
Abstract: the article presents the results of a scientific and methodological study of the problem of evaluation the Earth's deformation in terms of static modeling of dilatation on a global (planetary) scale.
The purpose of the study: testing of the method for evaluation of three-dimensional deformations, developed on the basis of the theory of transformations of Riemannian space images, using the coordinates of the stations of the global IGS GNSS network.
Research result. The method was tested on an empirical data sample formed by the coordinates of 433 permanently operating stations of the class A accuracy of the global IGS GNSS network during 2008–2014. The cut-off dates of the research period is tied to verifications of the corresponding ITRF solutions of the ITRS reference system. The coordinate sample was formed based on the JPL Comb database of the SOPAC archive, which, from the point of view of its intended purpose, is recommended for use for geodynamics needs.
The functional model of deformation is represented by the system of three empirical formulas, which are formed based on the results of approximation of series of spherical functions from three variables with powers alternately from the first to the ninth. The approximation was implemented on an empirical data sample using the least squares method. Comparison of results of evaluation the approximation accuracy showed large, sometimes more than twice as many, values of errors corresponding to a linear function of three variables compared to the approximation errors of functions with higher order powers. This became the basis for stating the fact of nonlinear trends in the Earth's deformation during the research period.
Empirical formulas, which are constructed based on the results of approximation of series of all powers, are alternately used to form of the metric deformation tensor with the subsequent calculation of its own invariants and the dilatation characteristic - the relative volumetric expansion of the Earth. An analysis of the obtained results and the comparison with analogues determined by other authors are presented. Among other things, in particular, the results of calculation the relative volumetric expansion using series of all powers are consistent with the trend of relative reduction of the Earth's volume. Also, the result of its calculation based on the first-degree series, which corresponds to a linear function, within its accuracy coincides with the value of the scale factor, which is its analogue in the linearized form of the ITRF2014-ITRF2008 transformation. Based on nonlinear functional models, the optimal final result of the static modeling of the Earth's dilatation is derived.
Scientific novelty: the fact of nonlinear trends in the deformation of the Earth on a planetary scale during 2008–2014, and the dilatation of the Earth by the value of the relative volumetric expansion of -32х10-9 was confirmed.
References
1. Іщенко, М. (2018). Дослідження деформацій земної кори на території України за допомогою GNSS спостережень. Штучні супутники, 53(3), 117-126. [Ishchenko, M. (2018) Doslidzhennia deformatsii zemnoi kory na terytorii Ukrainy za dopomohoiu GNSS sposterezhen. Shtuchni suputnyky, 53(3), 117-126.] https://doi:10.2478/arsa-2018-0009
2. Марченко, О.М., Третяк, К.Р., Ярема, Н.П. (2018). Референцні системи в геодезії. Львів: Львівська політехніка. [Marchenko, O.M., Tretiak, K.R., Yarema, N.P. (2018). Referentsni systemy v heodezii. Lviv: Lvivska politekhnika.]
3. Тадєєва, О.О., Тадєєв, О.А., Черняга, П.Г. (2012). Достовірність результатів опрацювання геодезичних даних методом скінченних елементів. Геодинаміка, 2(13), 28–33. [Tadieieva, O.O., Tadieiev, O.A., Cherniaha, P.H. (2012). Dostovirnist rezultativ opratsiuvannia heodezychnykh danykh metodom skinchennykh elementiv. Heodynamika, 2(13), 28–33.] https://doi.org/10.23939/jgd2012.02.028
4. Тадєєв, О. (2017). Оцінювання тривимірних деформаційних полів Землі методами проективно-диференціальної геометрії. Дилатаційні поля Землі. Сучасні досягнення геодезичної науки та виробництва, І(33), 53-60. [Tadieiev, O. (2017). Otsiniuvannia tryvymirnykh deformatsiinykh poliv Zemli metodamy proektyvno-dyferentsialnoi heometrii. Dylatatsiini polia Zemli. Suchasni dosiahnennia heodezychnoi nauky ta vyrobnytstva, I(33), 53-60.]
5. Тадєєв, О. (2023). Перспективи оцінювання тривимірних деформацій Землі за даними глобальних навігаційних супутникових систем. Технічні науки та технології, 4(34), 265–276. [Tadieiev, O. (2023). Perspektyvy otsiniuvannia tryvymirnykh deformatsii Zemli za danymy hlobalnykh navihatsiinykh suputnykovykh system. Tekhnichni nauky ta tekhnolohii, 4(34), 265–276.] https://doi.org/10.25140/2411-5363-2023-4(34)-265-276
6. Тадєєв, О. (2015). Проблеми та перспективи оцінювання деформаційних полів Землі за геодезичними даними. Геодезія, картографія і аерофотознімання, 82, 73-94. [Tadieiev, O. (2015). Problemy ta perspektyvy otsiniuvannia deformatsiinykh poliv Zemli za heodezychnymy danymy. Heodeziia, kartohrafiia i aerofotoznimannia, 82, 73-94.] https://doi.org/10.23939/istcgcap2015.02.073
7. Altamini, Z., Rebischung, P., Metivier, L., Collilieux, X. (2016). ITRF2014: A new release of the International Terrestrial Reference Frame modeling nonlinear station motions. Journal of Geophysical Research: Solid Earth, 121(B8), 6109-6131. https://doi.10.1002/2016JB013098
8. Altiner, Y. (1999). Analytical surface deformation theory for detection of the Earths crust movements. Berlin: Springer.
9. Dermanis, A. (2009). The evolution of geodetic methods for the determination of strain parameters for earth crust deformation. In Arabelos, D., Kontadakis, M., Kaltsikis, Ch., Spatalas, S. (Eds.), Terrestrial and stellar environment. Publication of the school of rural & surveying engineering, Aristotle university of Thessaloniki, 107-144.
10. Dong, D., Herring, T.A., King, R.W. (1998). Estimating regional deformation from a combination of space and terrestrial geodetic data. Journal of Geodesy, 72(4), 200-214.
11. Grafarend, E.W., Voosoghi, B. (2003). Intrinsic deformation analysis of the Earth’s surface based on displacement fields derived from space geodetic measurements. Case studies: present-day deformation patterns of Europe and of the Mediterranean area (ITRF data sets). Journal of Geodesy, 77, 303–326. https://doi: 10.1007/s00190-003-0329-2
12. Hartmann, F., Katz, C. (2007). Structural analysis with finite elements. Berlin, Heidelberg, New York: Springer.
13. Kiamehr, R., Sjoberg, L.E. (2005). Analysis of surface deformation patterns using 3D finite element method: A case study in the Skane area, Sweden. Journal of Geodynamics, 39(4), 403–412. https://doi.org/10.1016/j.jog.2005.03.001
14.. Moritz, H., Muller, I.I. (1987). Earth’s Rotation. Theory and estimations. New York: Ungar.
15. Petit, G., Luzum, B. (2010). IERS Conventions 2010. IERS Technical Note; 36. Frankfurt am Main: Verlag des Bundesamts fur Kartographie und Geodasie. http://www.iers.org/SharedDocs/Publikationen/EN/IERS/Publications/tn/TechNote36/tn36_031.pdf
16. Pietrantonio, G., Riguzzi, F. (2004). Three-dimensional strain tensor estimation by GPS observations: methodological aspects and geophysical applications. Journal of Geodynamics, 38(1), 1–18. https://doi.org/10.1016/j.jog.2004.02.021
17. Savchuk, S., Tadyeyev, A., Prokopchuk, A. (2017). Analysis and research results of GNSS data representativeness in estimation of modern horizontal motion of the earth’s surface (on the example of Europe’s territory). Geodesy, cartography and aerial photography. 86. 19-34. https://doi.org/10.23939/istcgcap2017.02.019
18. Sokolnikoff, I.S. (1964). Tensor analysis: Theory and applications to geometry and mechanics of continua. New York, London, Sydney: John Wiley & Sons.
19. Terada, T., Miyabe, N. (1929). Deformation of the earth crust in Kwansai districts and its relation to the orographic feature. Bulletin of Earthquake Research Institute, Univ. Tokyo, 7, 223-239.
20. International Association of Geodesy (2024). (Джерело)
21. International GNSS Service (2024). (Джерело)
22. ITRS Center IERS (2025). (Джерело)
23. Quasi-Observation Combination Analysis (2024). (Джерело)
24. Scripps Orbit and Permanent Array Center (2024). (Джерело)
