The use of the simplex finite element model in evaluation of the deformation of the earth's surface in South-East Europe (2014-2024)
DOI:
https://doi.org/10.31861/Keywords:
finite elements,, simplex,, tensor,, deformation,, thematic mapAbstract
The article presents the results of a scientific and methodological study of the problem of evaluation of the deformation of the earth's surface in the most tectonically active region of Europe - its southeastern part. The results of modeling of horizontal deformations of the earth's surface using the method of finite elements in the simplex form are presented.
Coordinates of 16 European permanent GNSS stations from the JPLComb database of the SOPAC archive during 2014-2024 were used as input data. They divided the research area into 17 simplexes. The linear function is approximated using the least squares method based on displacements of vertices of the each simplex. Based on the obtained linear empirical formulas, functional deformation models and tensors were formed and relative indicators of dilation and extreme expansion were calculated for 2018, 2020, 2022 and 2024 compared to 2014.
Using the calculated characteristics of the deformation of the earth's surface, schematic maps of the corresponding thematic direction were created. At this stage of modeling, commonly accepted thematic mapping tools were used to display the spatial distribution of deformation characteristics. The used tools meet the requirements of the generalization of planar localization objects from the point of view of visibility and visual perception of images of objects and phenomena of nature. The created thematic maps were used to analyze and interpret the obtained results of modeling of horizontal deformations of the earth's surface in the southeastern part of Europe.
Analysis of results of modeling of deformations of the earth's surface did not show the significant differentiation in terms of the spatial distribution of calculated values of dilation and extreme expansions. This result is justified by the limited possibilities of the theoretical basis of the used method and research model, because the simplex model of finite elements is able to provide an assessment of exclusively linear patterns of deformation. Instead, the obtained results showed the clear regularities of the multidirectional action of extreme expansions. Based on them, the final conclusions regarding the course of geodynamic processes in the studied area were formulated.
In order to increase the effectiveness of evaluation the deformations of the earth's surface in tectonically active regions, recommendations on the use of non-linear deformation models have been substantiated.
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., Перій, С., Ломпас, О., Голубінка, Ю., Марченко, Д., Крамаренко, С., Салаву, А. (2019) Визначення тензора швидкості горизонтальної деформації в Західній Україні. Геодинаміка, 2(27), 5-17. [Marchenko, O., Perii, S., Lompas, O., Holubinka, Yu., Marchenko, D., Kramarenko, S., Salavu, A. (2019) Vyznachennia tenzora shvydkosti horyzontalnoi deformatsii v Zakhidnii Ukraini. Heodynamika, 2(27), 5-17.] https://doi.org/10.23939/jgd2019.02.005.
3. Марченко, О.М.,Третяк, К.Р., Ярема, Н.П., Джуман, Б.Б., Сідоров, І.С. (2012) Поле лінійних швидкостей та рухи земної кори у регіоні Південно-Східної Європи. Геодинаміка, 2(13), 18-27. [Marchenko, O.M.,Tretiak, K.R., Yarema, N.P., Dzhuman, B.B., Sidorov, I.S. (2012) Pole liniinykh shvydkostei ta rukhy zemnoi kory u rehioni Pivdenno-Skhidnoi Yevropy. Heodynamika, 2(13), 18-27.] https://doi.org/10.23939/jgd2012.02.018.
4. Тадєєв, О. (2024) Математико-картографічне моделювання деформації земної поверхні території Європи з використанням GNSS-даних. Науковий вісник Чернівецького університету : Географія, 849, 63-76. [Tadieiev, O. (2024) Matematyko-kartohrafichne modeliuvannia deformatsii zemnoi poverkhni terytorii Yevropy z vykorystanniam GNSS-danykh. Naukovyi visnyk Chernivetskoho universytetu : Heohrafiia, 849, 63-76.] https://doi.org/10.31861/geo.2024.849.63-76 .
5. Тадєєв, О.А., Машкін, М.С. (2023) Оцінювання горизонтальних деформацій земної поверхні території України методом скінченних елементів (2014–2023рр.). Вісник Національного університету водного господарства та природокористування. Серія: Технічні науки, 4(104), 119-128. [Tadieiev, O.A., Mashkin, M.S. (2023) Otsiniuvannia horyzontalnykh deformatsii zemnoi poverkhni terytorii Ukrainy metodom skinchennykh elementiv (2014–2023rr.). Visnyk Natsionalnoho universytetu vodnoho hospodarstva ta pryrodokorystuvannia. Seriia: Tekhnichni nauky, 4(104), 119-128.] http://ep3.nuwm.edu.ua/id/eprint/30166.
6. Тадєєв, О.А. (2013) Особливості тектонофізичної інтерпретації геодезичних даних в геодинамічних дослідженнях. Вісник Національного університету водного господарства та природокористування. Серія: Технічні науки, 1(61), 224-232. [Tadieiev, O.A. (2013) Osoblyvosti tektonofizychnoi interpretatsii heodezychnykh danykh v heodynamichnykh doslidzhenniakh. Visnyk Natsionalnoho universytetu vodnoho hospodarstva ta pryrodokorystuvannia. Seriia: Tekhnichni nauky, 1(61), 224-232.] http://ep3.nuwm.edu.ua/id/eprint/1051.
7. 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.
8. Altiner, Y., Bacic, Z., Basic, T., Coticchia, A., Medved, M., Mulic, M., Nurce, B. (2006) Present-day tectonics in and around the Adria plate inferred from GPS measurements. In Dilek, Y., Pavlides, S. (Eds.), Postcollisional tectonics and magnetism in the Mediterranean region and Asia, 43–55. Geological Society of America Special Paper 409. https://doi: 10.1130/2006.2409(03).
9. Battaglia, M., Murray, M.H., Serpelloni, E., Burgmann, R. (2004) The Adriatic region: An independent microplate within the Africa-Eurasia collision zone. Geophysical Research Letters, 31, p.L09605. https://doi:10.1029/2004GL019723.
10. Bird, P. (2003) An updated digital model of plate boundaries. Geochemistry, Geophysics, Geosystems, 4(3), 52p. https://doi:10.1029/2001GC000252.
11. 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.
12. 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(5-6), 303-326. http://doi: 10.1007/s00190-003-0329-2.
13. Hartmann, F., Katz, C. (2007) Structural analysis with finite elements. Berlin, Heidelberg, New York: Springer.
14. McClusky, S., Balassanian, S., Barka, A., Demir, C., Ergintav, S., Georgiev, I., Gurkan, O., Hamburger, M., Hurst, K., Kahle, H., Kastens, K., Kekelidze, G., King, R., Kotzev, V., Lenk, O., Mahmoud, S., Mishin, A., Nadariya, T.M., Ouzounis, A., Paradissis, D., Peter, Y., Prilepin, M., Reilinger, TM R., Sanli, I., Seeger, H., Tealeb, A., Toks M.N., Veis G. (2000) Global Positioning System constraints on plate kinematics and dynamics in the eastern Mediterranean and Caucasus. Journal of geophysical research. Solid earth, 105(В3), 5695-5719. https://doi.10.1029/1996JB900351.
15. 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 .
16. 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.
17. Tsuboi, C. (1933) Investigation on the deformation of the earth's crust found by precise geodetic means. Japan J. Astron. and Geophys, 10, 93-248.
18. International Association of Geodesy (2023). Commission 3 – Earth Rotation and Geodynamics. (Джерело)
19. Scripps Orbit and Permanent Array Center (2024). (Джерело)
