Earth’s figure changes – geodynamic factor of stressed-deformed litosphere state

https://doi.org/10.23939/jgd2019.01.028
Received: April 13, 2019
1
Engineering geodesy department of Lviv Polytechnic National University
2
Engineering geodesy department of Lviv Polytechnic National University
3
Lviv Polytechnic National University

Purpose. The purpose of this work is to show how redistribution of masses occurs as a result of gravity-rotational and endogenous forces in the evolutionary self-development of the planet, which leads to the transformation of the lithosphere from the sphere to the biaxial and then to triaxial ellipsoid, and vice versa; and changes in compression and the movement of the pole in geological time. Determine the deformation of the figure of the lithosphere due to the reorientation of the figure's pole. Methodology. The figure of the lithospheric surface is geometrically rotated relative to the figure of the geoid. The orientation of these figures and the parameters of the ellipsoids that approximate them, have changed during the geological time. Such placement of the lithospheric figure and of the geoid figure can create a stress aimed at bringing the distribution of the lithosphere masses into conformity with the figure of the geoid. The calculation of the parameters of biaxial and triaxial ellipsoids was performed based on the data of the digital Earth surface model ETOPO1. Data from the digital modeling of the paleoDEM relief, obtained in the work of K. Skotese and N. Wright have been used for modelling the transformation of the Earth's figure and in the estimation of the impact of its reorientation on the stress-strain state of the lithosphere in the ancient geological epochs. Results The parameters of biaxial and triaxial ellipsoids were calculated for fixed moments of geological time. A comparative analysis of the results of changes in the Earth's figure for paleoDEM and created on the basis of raster images of DSMs, built on palaeogeological data by R. Blakey and K. Skotese, were carried out. The formulas for calculation of displacements and deformations, which are related to the transformation of the figure and the orientation of the upper shell of the planet, are given. The interpretation of the research results of planetary dynamics of the Earth's lithosphere figure and the global deformation state are presented. Scientific novelty. The characteristics of the deformation state of the Earth's lithosphere according to modeling of geopaleo-reconstruction in geological time are obtained. Given is the interpretation of the role of gravity-rotational forces in the formation of the global field of stress and the transformation of the lithospheric figure. Practical significance. The results will be used in further researches aimed at studying the planetary characteristics of our planet, the dynamics of its changes in time, and the global tension.

1. Amante, C., & Eakins, B. W. (2009). ETOPO1 arc-minute global relief model: procedures, data sources and analysis.
2. Blakey R. (2016). Global Paleogeography. Retrieved from https://www2.nau.edu/rcb7/
3. Hofmann-Wellenhof, B., and Moritz H. (2007)."Physical surveying." M.: MIIGAiK.
4. Khain, V. E. (2010). Constructing a truly global model of Earth's dynamics: basic principles. Geology and Geophysics, 51(6), 753-760. Retrieved from http://www.sibran.ru/upload/iblock/074/074591d1edc11bd8e6d97ad317f48974.pdf
https://doi.org/10.1016/j.rgg.2010.05.001
5. Krasovsky, F. N. (1947). On some scientific problems of astronomical geodesy in connection with the study of the structure of the hard shell of the Earth. Fav. cit, 1, 251-269.
6. Krasovsky, F. N. (1955). Selected works. In 4 volumes. T. Iv.
7. Levin, B. V. (2001). The role of the movements of the inner core of the Earth in tectonic processes. Fundamental problems of general tectonics. M.: Scientific world, 444-460.
8. Mank, W., MacDonald, G., (1964). Rotating the Earth: World.
9. Marchenko, O. M., Tretiak K. R., & Yarema N. P. (2013). Reference systems in geodesy. Lviv Polytechnic Publishing House.
10. Mashimov, M. M. (1999). Essay on subject areas and interpenetration of geodesy, iconometry and cartography of modern times (as a matter of discussion). Proceedings of higher educational institutions. Geodesy and aerial photography, (3), 44-58.
11. Mashimov, M. M. (1999). Physical geodesy: the metamorphosis at the beginning of the path, the revival of Krasovsky's teachings in modern times (as a matter of discussion). Proceedings of higher educational institutions. Geodesy and aerial photography, (6), 63-76.
12. Molodensky, M. S. (1945). The role of geophysics and geology in the study of the figure of the Earth. Sat scientific and technical and manuf. articles on geodesy, cartography, topography, aerial survey and gravimetry, (8), 24.
13. Molodensky, M. S. (1958). Current tasks of studying the figure of the Earth. Geodesy and cartography, (7), 3-5.
14. Moritz, H. (1994). Figure of the Earth: Theoretical geodesy and the internal structure of the Earth. Kiev: Publishing House of the National Academy of Sciences of Ukraine.
15. Odesskyi, I. A. (2004). Rotational-pulsation regime of the Earth and its geological studies.
16. Rashevsky P. K. (1967) Riemannian geometry and tensor analysis. M.: Science.
17. Rebetskii, Y. L. (2009, October). Estimation of stress values in the method of cataclastic analysis of shear fractures. In Doklady Earth Sciences (Vol. 428, No. 1, pp. 1202-1207). MAIK Nauka/Interperiodica.
https://doi.org/10.1134/S1028334X09070368
18. Rebetskii, Y. L. (2016, July). Estimation of the influence of daily rotation of the earth on the stress state of the continental crust. In Doklady Earth Sciences (Vol. 469, No. 1, pp. 743-747). Pleiades Publishing.
https://doi.org/10.1134/S1028334X1607014X
19. Rebetsky, Y. L. (2015). On the specific state of crustal stresses in intracontinental orogens. Geodynamics & Tectonophysics, 6(4), 437-466.
https://doi.org/10.5800/GT-2015-6-4-0189
20. Rebetsky, Y. L., & Marinin, A. V. (2006). Preseismic stress field before the Sumatra-Andaman earthquake of 26.12. 2004: a model of metastable state of rocks. Russian Geology and Geophysics, 47(11), 1173-1185.
21. Rebetsky, Y. L., & Tatevossian, R. E. (2013). Rupture propagation in strong earthquake sources and tectonic stress field. Bulletin de la Societe Geologique de France, 184(4-5), 335-346.
https://doi.org/10.2113/gssgfbull.184.4-5.335
22. Scheidegger, A. (1987). Fundamentals of Geodynamics (a Russian translation), 384 pp. Nedra, Moscow.
23. Scotese, C. R. (2017). PALEOMAP Project. Retrieved from http://www.scotese.com/
24. Scotese, C. R., & Wright, N. (2018). PALEOMAP Paleodigital Elevation Models (PaleoDEMS) for the Phanerozoic PALEOMAP Project, https://www.earthbyte.org/paleodem-resourcescotese-and-wright-2018/
25. Stovas, M. V. (1975). Selected Works. Nedra, Moscow, 155 p.
26. Tadyeyev, O. (2017). Estimating three-dimensional earth deformation fields by methods of the projective differential geometry. Earth dilatation fields. Modern achievements in geodesic science and industry. 1(33), 53-60. Retrieved from http://ena.lp.edu.ua/bitstream/ntb/41367/2/2017v1__33__Tadyeyev_O-Estima...
27. Tserklevych, A. L., Zayats, O. S., & Shylo, Y. O. (2016). Approximation of the physical surface of the earth by biaxial and triaxial ellipsoid. Geodynamics, (1), 40-49.
https://doi.org/10.23939/jgd2016.01.040
28. Tserklevych, A. L., Zayats, O. S., & Shylo, Y. O. (2017). Dynamics of the Earth shape transformation. Kinematics and Physics of Celestial Bodies, 33(3), 130-141.
https://doi.org/10.3103/S0884591317030060
29. Tserklevych, A. L., Zayats, O. S., Shylo, Y. O., & Shylo, O. M. (2018). Generation of the Stressed State of the Lithosphere of the Earth and Mars Caused by the Reorientation of Their Figures. Kinematics and Physics of Celestial Bodies, 34(1), 19-36.
https://doi.org/10.3103/S0884591318010051
30. Tserklevych, A. L. & Shylo, Y. O. (2018). Shape of Earth's lithosphere and geotectonics. Dopov. Nac. akad. nauk Ukr. doi: https://doi.org/10.15407/dopovidi2018.01.067
https://doi.org/10.15407/dopovidi2018.01.067
31. Tyapkin, K. F., & Dovbnich M. M. (2009). New rotational hypothesis of structure formation and its geological and mathematical justification. Donetsk: «Noulidzh». Retrieved from http://www.evgengusev.narod.ru/fluidolit/tyapkin-2009.html
32. Zharkov, V. N., & Trubitsyn, V. P. (1980). Physics of planetary subsoil.