Aim. The aim of this work is multifold: to show, at a qualitative and approximately quantitative level, how the process of the evolutionary self-development of the planet is a result of the action of gravitational-rotational and endogenous forces, and to show that mass redistribution leads to the transformation of the figure of the lithosphere from a biaxial ellipsoid to a triaxial and vice versa; to show changes in compression, axial rotation speed, and pole displacement in geological time; and to determine the valid mass forces that cause the dynamics of the stress state in the upper shell of the Earth, based on the calculated parameters of the evolutionary changes in the shape of the surface of the lithosphere. Methods. The figure of the surface of the lithosphere is geometrically rotated relative to the figure of the geoid and in geological time the orientation of these figures and the parameters of the ellipsoids approximating them has changed. This arrangement in the figure of the lithosphere and the figure of the geoid can create a stress directed at bringing the mass distribution of the lithosphere in accordance with the figure of the geoid. Applying the parameters of the evolutionary changes in the shape of the lithosphere surface, it is possible to determine the valid mass forces that determine the dynamics of the Earth's stress state. The calculation of the parameters of the biaxial and triaxle ellipsoids was performed because of the data of the digital model of the ETOPO1 Earth's surface. The heights were averaged within the trapezoids of 5º × 5º for this model. To model the transformation of the Earth's shape and to assess the effect of its reorientation on the stress-strain state of the lithosphere in distant geological epochs, two variants of raster map sets of paleo-reconstructions of continental and water surface locations were used. They were independently created by R. Blakey and K. Scotese. All bitmaps were created sequentially in certain colors. Having found the connection between the ETOPO1 model height image and the raster maps of paleore-constructions, one can go to the digital surface relief model (DSRM) of the Earth's lithosphere to visualize geological epochs tied to corresponding maps with images of the continents and the water surface. Results. An algorithm is proposed for determining the Earth's lithospheric model from data of raster maps of paleo-reconstructions and calculating parameters of biaxial and triaxle ellipsoids at fixed moments of geological time. Formulas for calculating the tangential mass forces resulting from the displacement of the poles and the shape of the lithosphere, and changes in the speed of rotation of the planet around its axis are given. The interpretation of the study of the planetary dynamics of the Earth's lithosphere and the global stress state is given. The scientific novelty. The concept of «geoevolutionary» plumb line deviation, which was used for computations of tangential forces acting on the top shell of the planet, is introduced. Interpretation of the role of gravitational and rotation forces in formation of the global stress field in the Earth’s tectonosphere is given. The practical significance. The results will be used in further investigations in the study of planetary characteristics, its dynamical variations, and the global stress state of our planet.
- Avsyuk Yu. N., Zverev V. P., Makarov V. . i dr Energetika ekzogennyih geologicheskih protsessov [Energetics of exogenous geological processes]. Opasnyie ekzogennyie protsessyi. Moscow: GEOS. 1999, pp. 49–86 [in Russian].
- Blinov V. F. Rastuschaya Zemlya: iz planet v zvezdyi [Growing Earth: from planets to stars]. Elektronnaya monografiya. Kyiv, 2011, 305 p [in Ukrainian].
- Bozhko N. A., Barkin Yu. V. Disimmetriya tektonicheskih protsessov v hode superkontinentalnoy tsiklichnosti kak dinamicheskie sledstviya otnositelnyih polyarnyih smescheniy yadra i mantii Zemli [Dysimmetry of tectonic processes during supercontinental cyclicity as dynamic consequences of relative polar displacements of the Earth's core and mantle] Materialyi 42-go tekt. soveschaniya. Moscow: GEOS. 2009,. T. 1, pp. 66—70 [in Russian].
- Goncharov M. A. Pod'em s vsestoronnim gorizontalnyim rastyazheniem Antarktiki i opuskanie s vsestoronnim gorizontalnyim szhatiem Arktiki kak sledstvie severnoy komponentyi dreyfa kontinentov [The lifting with a comprehensive horizontal extension of the Antarctic and subsidence with a comprehensive horizontal compression of the Arctic as a consequence of the northern component of the continental drift] Materialyi 42-go tekt. soveschaniya. Moscow: GEOS. 2009,. pp. 151–155 [in Russian].
- Krasovskiy F. N. Izbrannyie sochineniya [Selected publications]. Moscow: Geodezizdat. T. 1, 1953, 372 p.; T. 2, 1956, 220 p; T. 3, 1955, 816 p.; T. 4, 1955, 574 p [in Russian].
- Krasovskiy F. N. O nekotoryih nauchnyih zadachah astronomo-geodezii v svyazi s izucheniem tverdoy obolochki Zemli [On some scientific problems of astronomical-geodesy in connection with the study of the hard shell of the Earth] Tr. Inst. teoretich. Geofiziki AN SSSR. 1947, M 2. pp. 3–21 [in USSR].
- Kropotkin P. H., Trapeznikov Yu. A. Variatsii uglovoy skorosti vrascheniya Zemli, kolebaniy polyusa i skorosti dreyfa geomagnitnogo polya i ih vozmozhnaya svyaz s geotektonicheskimi protsessami [Variations in the angular velocity of the Earth's rotation, pole oscillations and drift velocity of the geomagnetic field and their possible connection with geotectonic processes]. Izv. AN SSSR. Ser. geol. 1963, no 11, pp. 32–50 [in USSR].
- Kuznetsov V. V. Printsip minimizatsii gravitatsionnoy energii Zemli i mehanizmyi ego realizatsii [The principle of minimizing the Earth's gravitational energy and the mechanisms for its realization]. Vestnika Otdeleniya nauk o Zemle RAN. Elektronnyiy nauchno-informatsionnyiy zhurnal. 2005, no 1(23), pp. 1–27 [in Russian].
- Levin B. V. Rol dvizheniy vnutrennego yadra Zemli v tektonicheskih protsessah [The role of movements of the inner core of the Earth in tectonic processes]. Fundamentalnyie problemyi obschey tektoniki. Moscow: Nauchnyiy mir, 2002, pp. 444–461 [in Russian].
- Lichkov B. L. Prirodnyie vodyi Zemli i litosferyi [The natural waters of the Earth and the lithosphere]. Moscow–Leningrad: Izd.- vo AN SSSR,196, 164 p.
- Mank U., Makdonald G. Vraschenie Zemli [Rotation of the Earth]. Moscow: Mir, 1964, 384 p [in Russian].
- Mashimov M. M. Fizicheskaya geodeziya: metamorfozyi v nachale puti; vozrozhdenie ucheniya Krasovskogo v noveyshee vremya [Physical geodesy: metamorphosis at the beginning of the path; the revival of Krasovsky's teaching in modern times]. Izv. vuzov. Geodeziya i aerofotos'emka. 1999, no 6, pp. 63-76.
- Melnikov O. A. Rotatsionnyiy rezhim Zemli – otpravnoy punkt i osnova chislennogo i fizicheskogo modelirovaniya lyubyih geologicheskih protsessov [Rotational mode of the Earth - the starting point and the basis for numerical and physical modeling of any geological processes]. Tektonika i geodinamika kontinentalnoy litosferyi. Materialyi HHHV1 Tektonicheskogo soveschaniya. Moscow: GEOS. 2003, T. 2, pp. 40–44 [in Russian].
- Menard G. U. Geologiya dna Tihogo okeana [Geology of the bottom of the Pacific Ocean]. Moscow: Mir, 1966, 275 p [in Russian].
- Mescheryakov G. On the unique solution of the inverse problem of the potential theory. Reports of the Ukrainian Academy of Sciences. Kiev, Series A. 1977, no. 6, pp. 492–495 [in Ukrainian].
- Mirlin E. G. Problema vihrevyih dvizheniy v «tvyordyih» obolochkah Zemli i ih roli v geotektonike [The problem of vortex motions in the "hard" shells of the Earth and their role in geotectonics]. Geotektonika. 2006, no 4, pp 43–60.
- Molodenskiy M. S. Rol geofiziki i geologii v issledovanii figuryi Zemli [The role of geophysics and geology in the study of the figure of the Earth]. Sb. nauchno-tehn. i proiz. statey po geodezii, kartografii, topografii, aeros'emke i gravimetrii. 1945, no. 98, pp. 24-30.
- Molodenskiy M. S. Sovremennyie zadachi izucheniya figuryi Zemli [Modern tasks of studying the figure of the Earth]. Geodeziya i kartografiya. 1958, no 7, pp. 3–5.
- Mushketov D. I. Regionalnaya geotektonika [Regional geotectonics]. Leningrad– Moscow: ONTI, 1935, 527 p [in Russian].
- Odesskiy I. A. Rotatsionno-pulsatsionnyiy rezhim Zemli i ego geologicheskie issledovaniya [Rotational-pulsation regime of the Earth and its geological investigations]. SPb.: Pangeya. 2004, 27 p [in Russian].
- Pavlenkova N .I. Nereshennyie problemyi globalnoy tektoniki i vozmozhnyie puti ih resheniya [Unsolved problems of global tectonics and possible solutions to them]. Available at: https://www. youtube.com/watch?v=deVM7FB29FE
- Sludskiy F. A. Obschaya teoriya figuryi Zemli [General theory of the figure of the Earth]. Moscow: MGU, 1888, 98 p [in Russian].
- Stovas M. V. Izbrannyie trudyi [Selected publications]. Moscow: Nedra, 1975, 153p [in Russian].
- Tyapkin K. F., Dovbnich M. M. Novaya rotatsionnaya gipoteza strukturoobrazovaniya i ee geologo-matematicheskoe obosnovanie [New rotational hypothesis of structure formation and its geological and mathematical justification]. Donetsk: «Noulidzh», 2009, 342 p [in Ukrainian].
- Rastsvetaev L. M. Globalnyie sdvigi i zonyi skalyivaniya planetnyih tel. [Global shifts and zones of movement of planetary bodies]. Sdvigovyie tektonicheskie narusheniya i ih rol v obrazovanii mestorozhdeniy poleznyih iskopaemyih. Moscow: Nauka, 1991, pp. 137–148 [in Russian].
- Hain V. E. Ob osnovnyih printsipah postroeniya podlinno globalnoy modeli dinamiki Zemli [On the basic principles of building a truly global model of the dynamics of the Earth]. Geologiya i geofizika. 2010, t. 51, no 6, pp. 753–760.
- Tserklevych A. L., Zaiats O. S. Heodynamichna evoliutsiia fihury Zemli ta Marsa [Geodynamic evolution of the figure of the Earth and Mars]. Heodynamika. 2012, no. 2(13), pp. 38–42 [in Ukrainian].
- Tserklevych A. L., Zaiats O. S., Shylo Ye. O. Aproksymatsiia vysot fizychnoi poverkhni Zemli dvovisnym i tryvisnym elipsoidamy [Approximation of heights of the physical surface of the Earth by biaxial and triaxial ellipsoid]. Heodynamika. 2016, no. 1(20), pp.40–49 [in Ukrainian].
- Tserklevych A. L., Zaiats O. S., Shylo Ye. O. Dynamika transformatsii fihury Zemli [The dynamics of the transformation of the figure of the Earth]. Kynematyka y fyzyka nebesnыkh tel. 2017, T 33, no. 3, pp. 54–69 [in Ukrainian].
- Sheydeger A. Osnovyi geodinamiki [Fundamentals of Geodynamics]. Moscow: Nedra, 1987, 384 p. [in Russian].
- Shen E. L. Gravitatsionnaya energiya i vnutrennyaya struktura planet [The gravitational energy and internal structure of the planets] Avtoref. dis. … k.f.-m. nauk: spets. 01.04.12 «Geofizika». Kyiv, 1980, 14 p. [in Ukrainian].
- Blakey R. Global Paleogeography Available at:https://www2.nau.edu/ rcb7/globaltext2.html [in USA]
- Chandrasekhar S. Ellipsoidal figures of equilibrium. Chandrasekhar. New Haven and London: Yale University Press, 1969.
- Gauss K. F. Allgemeine Lehrsätze in Beziehung auf die im verkehrten Verhaltnisse des Quadrats der Entfernung wirkenden Anziehungs und Abstossungskrafte. Gauss. Werke, 5, Göttingen. 1867, pp. 197–244.
- Maloof A. C., G.P .Halverson, J. L. Kirschvink at al. Combined paleomagnetic, isotopic, and stratigraphic evidence for true polar wander from the Neoproterozoic Akademikerbreen Group, Svalbard, Norway. Geological Society of America Bulletin. 2006, v. 118, no. 9/10, pp. 1099–1124 [in USA].
https://doi.org/10.1130/B25892.1 - Marchenko A. N. The Earth’s global density distribution and gravitational potential energy. In M.G.Sideris (ed.) Marchenko. Observing our Changing Earth, Int. Assoc. of Geodesy Symp. 133, 2009, pp. 483–491.
- Maxwell J. K. A Treatise on Electricity and Magnetism. 2nd Edition, Vol. 1, Oxford, 1881, 464 p.
- Moritz H. The Figure of the Earth. Theoretical Geodesy and Earth’s Interior. Karlsruhe: Wichmann, 1990, 279 p.
- National Centers for Environmental Information, ETOPO1 Global Relief Model Available at: https://www.ngdc.noaa.gov/mgg/global/ global.html [in USA].
- Rogister Y., B. Valette. Influence of liquid core dynamics on rotational modes. Geophysical Journal International. 2009, 176 (2), pp. 368–388 [in USA].
https://doi.org/10.1111/j.1365-246X.2008.03996.x - Rubincam D. P. Gravitational potential energy of the Earth: A spherical harmonic approach. Journal of Geoph. Res. 1979, Vol. 84, no. B11, pp. 6219–6225.
https://doi.org/10.1029/JB084iB11p06219 - Scoppola B., D.Boccaletti, M. Bevis, E. Carminati, C. Doglioni. The westward drift of the lithosphere: a rotational drag? Geol. Soc. Amer. Bull. 2006, no. 2, v.118, pp. 199–209 [in USA].
https://doi.org/10.1130/B25734.1 - Shuanggen Jin, Zhu Wenyao. Quantitative analysis of the slowing expansion of the South hemisphere. Proceedings of colloquium "APSG-Irkutsk" Moscow: GEOS. 2002, pp. 154–162 [in Russian].
- Thomson W, P. Tait. Treatise on Natural Philosophy. Cambridge University Press. 1883, Vol.2, no. 36, pp. 497–502.
- Tserklevych A., O. Zayats, Y. Shylo. Dynamics of the Earth Shape Transformation. Kinematics and Physics of Celestial Bodies. 2017, Vol. 33, No. 3, pp. 130–141 [in USA].
https://doi.org/10.3103/S0884591317030060 - Wen-Bin Shen W., Rong Sun R., Barkin Y., Ziyu Shen Z. Estimation of the asymmetric vertical variation of the southern and northern hemispheres of the earth. Geodynamics & Tectonophysics. 2015, 6(1), pp.45–61.