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  4. Shape of the Earth and geodynamics

Shape of the Earth and geodynamics

JGD.
2017;
Volume 2(23) 2017, Number 2(23) 2017
: 141-163
https://doi.org/10.23939/jgd2017.02.141
Received: August 05, 2017
Authors:
  1. Anatolii Tserklevych
  2. Yevhenii Shylo
  3. Olha Shylo
1
Engineering geodesy department of Lviv Polytechnic National University
2
Engineering geodesy department of Lviv Polytechnic National University
3
Lviv Polytechnic National University

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.

biaxial and triaxial ellipsoid
digital surface relief model of the Earth's lithosphere
tangential mass forces
stress state of lithosphere
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