04. Faddeev A.O., Pavlova S.A., Nevdakh T.M. Mathematical Models and Evaluation Software for Stress-Strain State of the Earth’s Lithosphere

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UDK 519.87:004.4

DOI: 10.15507/2658-4123.029.201901.051-066

Mathematical Models and Evaluation Software for Stress-Strain State of the Earth’s Lithosphere

Alexander O. Faddeev
Professor, Chair of Mathematics and Information Technologies, The Academy of the FPS of Russia (1 Sennaya St., Ryazan 390000, Russia), D.Sc. (Engineering), Associate Professor, ResearcherID: I-3739-2018, ORCID: https://orcid.org/0000-0002-7259-1693, This email address is being protected from spambots. You need JavaScript enabled to view it.

Svetlana A. Pavlova,
Associate Professor, Chair of Mathematics and Information Technologies, The Academy of the FPS of Russia (1 Sennaya St., Ryazan 390000, Russia), Ph.D. (Engineering), ResearcherID: I-2969-2018, ORCID: https://orcid.org/0000-0001-8634-9163, This email address is being protected from spambots. You need JavaScript enabled to view it.

Tatiana M. Nevdakh
Lecturer, Chair of Mathematics and Information Technologies, The Academy of the FPS of Russia (1 Sennaya St., Ryazan 390000, Russia), ResearcherID: I-3611-2018, ORCID: https://orcid.org/0000-0002-4799-0748, This email address is being protected from spambots. You need JavaScript enabled to view it.

Introduction. For the purposes of this article, geodeformation processes mean processes associated with deformations arising from the movement of species and blocks of the lithosphere at various depths, including surfaces. The objective is to reconstruct geodynamic stress fields, which cause modern shifts and deformations in the Lithosphere. A mathematical model and software for estimating the stress-strain state of the Earth Lithosphere are considered.
Materials and Methods.For mathematical modeling of stresses, isostatically reduced data on abnormal gravitation field were used. The methods of continuum mechanics and methods of the theory of differential equations were used to design a model for estimating the stressstrain state of the Earth Lithosphere. For processing input, intermediate and outcoming data, the Fourier transform method of spectral analysis for constructing grid functions and spectral-temporal method were used. To model for the stress-strain state of the Lithosphere globally, stress calculation was corrected on the basis of sputnik-derived velocity data at the surface of the earth crust. The data on the rates of horizontal and vertical movements at the surface of the Earth crust were processed to obtain a distribution of velocities in the uniform grid embracing longitudes and latitudes. The processing procedure was carried out on the basis of the Kraiging method. The software was developed in Borland Delphi 7.0 programming environment.
Results. Based on the data on the abnormal gravitation field in isostatic reduction and information on the distribution of velocities of horizontal motions on the surface of the Earth crust, a mathematical model of the stress-strain state of the Lithosphere was constructed. With the help of the obtained mathematical model and software complex, the stress-strain state of the Lithosphere was calculated at various depth using elastic and elastic-viscous models, and maps of equipotential distribution of shear elastic-viscous deformations in the lithosphere at the depth of 10 km were constructed.
Discussion and Conclusion. The presented mathematical model and software allow restoring fields of both elastic and elastic-viscous deformations that is fundamental for quantification of elastic-viscous shear stresses deep in the Earth Lithosphere.

Keywords: mathematical model, geodynamic stability, stress tensor, displacement vector, shear deformation, viscosity; lithosphere

For citation: Faddeev A.O., Pavlova S.A., Nevdakh T.M. Mathematical Models and Evaluation Software for Stress-Strain State of the Earth’s Lithosphere. Inzhenernyye tekhnologii i sistemy = Engineering Technologies and Systems. 2019; 29(1):51-66. DOI: https://doi.org/10.15507/2658-4123.029.201901.051-066

Contribution of the authors: A. O. Faddeev – scientific management, formulation of the basic research concept, writing the draft and drawing conclusions; S. A. Pavlova – analysis of analytical and practical materials, computer processing; T. M. Nevdakh – conducting a critical analysis of research and finalizing the text, literary and patent analysis.

All authors have read and approved the final version of the paper.

Received 20.04.2018; revised 10.09.2018; published online 29.03.2019

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