DOI: https://doi.org/10.24028/gzh.0203-3100.v39i1.2017.94012

Analysis of results of interpretation of elastic parameters of solid core of the Earth from the standpoint of current geomechanics

H.H. Guliyev

Abstract


It follows from the basic principles of mechanics of deformable solids relating to the strength, stability and propagation of elastic waves that the inner core of the Earth cannot exist in the form of a spherical structure in the assumed thermobaric conditions and calculation values of physico-mechanical parameters. Pressure level reaches a value that is significantly greater than the theoretical limit of medium strength in the model approximations at the surface of the sphere of the inner core. On the other hand, equilibrium state of the sphere is unstable by the geometric forming at much lower loads under the influence of the "dead" surface loads. In case of the action of "follower" loads, the assumed pressure value on the surface of the sphere is comparable with the value of the critical load of "internal" instability. In these cases, due to the instability of the equilibrium state, propagation of homogeneous deformations becomes uneven in the sphere. Moreover, the elastic waves with actual velocity cannot propagate in such conditions in solid medium. Violation of these fundamental conditions of mechanics needed in determining the physical and mechanical properties of the medium must be taken into account in the integrated interpretations of seismic and laboratory (experimental) data. In this situation, application of linear elasticity theory and elastic waves, despite compliance with the required integral conditions on the mass, moment of inertia and natural oscillations of the Earth, does not ensure the reliability of results on the structure and composition of the Earth's core.


Keywords


Earth's core; high pressure; instability; elastic waves with actual velocity

References


Abasov М. Т., Kuliev G. G., Dzhevanshir R. D., 2000. Development model of the Lithosphere. Vestпік RAN 70(2), 129—135 (in Russian).

Avsyuk Yu. N., 2001. Extraterrestrial factors affecting tectogenesis. In: Fundamental problems of global tectonics. Moscow: Nauchnyy Mir, 425—443 (in Russian).

Avsyuk Yu .N., 1973. Motion of the inner core. Doklady AN SSSR 212(5), 1103—1105 (in Russian).

Bullen K. E., 1978. The density of the Earth. Moscow: Mir, 442 p. (in Russian).

Guz A. N., 1989. Fracture mechanics of composite materials under compression. Kyiv: Naukova Dumka, 632 p. (in Russian).

Guz A. N., 1986a. Fundamentals of three-dimensional theory of stability of deformable bodies. Kiev: Vishcha shkola, 511 p. (in Russian).

Guz A. N., 1986b. Elastic waves in bodies with initial stresses. Vol. 2. Propagation patterns. Kiev: Naukova Dumka, 536 p. (in Russian).

Guz A. N., 1979. Stability of elastic bodies under uniform compression. Kiev: Naukova Dumka, 144 p. (in Russian).

Zharkov V. N., 2012. Physics of the Earth's interior. Moscow: Nauka і obrazovaniye, 384 p. (in Russian).

Guliyev H. H., 2009. Nonlinear actions of elastic medium and their effect on the propagation velocity of elastic waves. Izvestiya NANA. Ser. Nauki о Zemle (2), 31—39 (in Russian).

Guliyev H. Н., 2013. Deformations, corresponding to processes of consolidation, deconsolidation and phase transitions in internal structures of the Earth. Geofizicheskiy zhurnal 35(3), 166—176 (in Russian).

Kuliev G. G., 1988. Fundamentals of the mathematical theory of the stability of wells. Baku: Elm, 170 p. (in Russian).

Guliyev H. H., Askerov A. D., 2007. The solution of nonlinear problem on increase of environment density of the Earth depths and its instability. Izvestiya NANA. Ser. Nauki о Zemle (1), 38—50 (in Russian).

Kuskov O. L., Khitarov N. I., 1982, Thermodynamics and geochemistry of the core and mantle of the Earth. Moscow: Nauka, 279 p. (in Russian).

Levin В. V., 2001. The role of the Earth's inner core movements in the tectonic processes. In: Fundamental problems of global tectonics. Moscow: Nauchnyy Mir, 444—460 (in Russian).

Litasov K. D., Shatskiy A. F., 2016. Composition of the Earth's core: A review. Russian Geology and Geophysics 57(1), 22—46. doi:10.1016/j.rgg.2016.01.003.

Lobkovskiy L. I., Nikishin A. M., Khain V. E., 2004. Modern problems of geotectonics and geodynamics. Moscow: Nauchnyy Mir, 612 p. (in Russian).

Lyav A.I., 1935. The mathematical theory of elasticity. Moscow: The combined scientific and technical publishing. 676 p. (in Russian).

Molodenskiy M. S., 2001. The gravitational field. The figure and the internal structure of the Earth. Moscow: Nauka, 569 p. (in Russian).

Pushcharovskiy Yu. M., Pushcharovskiy D. Yu., 2011. When, how and why were the Earth's geospheres formed. Priroda (5), 25—31 (in Russian).

Rabotnov Yu. N., 1988. Mechanics of deformable solids. Moscow: Nauka, 569 p. (in Russian).

Sadovskiy M. A., Nikolaev A. V., 1982. New methods of seismic exploration. Prospects of development. Vestnik AN SSSR (1), 57—64 (in Russian).

Sedov L. I., 1970. Mechanics of the continuum medium. Vol. 1. Moscow: Nauka, 492 p. (in Russian).

Sorokhtin O. G., Ushakov S. A., 2002. Earth Development, Moscow: MGU Publ. House, 506 p. (in Russian).

Trusdell K., 1975. Initial course of rational mechanics of continuum media. Moscow: Nauka, 529 p. (in Russian).

Akbarov S. D., 2015. Dynamics of pre-strained bi-material elastic systems: linearized three-dimensional approach. Switzerland: Springer, 1004 p. doi:10.1007/978-3-319-14460-3.

Akbarov S. D., 2013. Stability loss and buckling delamination: three-dimensional linearized approach for elastic and viscoelastic composites. Berlin: Springer, 448 p. doi:10.1007/978-3-642-30290-9.

Anderson D. L., 2007. New theory of the Earth. New York, Cambridge: University Press, 385 p.

Anderson O. L., 1995. Equations of state of solids for geophysics and ceramic science. New York: Oxford University Press., 240 p.

Biot M. A., 1965. Mechanics of incremental deformation. New York: Willey, 506 p.

Birch F., 1952. Elasticity and constitution of the Earth's interior. J. Geophys. Res. 57(2), 227—286. doi:10.1029/JZ057i002p00227.

Deuss A., 2014. Heterogeneity and anisotropy of Earth's inner core. Annu. Rev. Earth Planet. Sci. 42, 103—126. doi: 10.1146/annurev-earth-060313-054658.

Dobretsov N. L., Shatskiy A. F., 2012. Deep carbon cycle and geodynamics: the role of the core and carbonatite melts in the lower mantle. Russian Geology and Geophysics 53(11), 1117—1132. doi: 10.1016/j.rgg.2012.09.001.

Dziewonski A.M., Anderson D.L., 1981. Preliminary reference Earth model. Phys. Earth Planet. Int. 25(4), 297—356. doi:10.1761 l/DP/9991844.

Guliyev H. H., 2010. A new theoretical conception concerning the tectonic processes of the Earth. New Concepts in Global Tectonics Newsletter (56), 50—74.

Guliyev H. H., 2011. Fundamental role of deformations in internal dynamics of the Earth. New Concepts in Global Tectonics Newsletter (61), 33—50.

Kennett B. L. N., Engdahl E. R., 1991. Traveltimes for global earthquake location and phase identification. Geophys. J. Int. 105(2), 429—465. doi:10.11 ll/j.l365-246X.l991.tb06724.x.

Kennett B. L. N., Engdahl E. R., Buland R., 1995. Constraints on seismic velocities in the Earth from traveltimes. Geophys. J. Int. 122(1), 108—124, doi:10.l lll/j.l365-246X.1995.tb03540.x.

Kuliev G. G., 1988. A new approach to calculation of the theoretical ultimate strength of materials. Strength of materials 20(5), 623—629. doi:10.1007/BF01528552.

Molodenskii S. M., 2010. Correctives to the scheme of the Earth's structure inferred from new data on nutation, tides, and free oscillations. Izvestiya, Physics of the Solid Earth 46(7), 555—579. doi: 10.1134/S1069351310070013.

Molodenskii S. M., Molodenskaya M. S., 2015. Attenuation of free spheroidal oscillations of the Earth after the M-9 Earthquake in Sumatra and the super-deep Earthquake in the Sea of Okhotsk: I. the Admissible Q-factor range for the fundamental mode and overtones of the free spheroidal oscillations. Izvestiya, Physics of the Solid Earth 51(6), 821—839. doi:10.1134/S1069351315060051.

Molodenskii S. M., Molodenskii M. S., 2015. Attenuation of free spheroidal oscillations of the Earth after the M - 9 Earthquake in Sumatra and super-deep earthquake in the Sea of Okhotsk: II. interpretation of the observed Q-factor. Izvestiya, Physics of the Solid Earth 51(6), 840—856. doi:10.1134/ S1069351315060063.

Morelli A., Dziewonski A. M., 1993. Body-wave traveltimcs and a spherically symmetric P- and S-wave velocity model. Geophys. J. Int. 112(2), 178—194. doi:10.11 ll/j.l365-246X.1993.tb01448.x.

Nimmo F., 2015. Energetics of the core. Vol. 8. In: Treatise on geophysics (second edition). Oxford: Elsevier, 27—55. http://dx.doi.org/10.1016/B978-0-444-53802-4.00139-l.

Souriau A., Calvet M., 2015. Deep earth structure: The Earth's cores. Vol. 1. In: G. Schubert (Editor-in- Chief). Treatise on geophysics (second edition). Oxford: Elsevier, 725—757. http://dx,doi.org/l0.10l6 /В978-0-444-53802-4.00020-8.

Sumita I., Bergman M. I., 2007. Inner-Core Dynamics. Vol. 8. In: Treatise on Geophysics. Oxford: Elsevier, 299—318. http://dx.doi.org/10.1016/B978-044452748-6.00132-2.

Thurston R., Brugger K., 1964. Third-order elastic constants and velocity of small amplitude elastic waves in homogeneously stressed media, Phys. Rev. 133(6A), 1604—1610. doi:http://dx.doi.org/ 10.1103/PhysRev.133.A1604.