Deformations of the Earth’s mantle due to core displacements

Abstract

The planet is assumed to consist of an absolutely rigid sphere to which the viscous elastic spherical shell (the mantle) is connected from the external side. In the undeformed state the centres of mass of the mantle and the core coincide and the shells have concentric positions. The centre of mass of the core is considered to be displaced according to a definite law relative to the centre of mass of the mantle in its undeformed state among to the differential action from external celestial bodies. The solution of the problem of elasticity is obtained using a restricted treatment by taking into account only the mutual interaction of the mantle and the moving core and by neglecting the non-sphericities of the core and the mantle. The corresponding effects of the mantle deformations caused by the external bodies are known and can be studied separately on the basis of the principle of superposition. The deformations of the Earth's mantle due to secular drift of the core along the polar axis are described. The phenomenon of the contrasting tendencies in the deformations northern and southern hemispheres of the Earth (expansion and contraction, respectively) is discovered. The evaluation of the velocity of the core drift relative to the mantle's centre of mass has been obtained and was found to be equal to 8.0 cm year −1 .

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“…In this case, the displacement of the center of mass is determined with respect to the reference coordinate system of the mantle. One may consider the second effect of the change in the mean radii of the Earth hemispheres, which is caused by deformation of the surface of the mantle due to the gravitational effect of displacement of the center of mass [Barkin, Shatina, 2005]. According to our theoretical (dynamic) estimates, this effect is very small, about 0.014 mm/yr in the northern hemisphere, and about -0.014 mm/yr in the southern hemisphere (near the poles).…”

“…The geodetically observed length variations of latitude circles of the Earth testify an asymmetry shape variations of the northern and southern hemispheres as an important consequence of the mantle deformation due to gravitational action of the drifting core of the Earth [Barkin, 2002;Barkin, Shatina, 2005;Barkin, Shuanggen, 2006]. The circles are pulled together in the southern hemisphere and stretched in the northern hemisphere.…”

“…Meanwhile, this phenomenon is also supported by the secular radial motions of geodetic observations and the secular geocenter motion trend towards the Sorth Pole of the Earth. These relative motions of the Earth shells lead to inverse changes of the Earth shape which are manifested as formation of fluxes on the Earth surface as well as the intensity of many natural processes in the hemispheres [Barkin, 2002;Barkin, Shatina, 2005]. The secular asymmetrical change of the Earth hemispheres is an important signal to the Earth interior activities, such as relative oscillations or deformations of the core and mantle induced by the forced core-mantle interaction.…”

“…1) with the shape of the geoid. Theoretical values of the rates of secular lengthening of latitude circles are determined by the following equation [Barkin, Shatina, 2005;Barkin, 2007].…”

“…The dynamic theory [Barkin, 2002] predicts another subtle effect -contrasting secular variations of the northern hemisphere average radii (slow growth with velocity) and the southern hemisphere average radii (slow down) by deformation of the Earth's mantle [Barkin, Shatina, 2005]. The dynamic effect is very small and corresponds to the maximum value of the strain rate of the hemispheres (near the poles) at about 0.033 mm/yr [Barkin, 2011[Barkin, , 2013Barkin et al, 2013aBarkin et al, , 2013b.…”