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 .
In previous studies, the northern hemisphere of the Earth is considered to be in compression while the southern one is in expansion. In this study, based on three different methods, we calculate average vertical variations of the two hemispheres from velocity field data under the ITRF2008 (International Terrestrial Reference Frame 2008) solution. Results show that the northern hemisphere is in expansion at the rate about 1 mm/yr, while the compression rate of the southern hemisphere is one order smaller than the expansion rate of the northern one. After the post glacial rebound effect is subtracted, results show that the expansion and compression rates of the northern and southern hemispheres are 0.46 mm/yr and -0.19 mm/yr, respectively. Transformation between the velocity fields under ITRF2008 and ITRF2000 can explain why different authors have different conclusions about the expansion/compression pattern of one hemisphere or the other. Anyway, the entire Earth is expanding at a rate about 0.2 mm/yr, and this estimation coincides with results of our previous studies. The mean variation rates of the radii at different latitudes have been calculated.
Thermal expansionEarth expansion Sea level rise (SLR) Space-geodetic data Velocities altimetry Earth's solid surface a b s t r a c t According to the space-geodetic data recorded at globally distributed stations over solid land spanning a period of more than 20-years under the International Terrestrial Reference Frame 2008, our previous estimate of the average-weighted vertical variation of the Earth's solid surface suggests that the Earth's solid part is expanding at a rate of 0.24 ± 0.05 mm/a in recent two decades. In another aspect, the satellite altimetry observations spanning recent two decades demonstrate the sea level rise (SLR) rate 3.2 ± 0.4 mm/a, of which 1.8 ± 0.5 mm/a is contributed by the ice melting over land. This study shows that the oceanic thermal expansion is 1.0 ± 0.1 mm/a due to the temperature increase in recent half century, which coincides with the estimate provided by previous authors. The SLR observation by altimetry is not balanced by the ice melting and thermal expansion, which is an open problem before this study. However, in this study we infer that the oceanic part of the Earth is expanding at a rate about 0.4 mm/a. Combining the expansion rates of land part and oceanic part, we conclude that the Earth is expanding at a rate of 0.35 ± 0.47 mm/a in recent two decades. If the Earth expands at this rate, then the altimetry-observed SLR can be well explained. g e o d e s y a n d g e o d y n a m i c s 2 0 1 5 , v o l 6 n o 4 , 2 4 8 e2 5 2
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.