Displacements due to surface temperature variation on a uniform elastic sphere with its centre of mass stationary

We investigate the displacement field induced by temperature variation within a spherical thermal boundary layer under an Earth-like condition of surface heating by deriving analytical solutions on a uniform elastic sphere under the constraint that its centre of mass remains stationary in space. Similar to strain solutions, our displacement solution consists of spectra of two distinctive modes: an exponential mode relating to the thermal body force and a power-law mode relating to the (equivalent) thermal surface loading. The exponential modes of the thermal body force in our solution turn out to be identical to that in a classic half-space solution, while the effect of thermal loading by the power-law modes in our spherical solution is different from the exponential modes of thermal loading in the half-space solution. The thermal surface loading is found, by analytical and numerical analyses, equally important in order of magnitude as the thermal body force in producing the radial displacement at the surface throughout the entire harmonic spectrum. The transverse displacement arises mainly from the power-law modes of thermal surface loading. Numerical simulations, based on NASA's space-borne observation of the global land surface temperature (ocean is masked out), have shown unique patterns in the annual variation of the global displacement field that fits the climatological and geographical settings. The predicted amplitude of the thermally induced surface deformation in global scale is at the millimetre level with the largest similar to 2 mm for radial displacement and similar to 1 mm for transverse displacement. Comparative analysis shows that the radial displacement field is asymptotically proportional to the surface temperature distribution, which justifies the use of the half-space solution as a good approximation for modelling the global radial displacement. The transverse displacement obtained by patched half-space solution fails to capture the long-range transverse variations on a spherical surface, and thus, is inadequate for modelling and synthesizing the global transverse displacement.