Deformation of a spherical, viscoelastic, and incompressible Earth for a point load with periodic time change

SUMMARY Planetary-scale mass redistributions occur on Earth for certain spatiotemporal periods, and these surface mass changes excite the global periodic loading deformations of a viscoelastic Earth. However, the characteristics of periodic viscoelastic deformations have not been well investigated even in a simple earth model. In this study, we derive the semi-analytical Green's functions (fully analytical Love numbers) for long-standing point sources with given periods using a modified asymptotic scheme in a homogeneous Maxwell spherical earth model. Here, the asymptotic scheme is needed in order to obtain accurate semi-analytical time-dependent Green's functions. The amplitudes and phases of the Green's functions may be biased if only the series summations of the Love numbers are used because the influence of viscoelasticity is degree-dependent. We compare the viscoelastic and elastic periodic Green's functions with different material viscosities and loading periods and investigate the amplitude increase percentage and phase delay of the periodic displacement and geoid change. For example, our analysis revealed that the viscosity increases the amplitude by 40–120 per cent and delays the phase approximately −100° to 60° for the displacement and geoid change when bearing a 10-yr loading period, assuming a viscosity of 1018 Pa s and a shear modulus 4 × 1010 Pa.