Periodic surface loading using GRACE data for a layered viscoelastic earth model based on a direct relationship between geoid and displacement

Loading theory is fundamental in explaining deformation resulting from surface mass changes. Although various theoretical methods, including the classical elastic loading theory by W. E. Farrell and I. M. Longman, have been proposed, a viscoelasticity-based theory may be required to address long timescale loading problems, such as annual and interannual deformation, as well as longer timescale loading effects. In this study, we use a semi-analytical approach to simulate the continuous periodic loading deformation of a viscoelastic, spherical, layered earth model with linear rheology profiles. We provide a series of formulas in the spectral domain for the spatiotemporal displacement, which establish connections between mass, geoid and displacement solely through the utilization of complex Love numbers and Stokes coefficients, thereby circumventing the need for viscoelastic Green's function. Using our newly proposed method, we investigate the viscoelastic loading deformation caused by annual cyclic mass loading, considering both steady-state creep and additional transient creep with a wide range of viscosities. The results indicate that when utilizing steady-state viscosity values constrained by GIA data, the viscoelastic effect is not evident in the annual cyclic load deformation. However, incorporating the Burgers model with transient creep mainly constrained by post-seismic deformation influences the amplitude and phase of the annual cyclic loading, highlighting the role of rheology. Furthermore, we observe that the horizontal displacement in periodic load deformation exhibits a higher sensitivity to the viscosity of the model compared to the geoid and vertical displacement, regardless of the rheological model used.