Internal Mass-Induced Elastic Deformation: A Semi-Analytic Approach

This research presents an innovative semi-analytical method to study the deformation of a viscoelastic, spherical, layered Earth model under periodic loading. We explore the effects of surface mass changes on deformation over various timescales, including annual and interannual, using a linear rheology profile. Our approach leverages a novel set of formulas in the spectral domain, linking mass, geoid, and displacement through complex Love numbers and Stokes coefficients. This technique bypasses the traditional reliance on viscoelastic Green’s functions. In our analysis, we particularly focus on the impact of annual cyclic mass loading on viscoelastic loading deformation. We consider both steady-state creep and additional transient creep across a broad spectrum of viscosities. Our findings reveal that while steady-state viscosity values, constrained by Glacial Isostatic Adjustment (GIA) data, show minimal viscoelastic impact on annual load deformation, the inclusion of transient creep, primarily informed by post-seismic data and modeled through the Burgers model, significantly alters the deformation's amplitude and phase. This underscores the importance of rheological properties in understanding Earth's deformation. Furthermore, our results demonstrate a notable difference in how the horizontal displacement, as opposed to geoid and vertical displacement, responds to viscosity changes. This disparity is observed regardless of the rheological model applied, indicating a greater sensitivity of horizontal displacement to viscosity variations in periodic load deformation. Our study provides new insights into the complexities of Earth's viscoelastic response to cyclic loading, contributing to a deeper understanding of geophysical processes.