Theoretical viscoelastic deformations due to an expansion source in a spherical earth model

Abstract

Sources of expansion, such as nuclear explosions and magma chambers, can cause various surface effects, such as displacement and gravity field change on the Earth. The deformation simulation of an expansion source can be traced back to certain classic works nearly 70 yr ago, which were primarily based on a half-space earth model. However, the deformation of expansion sources in a spherical earth model has not been presented in the context of the semi-analytical viscoelastic Love numbers framework. In this study, we present the deformation Green's function for an expansion source in a spherical, non-rotating, viscoelastic, isotropic layered earth model using a semi-analytical method. We further obtain the analytical Green's functions for an elastic model in the near field. In addition, the influence of the stratification, curvature, and viscosity on the deformation is analysed using a layered spherical earth model. The suitability and effectiveness of the formulas are verified by numerical experiments and compared with previous results. The method presented in this paper is useful for explaining the viscoelastic deformations caused by the deep expansion source, for example, large magma chambers and upwelling of a mantle plume, in the layered viscoelastic earth model.