Using commercial finite element packages for the study of earth deformations, sea levels and the state of stress

TLDR

Commercial finite element packages require modifications before they can be used for long‑wavelength deformation or viscoelasticity studies, and interpreting their outputs is crucial for modeling stress states. The paper details how and why commercial FE codes must be modified under incompressibility assumptions. The authors modify commercial FE codes for incompressibility, model both non‑self‑gravitating flat earth and self‑gravitating spherical earth (with a 5‑iteration convergence procedure), and implement a gravitationally self‑consistent sea‑level equation on the spherical earth. Analytical and numerical tests confirm the modifications, showing good agreement with conventional spectral methods.

Abstract

Modifications to commercial finite element (FE) packages must be applied before they can be used for geophysical studies involving long wavelength deformation or viscoelasticity. This paper provides in detail how and why the commercial codes have to be modified when incompressibility is assumed. Both the non-self-gravitating flat earth and self-gravitating spherical earth will be considered. The latter involves an iterative procedure, which converges within 5 iterations. This is demonstrated both analytically and numerically. In addition, implementation of the gravitationally self-consistent sea level equation on a self-gravitating spherical earth is also described. Good agreement between numerical results obtained with this coupled finite-element method and the conventional spectral method is also demonstrated. In all cases, the interpretation of the outputs of FE models are particularly important in modelling the state of stress.