A commercial finite element approach to modelling Glacial Isostatic Adjustment on spherical self-gravitating compressible earth models

Abstract

SUMMARY This paper presents a method that modifies commercial engineering-oriented finite element packages for the modelling of Glacial Isostatic Adjustment (GIA) on a self-gravitating, compressible and spherical Earth with 3-D structures. The approach, called the iterative finite element body and surface force (FEMIBSF) approach, solves the equilibrium equation for deformation using the ABAQUS finite element package and calculates potential perturbation consistently with finite element theory, avoiding the use of spherical harmonics. The key to this approach lies in computing the mean external body forces for each finite element within the Earth and pressure on Earth's surface and core–mantle boundary (CMB). These quantities, which drive the deformation and stress perturbation of GIA but are not included in the equation of motion of commercial finite element packages, are implemented therein. The method also demonstrates how to calculate degree-1 deformation directly in the spatial domain and Earth-load system for GIA models. To validate the FEMIBSF method, loading Love numbers (LLNs) for homogeneous and layered earth models are calculated and compared with three independent GIA methodologies: the normal-mode method, the iterative body force method and the spectral-finite element method. Results show that the FEMIBSF method can accurately reproduce the unstable modes for the homogeneous compressible model and agree reasonably well with the Love number results from other methods. It is found that the accuracy of the FEMIBSF method increases with higher resolution, but a non-conformal mesh should be avoided due to creating the so-called hanging nodes. The role of a potential force at the CMB is also studied and found to only affect the long-wavelength surface potential perturbation and deformation in the viscous time regime. In conclusion, the FEMIBSF method is ready for use in realistic GIA studies, with modelled vertical and horizontal displacement rates in a disc load case showing agreement with other two GIA methods within the uncertainty level of GNSS measurements.

Influence of GIA Uncertainty on Climate Model Evaluation With GRACE/GRACE‐FO Satellite Gravimetry Data

“…Our approach is closely related to the work of Pan et al (2022) who similarly utilized an ensemble of GIA models with horizontally and vertically variable Earth structures to assess in particular variations in global mean sea-level since the last glacial maximum. All 56 GIA simulations considered in this study are performed with the VILMA model, that has been applied in many GIA-related studies in the past (Bagge et al, 2021;Dobslaw et al, 2020;Hoening et al, 2023;Huang et al, 2023;Klemann et al, 2008Klemann et al, , 2015Martinec et al, 2018;Schachtschneider et al, 2022). The numerical code solves the sea level equation in the spherical domain and accounts for continuum-mechanics, viscoelasticity, rotational feedback, self-gravitation, mass conservation, and the migration of coastlines.…”