A commercial finite element approach to modelling Glacial Isostatic Adjustment on spherical self-gravitating compressible earth models
Bibliographic record
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.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".