Using commercial finite-element packages for the study of Glacial Isostatic Adjustment on a compressible self-gravitating spherical earth – 1: harmonic loads
Bibliographic record
Abstract
A new generation of numerical models is being developed to model Glacial Isostatic Adjustment in a self-gravitating spherical earth with lateral heterogeneity and/or nonlinear rheology in the mantle. Of special interest is the Iterative Stress Transform (IST) method (also known as Coupled Laplace-Finite Element method) because it uses commercial finite-element packages which are readily available, well tested and reliable. Although the IST method is efficient and can produce very accurate results, it is mainly developed for incompressible earth models. So there are efforts to generalize the IST method for more realistic compressible earths. Here, we will extend the finding of Bängtsson & Lund to confirm that the IST method is not likely to be generalized for a compressible earth. Next, a new approach, called the Iterative Body Force (IBF) is presented, which aims to replace all body forces in each element by their volumetric average and solve the governing differential equations iteratively. The result of the IBF approach is then benchmarked with the conventional normal mode method (NMM) for laterally homogeneous axisymmetric earth models forced by Heaviside harmonic loads. For incompressible earth models, the IBF approach gives excellent agreement with NMM that uses analytical propagation method. For compressible earth models, good agreement is also obtained with NMM that uses the numerical integration method, provided that the timescale of compressional instability is long compared with the loading period. However, the agreement deteriorates if the effect of gravitational instability is significant because the numerical errors grow differently for each method. Finally, the IBF approach is used to study the spatiotemporal evolution of body forces and understand the development of instability. It is shown that compression in a uniform layer can result in the top becoming denser than the bottom of the same layer which promotes Rayleigh–Taylor instability. If this can be suppressed by the stabilization forces of pre-stress advection and internal buoyancy of the layer, then stability remains. However, if the compressional instability becomes large enough to change the direction of the pre-stress advection force, then the deformation can grow so large that convection instability can be triggered.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.012 | 0.004 |
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 source (direct Gemma or distilled Codex), 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".