Surface loading of a viscoelastic planet--III. Aspherical models
Bibliographic record
Abstract
In Paper I of this series we developed a generalized normal‐mode formalism for computing the response of an aspherical, self‐gravitating, linear viscoelastic earth model to a surface load. In the present article we introduce an expansion for the normal modes of an aspherical earth model, using as basis functions the normal modes of a spherically symmetric reference model. This expansion leads to a non‐linear eigenvalue problem for the expansion coefficients and decay rates. We develop a linearization of this problem using perturbation theory, which incorporates arbitrary levels of coupling between normal‐mode multiplets. As an illustration, we consider the special case of radial perturbations to a spherically symmetric model, and compare predictions based upon perturbation theory with those based upon the usual non‐perturbative forward theory. We demonstrate that including overtone coupling is necessary for the accurate prediction of perturbations to the normal‐mode decay times and eigenfunctions. These calculations suggest that our theory can accurately accommodate order of magnitude lateral variations in mantle viscosity and significant changes in lithospheric thickness.
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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 | 0.000 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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".