Earth's long-period wobbles: a Lagrangean description of the Liouville equations
Bibliographic record
Abstract
The two low-frequency wobble modes of the Earth are the Chandler wobble (CW) and the inner core wobble (ICW). The CW period is about 400 d for an ocean-free model, and the ICW period has previously been estimated to be about 6.6 yr. The latter mode is particularly difficult to compute due to approximations that must be introduced to describe the response of the fluid core at long periods. Here we construct a Lagrangean formulation of the Liouville equations for the solid parts of the Earth, with disturbances from hydrostatic equilibrium referred to a uniformly rotating reference frame. Gravitational coupling, elastic deformation of the solid parts and compressibility of the fluid core are included, but not dissipative mechanisms. We show that at these low frequencies the Poisson equation for the gravitational perturbation can be solved without explicit knowledge of the outer core flow. Deformation of the solid parts can be assumed to be described by static Love numbers. With these assumptions, we find that the CW solution is essentially the same as in classic results using the linear momentum equations. On the other hand, the ICW is here found to have a period of about 7.5 yr for PREM, some 15 per cent longer than previous studies as a consequence of elastic deformation of the inner core. The existence of the ICW depends crucially on the gravitational torque exerted by the mantle on the inner core.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".