A new description of Earth's wobble modes using Clairaut coordinates 2: results and inferences on the core mode spectrum
Bibliographic record
Abstract
Numerical solutions are presented for the formulation of the linear momentum description of Earth's dynamics using Clairaut coordinates. We have developed a number of methods to integrate the equations of motion, including starting at the Earth's centre of mass, starting at finite radius and separating the displacement associated with the primary rigid rotation. We include rotation and ellipticity to second order up to spherical harmonic T<f>$_5^m$</f>, starting with the primary displacement T<f>$_1^m$</f> with <it>m</it> = ±1. We are able to confirm many of the previous results for models PREM (with no surface ocean) and 1066A, both in their original form and with neutrally stratified liquid cores. Our period search ranges from the near-seismic band [0.1 sidereal days (sd)] to 3500 sd, within which we have identified the four well-known wobble-nutation modes: the Free Core Nutation (retrograde) at −456 sd, the Free Inner Core Nutation (FICN, prograde) at 468 sd, the Chandler Wobble (prograde) at 402 sd, and the Inner Core Wobble (ICW, prograde) at about 2842 sd (7.8 yr) for neutral PREM. The latter value varies significantly with earth model and integration method. In addition we have verified to high accuracy the tilt-over mode at 1 sd within a factor 10−6. In an exhaustive search we found no additional near-diurnal wobble modes that could be identified as nutations. We show that the eigenfunctions for the as-yet-unidentified ICW are extremely sensitive to the details of the earth model, especially the core stability profile and there is no well-defined sense of its wobble relative to the mantle. Calculations are also done for a range of models derived from PREM with homogeneous layers, as well as with incompressible cores. For this kind of model the ICW ceases to have just a simple IC rigid motion when the fluid compressibility is either unchanged or multiplied by a factor 10; in this case the outer core exhibits oscillations that arise from an unstable fluid density stratification. For the FICN our results for the truncation at harmonic T<inf>5</inf> show less change from the T<inf>3</inf> truncation than a similar result reported elsewhere. Finally, we give a thorough discussion of the complete spectrum of the characteristic determinant including the location of poles and non-wobble gravity modes, and discuss in general the dynamics of the inviscid core at periods short compared to those involved in the geodynamo.
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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 | 0.000 |
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 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".