The magnetic gradient tensor of a right circular cylinder: theoretical considerations in the determination of magnetisation direction
Bibliographic record
Abstract
This paper investigates the use of the magnetic gradient tensor and its eigenvectors to derive expressions for estimating the direction of magnetisation of a uniformly magnetised right circular vertical cylinder. Expressions for the gradient tensor, the eigenvalues and eigenvectors, the normalised source strength (NSS), and the direction of magnetisation on the axis of a vertical cylinder are shown to be identical in form to those previously derived for a magnetised sphere or dipole. However, the off-axis gradient tensor field of a vertical cylinder is significantly different to that of a magnetic sphere or dipole particularly at low observation heights. These differences lessen with increasing observation height and in more compact pipes. The normalised source strength displays a directional asymmetry in the eigenvector field of the gradient tensor above a pipe which is related to the direction of magnetisation. This azimuthal asymmetry in the NSS results exclusively from the horizontal components of magnetisation, which are perpendicular to the longitudinal face of the vertical cylinder. In contrast, the vertical component of magnetisation is normal to the circular planar face and produces radial symmetry in the NSS. Additionally, the paper details some unusual properties of the NSS which are attributable to non-dipole field components in the gradient tensor field which cause pairs of eigenvectors to interchange directions when ordered by their eigenvalues, as is done when calculating the NSS. This results in spatial discontinuities in the eigenvector fields arising from crossovers in the ordered eigenvalue surfaces which vary with both magnetisation direction and observation height. This phenomenon is not present in a dipole field and thus provides direct evidence of non-dipole field components. Understanding this complexity in the eigenvector field is essential to designing methodologies which can successfully estimate the direction of magnetisation over a uniformly magnetised cylinder. One proposed method based on the peak NSS, uses airborne gradient tensor data to accurately estimate magnetisation direction over a reversely magnetised pipe-like body in the Diavik diamond field of north-western Canada. The results are verified using a full tensor inversion.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".