On the roles of magnetization and topography in the scaling behaviour of magnetic-anomaly fields
Bibliographic record
Abstract
There is lack of agreement on the underlying cause of widely observed power-law scaling behaviour of magnetic-anomaly fields. Some workers ascribe this behaviour to intrinsic 3-D fractal distributions of magnetization in the crust of the Earth; others point to a power-law exponent β∼ 3, expected for a random ensemble of statistically independent magnetized prisms: the classic Spector & Grant model (SG model). We apply a perturbation approach to the Parker model to derive expressions for the power spectra of magnetic-anomaly fields in the presence of laterally varying magnetization and/or topography at the top of magnetic basement. Under appropriate assumptions, our modified Parker model reduces to either an SG model or a 2-D fractal model. In the case of fractal magnetization without topography, the power-law slope of the magnetic-anomaly field (after depth correction) is equal to the power-law slope for the magnetization distribution. In the case of fractal basement topography alone, the power-law slope is reduced by 2. Where both the magnetization and topography are fractal, the effects of magnetization tend to dominate the power-law behaviour of the associated magnetic-anomaly field. Two real-data examples from the Canadian Shield exhibit power-law exponents of 2.02 ± 0.02 and 1.42 ± 0.01, within a wavelength band of 2 to 100 km. These slopes are significantly different from previously cited values of ∼3, casting doubt on the general applicability of the β∼ 3 slope that is inherent to SG models at high wavenumber.
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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".