Stratified multifractal magnetization and surface geomagnetic fields-II. Multifractal analysis and simulations
Why this work is in the frame
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Bibliographic record
Abstract
In Paper I, we showed how anisotropic scaling spectral (second‐order) models of the magnetization (M) were realistic at both high‐ and intermediate‐wavenumber regimes of the surface magnetic field (B). However, in order to produce full stochastic M and surface B models, we need assumptions about statistical moments other than second order. The usual approach is to assume quasi‐Gaussian statistics so that all the statistical moments are scaling according to a single exponent. The corresponding fields are monofractal. All structures—both weak and strong—have the same unique fractal dimension, there are no strong anomalies and there are no intermittent transitions from one strata or region to another; such assumptions are quite unrealistic. Using seven surface B surveys, we show that the data are, on the contrary, multifractal, and we characterize their multifractal parameters in both the high‐ and intermediate‐wavenumber regimes with the help of universal multifractal exponents. Using anisotropic (stratified) multifractal models, we deduce the M statistics and produce M and surface B simulations with all statistical exponents quite near to those of the observed surface B field; they are also visually realistic, showing anomalies at all scales. Finally, we analyse the horizontal anisotropy of the surface B fields and use this to infer the M statistics. This enables us to produce anisotropic 3‐D M, B models with more realistic texture and morphology of structures. We conclude that both multifractality and scaling anisotropy are indispensable for realistic geophysical models.
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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) | 0.001 | 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 it