The structural index in gravity and magnetic interpretation: Errors, uses, and abuses
Bibliographic record
Abstract
ABSTRACT The structural index (SI) is based on the concept of Euler homogeneity, a description of scaling behavior. It has found wide use in potential-field depth estimation and is a constant integer for simple sources with single singularities (points, lines, thin-bed faults, sheet edges, infinite contacts). For these cases, the SI is identical to the index of a simple power-law field fall-off with distance. The simple Euler formulation is only strictly correct for such simple sources and integer SI values. The widespread use of the simple Euler method on more complex structures, using fractional SI values is likely to produce misleading results because the SI is no longer a constant for any given source. We examine a recently published example that used an arbitrary SI to estimate depth to the base of the crust for Africa and produced misleading results. Extension to more complex sources such as tabular bodies or thick steps requires one of several more generalized approaches, which recognize all variables with spatial dimensions (including source size parameters) and may make use of negative SI values, address omitted variable bias or use an explicit multiple-source formulation. An alternative approach using homogeneity via differential similarity transforms is probably the best way forward. An error in the literature is corrected: the gravity SI for a finite step is −1, but it requires a more generalized formulation. We develop a new terminology, fractional SI, s, which is permitted to take fractional values and makes no pretense to honor concepts of homogeneity.
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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 | 0.011 | 0.046 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.006 | 0.007 |
| Science and technology studies | 0.002 | 0.029 |
| Scholarly communication | 0.007 | 0.011 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.002 | 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".