Multiple-order moments of the transient electromagnetic response of a one-dimensional earth with finite conductance – theory
Bibliographic record
Abstract
The concept of moments of the electromagnetic response is useful in electromagnetic interpretation. Analytic formulae exist for low-order moments of a few conductivity models, enabling source parameters such as time constant, depth, conductance and conductivity to be estimated from the measured moments of the electromagnetic response. However, most models for which analytic formulae exist have conductivity varying abruptly as a function of depth or position. In this paper, we have derived a procedure that allows moments of any order to be calculated for a conductivity which has finite conductance but can otherwise vary arbitrarily with depth. The horizontal loop transient electromagnetic step response is computed as a sum of residues. Integration of the step response over time yields a mathematical expression for a moment of any order. We illustrate the procedure for a Gaussian conductivity function which varies smoothly with depth. The Gaussian model produces results that agree in specific limits with the thin sheet, thick sheet and half-space cases.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| 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 | 0.001 |
| 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".