On closed-form expressions for the approximate electromagnetic response of a sphere interacting with a thin sheet — Part 1: Theory in the frequency and time domain
Bibliographic record
Abstract
ABSTRACT In mineral exploration and geologic mapping of igneous and metamorphic terranes, the background is often dominantly resistive. The most important electromagnetic interaction is between a discrete conductor and an overlying sheet of conductive overburden (e.g., glacial clays or weathering products of the basement rocks). To enable the electromagnetic modeling of these common situations, here I provide closed-form expressions for the approximate electromagnetic response of a sphere embedded in highly resistive rocks and interacting with an overlying thin sheet. The sphere is assumed to be dipolar and excited by a locally uniform field. The expressions in the time and frequency domains are represented as sums of complete and incomplete cylindrical functions. New asymptotic approximations are provided for the efficient evaluation of the required incomplete cylindrical functions. The frequency-domain formulas are validated by numerical transformation to the time domain and comparison to the time-domain solution.
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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 | 0.001 | 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".