Analytical formulas for geometrical factor and sensitivity for long electrodes
Bibliographic record
Abstract
Abstract In the electrical resistivity method, electrodes are usually modelled as point current sources and point voltage measurements. If the burial depth of the electrode is significant compared with the spacing between electrodes, this point approximation may not be accurate. Common situations employing long electrodes include the use of metal‐cased boreholes as electrodes and small‐scale, high‐resolution environmental, engineering and archaeological surveys where electrode spacings may be very small. In this contribution, I present analytical expressions for the mutual resistance between long electrodes modelled as line current sources. Mutual resistances are then used to calculate geometrical factors. Additionally, I present an expression for the current density and use it to derive an analytical expression for the sensitivity of electrode arrays with long electrodes. The sensitivity is, in turn, used to calculate the mean depth and position which can be used as estimates of depth and position of investigation and as pseudosection plot points. Example calculations using the geometrical factor, sensitivity and mean depth are shown, and comparisons are made with simulations and lab‐scale experiments.
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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 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".