An Analytical Solution of the Electric Field Excited by a Vertical Electric Dipole Above a Lossy Half-Space: From Radio to Microwave Frequencies
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Bibliographic record
Abstract
In this article, an analytical solution of the electromagnetic radiation from a vertical electric dipole (VED) above a lossy half-space is proposed. The expression for the traditional solution is associated with the Sommerfeld-type integral, which is difficult to evaluate due to its highly oscillating and slowly decaying integrand. The solution for the intermediate Hertz potential is decomposed into two integrals and a rigorous closed-form solution in the near and far-field regions are presented for each term. Then, the scattered electric-field components are calculated from the intermediate Hertz potential. A numerical evaluation of the solution for different lossy half-spaces, such as seawater, wet earth, dry earth, and lake water, validates the accuracy of the proposed solution at various frequencies, from radio to microwave frequencies, as well as different distances from the antenna in the near and far-field regions.
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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 | 0.001 |
| 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 it