An Analytical Solution of Electromagnetic Radiation of a Vertical Dipole Over a Layered Half-Space
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Bibliographic record
Abstract
An analytical solution for the wave scattering generated by a vertical dipole above horizontally stratified media is proposed. The solution to the problem is given in terms of 2-D Fourier transforms, which leads to Sommerfeld-type integrals. The solution is decomposed into three terms and an analytical closed-form solution as a function of physical layers specification for the electric field intensity is deduced from the results. Two terms are expressed with hyperbolic functions and the third term is presented using the Gauss error function. A numerical evaluation of the integrals that constitute the formal result of the problem validates the accuracy and efficiency of the proposed solution at various frequencies as well as at different distances from the source. The presented solution is also implemented for the particular case of surface ocean scattering in the high frequency (HF) band and the overall behavior of the solution, which consists of three terms, is evaluated by their distance from the antenna in the near field 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 | 0.000 |
| 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 it