Bibliographic record
Abstract
The seldom mentioned ray angle diagram (RAD) allows visualization of important properties of acoustic propagation. Based on the sound speed profile and Snell’s law, the RAD presents depth on the ordinate and tan θ(z; cn) on the abscissa for the full ray cycle of selected rays, parameterized by the ray parameter, cn. The angle θ(z; cn) is the angle the ray makes with the horizontal at depth z. Equivalently, it is the angle of tilt of the wavefront at depth z. Because many useful characteristics of acoustic propagation depend on tan θ(z; cn), it is used as the abscissa of the RAD. The tilt integral is defined as the integral of tan θ(z; cn) with respect to z between the upper and lower limits of the ray. The tilt integral can be visualized by an “area” on the RAD. The WKB phase integral, which relates rays and normal modes, is an integral of tan θ(z; cn) with respect to depth. Individual mode characteristics and number of propagating normal modes are represented on the RAD. Relationships to the adiabatic invariant, time delay for matched field processing, depth dependence of ambient noise, range-averaged transmission loss, and low frequency mode cut-off are discussed.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.012 | 0.003 |
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".