An improved Gaussian beam caustic correction for Bellhop at low frequencies
Bibliographic record
Abstract
Gaussian beams are commonly used in ray-tracing to mitigate the effects of caustics and shadow zones. The problem is how to determine the width of these “fuzzy” beams. Porter and Bucker [J. Acoust. Soc. Am. 82, 1349–1359, 1987] proposed a method that expressed the beamwidth and curvature in terms of p and q of the dynamic ray equations. We call q the beamwidth factor. In the Gaussian beam implementation caustics are not caused by the crossing of two rays; rather they occur when the beamwidth factor, which appears in the denominator of the amplitude, becomes small. In practice, this is generally not a problem at high frequencies, but as the frequency gets lower the problem gets more severe. The widely used Bellhop model has a procedure, which “caps” the beamwidth when q becomes too small, but the procedure eventually breaks down at low frequencies. Here, we propose a different cap based on a cylindrical wave front converging to the focal point of a caustic. The various caps are compared with the “exact” normal mode solution for a shallow-water upward refracting environment, illustrating how the new cap provides better reduction of the caustic anomalies.
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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".