Echo, Reverberation, and Echo-to-Reverberation Ratio for a Short Pulse in a Range-Dependent Pekeris Waveguide
Bibliographic record
Abstract
In shallow water, active sonar performance is typically limited by reverberation, making the prediction of target echo, reverberation, and echo-to-reverberation ratio an important part of sonar performance prediction. In range-dependent shallow-water environments, the echo is often calculated without considering the effect of dispersion, and reverberation predictions are often limited to Lambert's rule for seabed scattering. In this paper, analytical formulae are derived for the echo, including the effect of time dispersion, and for reverberation for non-Lambert scattering laws. More specifically, the method for calculating the short-pulse echo intensity developed by Harrison and Nielsen is extended to a range-dependent bathymetry. For reverberation, the Zhou-Harrison method is also generalized to cover an arbitrary power law for the seabed scattering coefficient, combined with a range-dependent bathymetry. These formulae are applied to range-dependent test cases from an international workshop, and compared with predictions using a normal mode sum. Neglect of time dispersion is found to result in an error of up to 16 dB. Results for a cylindrically symmetric bathymetry differ by up to 14 dB from the corresponding results with a Cartesian symmetry.
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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) | 0.000 | 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 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".