A cautionary note on the use of range‐dependent propagation models in underwater acoustics

Numerous sound propagation models in underwater acoustics are based on the representation of a sound field in the form of a decomposition over normal modes. In the framework of such models, the calculation of the field in a range-dependent waveguide (as well as in the case of 3D problems) requires the computation of normal modes for every point within the area of interest (that is, for each pair of horizontal coordinates x,y). This procedure is often responsible for the lion’s share of total computational cost of the field simulation. In this study, we present formulae for perturbation of eigenvalues and eigenfunctions of normal modes under the water depth variations in a shallow-water waveguide. These formulae can reduce the total number of mode computation instances required for a field calculation by a factor of 5–10. We also discuss how these formulae can be used in a combination with a wide-angle mode parabolic equation. The accuracy of such combined model is validated in a series of numerical examples.

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Use of Underwater Acoustics in Marine Conservation and Policy: Previous Advances, Current Status, and Future Needs

Journal of Marine Science and Engineering ◽

10.3390/jmse9020173 ◽

2021 ◽

Vol 9 (2) ◽

pp. 173

Author(s):

Shane Guan ◽

Tiffini Brookens ◽

Joseph Vignola

Keyword(s):

World War Ii ◽

Sound Propagation ◽

Underwater Acoustics ◽

Marine Conservation ◽

Current Status ◽

Source Characterization ◽

Marine Animals ◽

Significant Information ◽

Propagation Models ◽

Interdisciplinary Field

The interdisciplinary field of assessing the impacts of sound on marine life has benefited largely from the advancement of underwater acoustics that occurred after World War II. Acoustic parameters widely used in underwater acoustics were redefined to quantify sound levels relevant to animal audiometric variables, both at the source and receiver. The fundamental approach for assessing the impacts of sound uses a source-pathway-receiver model based on the one-way sonar equation, and most numerical sound propagation models can be used to predict received levels at marine animals that are potentially exposed. However, significant information gaps still exist in terms of sound source characterization and propagation that are strongly coupled with the type and layering of the underlying substrate(s). Additional challenges include the lack of easy-to-use propagation models and animal-specific statistical detection models, as well as a lack of adequate training of regulatory entities in underwater acoustics.

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Stop Look And listen A cautionary note about curriculum reform

Journal of Dental Education ◽

10.1002/j.0022-0337.1971.35.11.tb00454.x ◽

1971 ◽

Vol 35 (11) ◽

pp. 677-679

Author(s):

HM Myers ◽

J Hancock

Keyword(s):

Curriculum Reform ◽

Cautionary Note

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Evaluating the Factor Structure of “Self-Concept” in Children: A Cautionary Note

Measurement and Evaluation in Guidance ◽

10.1080/00256307.1977.12022729 ◽

1977 ◽

Vol 9 (4) ◽

pp. 172-176 ◽

Cited By ~ 9

Author(s):

Robert J. Drummond ◽

Walter G. McIntire

Keyword(s):

Factor Structure ◽

Self Concept ◽

Cautionary Note

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A Cautionary Note on Incremental Fit Indices Reported by LISREL

Methodology ◽

10.1027/1614-1881.1.2.81 ◽

2005 ◽

Vol 1 (2) ◽

pp. 81-85 ◽

Cited By ~ 5

Author(s):

Stefan C. Schmukle ◽

Jochen Hardt

Keyword(s):

Factor Analysis ◽

Maximum Likelihood ◽

Structural Equation ◽

Structural Equation Models ◽

Null Model ◽

Likelihood Estimation ◽

Parameter Estimates ◽

Fit Indices ◽

Cautionary Note ◽

Confirmatory Factor

Abstract. Incremental fit indices (IFIs) are regularly used when assessing the fit of structural equation models. IFIs are based on the comparison of the fit of a target model with that of a null model. For maximum-likelihood estimation, IFIs are usually computed by using the χ2 statistics of the maximum-likelihood fitting function (ML-χ2). However, LISREL recently changed the computation of IFIs. Since version 8.52, IFIs reported by LISREL are based on the χ2 statistics of the reweighted least squares fitting function (RLS-χ2). Although both functions lead to the same maximum-likelihood parameter estimates, the two χ2 statistics reach different values. Because these differences are especially large for null models, IFIs are affected in particular. Consequently, RLS-χ2 based IFIs in combination with conventional cut-off values explored for ML-χ2 based IFIs may lead to a wrong acceptance of models. We demonstrate this point by a confirmatory factor analysis in a sample of 2449 subjects.

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