Acoustic scattering is a fundamental process that occurs when sound waves interact with objects in aquatic environments, such as fish, seaweed, or underwater structures. Accurate modeling of this process is crucial for various applications, including fisheries research, marine conservation, and underwater exploration. In this article, we will review the current state-of-the-art in numerical and analytical methods for modeling acoustic scattering in aquatic environments.

Numerical Methods

Numerical methods are widely used to model complex shapes and interactions that cannot be accurately described by analytical solutions. Two popular approaches are:

• Boundary Element Method (BEM): This method is based on the idea of dividing the problem domain into small elements, solving for the scattered field at each element, and then combining the results to obtain the total scattered field.
• Finite Element Method (FEM): This method involves discretizing the problem domain into small finite elements, solving for the unknowns at each element, and then combining the results to obtain the solution.

Both BEM and FEM can be used to model complex shapes and interactions, such as fish with dual-chambered swimbladders (Horne et al., 2000). However, they require significant computational resources and expertise in numerical methods.

Analytical Methods

Analytical methods are based on mathematical equations that describe the scattering process. Two popular approaches are:

• Diffraction-Wave-Boundary-Approximation (DWBA): This method is based on the idea of approximating the scattered field as a linear combination of plane waves.
• Kirchhoff-Ray-Mode (KRM): This method is based on the idea of using the Kirchhoff approximation to model the scattering process.

Analytical methods are often used for simple shapes and interactions, such as spheres or finite cylinders. They provide a fast and easy way to estimate the scattered field, but may not be accurate for complex scenarios.

Modeling Fluid-Like Objects

Fluid-like objects, such as flesh or seaweed, can be modeled using analytical or numerical methods. The choice of method depends on the complexity of the object's shape and the desired level of accuracy.

• Analytical models: Simple shapes, such as spheres or finite cylinders, can be modeled using analytical equations.
• Numerical models: Complex shapes, such as irregularly shaped flesh or seaweed, can be modeled using numerical methods like BEM or FEM.

Modeling Multiple Scattering

Multiple scattering occurs when sound waves interact with multiple objects in the environment. This process is difficult to model accurately, especially when the objects are close together or have complex shapes.

• Simple linear addition: One approach is to simply add the scattered fields from each object.
• Kirchhoff approximation: Another approach is to use the Kirchhoff approximation to model the scattering process for multiple objects.
• Numerical methods: BEM and FEM can be used to model multiple scattering, but require significant computational resources and expertise.

****, modeling acoustic scattering in aquatic environments requires a combination of numerical and analytical methods. The choice of method depends on the complexity of the shape, the desired level of accuracy, and the type of interaction being modeled. By understanding the strengths and limitations of each method, researchers can develop more accurate models for a wide range of applications.

References

Horne, J. K., Walline, P. D., & Jech, J. M. (2000). Comparing acoustic model predictions to in situ backscatter measurements of fish with dual-chambered swimbladders. Journal of Fish Biology, 57(5), 1105-1121.

Horne, J. K. (2003). The influence of ontogeny, physiology, and behaviour on the target strength of walleye pollock (Theragra chalcogramma). Ices Journal of Marine Science, 60(5), 1063-1074.

Macaulay, G. J., Peña, H., Fässler, S. M., Pedersen, G., & Ona, E. (2013). Accuracy of the Kirchhoff-approximation and Kirchhoff-ray-mode fish swimbladder acoustic scattering models. PloS One, 8(5), e64055.

License

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Acknowledgments

Hat tip to anyone whose code was used.
Inspiration: etc.

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