Engineering and the Environment, University of Southampton

Knowledge and understanding
Having successfully completed the module, you will be able to demonstrate knowlede and understanding of:

• How to employ the sonar equations, to model and assess the performance of sonar systems.
• The trade-offs involved when designing a sonar system.
• Elementary modelling of acoustic scattering: as it affects both acoustic targets and volume reverberation.
• The range of propagation models available.
• Ray tracing methods in a range independent, deep water, context and in shallow water through the use of the method of images.
• Normal mode methods for shallow water propagation modelling, assuming simple boundary conditions.
• The transduction mechanisms in marine mammals.
• The impact of human noise on marine mammals and the need to assess environmental impact of such sounds.

Cognitive (thinking) skills
Having successfully completed the module, you will be able to read, understand, and interpret the literature relating to underwater acoustics.

Practical, subject specific skills
Having successfully completed the module, you will be able to:

• Undergo a paper design of a sonar system in an idealised scenario.
• Advise on the selection of appropriate propagation models.
• Appreciate the factors that need to be considered when drawing up an eIA for underwater noise.

Key transferable skills
Having successfully completed the module, you will be better able to:

• Understand the issues associated with acoustic modelling in general.
• Appreciate system design issues.

The aims of this module are to provide an overview of mathematical techniques used in sonar system modelling.

• To provide a summary of sonar system performance evaluation techniques, through the "sonar equations".
• To offer a basic understanding of the principles of simple acoustic propagation models.
• To provide an appreciation of the impact of anthropogenic noise on marine mammals.

The Sonar Equations

• Classes of sonar systems: Active/passive, monostatic/bistatic.
• Definitions of the basic terms within the sonar equations.
• Signal detection criteria.
• Derivation of the passive sonar equation.
• Derivation of the active (noise-limited) sonar equations.

• Noise spectral level.
• Bandwidth.
• The effects of Doppler shifts.

• Simple models for geometric losses.
• Transmission loss due to absorption.

• Geometric scattering from a sphere.
• Rayleigh scattering from a sphere.
• Resonant scattering from a sphere.

• The reverberation limit.
• Calculation of volume reverberation level.
• The transition between reverberation and noise limited operations.

• Directivity of a uniform line array at the design frequency.
• Approximation for the directivity of a uniform line array at frequencies away from the design frequency.

• Range dependent vs range independent.
• 2-D and 3-D models.

• The eikonal and transport equations.
• Snell's law as obtained through the eikonal equation.
• Travel times and distances travelled along rays.
• Transmission loss along a ray.
• Focusing factors, shadow zones and caustics.
• Practical implementaiton of ray tracing models.

• General expression for shallow water, isospeed propagation.
• Specific solutions for various bottom conditions.