Principles of Sonar Performance Modelling

Sonar can be thought of as a kind of underwater radar, using sound instead of radio waves to interrogate its surroundings. But what is special about sound in the sea? Radio waves travel unhindered in air, whereas sound energy is absorbed relatively quickly. In water, the opposite is the case: low absorption and the presence of natural oceanic waveguides combine to permit propagation of sound over thousands of kilometers, whereas the sea is opaque to most of the electromagnetic spectrum.

The purpose of this chapter is to introduce the basic knowledge required by the reader to understand the description of the sonar equations introduced in Chapter 3, and no more than this. The knowledge is sub-divided into four general subject areas: oceanography, acoustics, signal processing, and detection theory. Further details of these four areas, omitted here for simplicity, are described in Chapters 4 and following.

The objective of this chapter is to illustrate the basic principles of sonar performance modeling. This is achieved by deriving the most important passive and active sonar equations, each accompanied by a worked example. These worked examples are intended to be didactic rather than realistic: enough realism is included in them to illustrate the underlying principles, but no more–where there is a conflict between simplicity and realism then simplicity is preferred, except at the expense of the principle itself.¹

This is the first of four chapters dealing further with each of the four main subjects introduced in Chapter 2.The purpose is to describe them in sufficient detail to equip the reader with the necessary knowledge to carry out predictions of sonar performance in realistic situations.The first subject of the four, and that of the present chapter, is oceanography.The remaining three are underwater acoustics (see Chapter 5), sonar signal processing (Chapter 6), and detection theory (Chapter 7).

While the scope of this chapter is not limited to bubble acoustics, this statement by Minnaert, published at the height of the quantum revolution, as part of his classic article “On musical air-bubbles and the sounds of running water” (Minnaert, 1933), is a stark reminder that we do not understand fully even the mundane. Nevertheless, important advances have been made in the intervening years, and the present chapter documents current theoretical knowledge of reflection, scattering, attenuation, and dispersion of underwater sound,¹ starting with a derivation of the wave equations for fluid and solid media in Section 5.2. The plane wave reflection coefficients for fluid–fluid and fluid–solid boundaries are described in Section 5.3, including the effects of layering. Section 5.4 deals with the scattering of sound from rigid and non-rigid bodies and from rough boundaries. Finally, the dispersive effect of impurities, in the form of bubbly water or suspended sediment, is described in Section 5.5.

Once a pressure disturbance has been converted to an electric current, it can be processed in various ways to enhance the signal-to-noise ratio before being presented to an operator for interpretation. In a modern sonar system, the processing is mostly carried out by a digital computer, which means that one of the first steps must be a conversion from an analogue signal to a digital one. Even before this, an analogue low-pass filter, known as an anti-alias filter, is used to remove frequencies that exceed the specification of the analogue-to-digital converter (ADC).

The behavior of underwater sound is central to sonar performance. A theoretical treatment is presented in Chapter 5, but on its own that is not enough. To inspire confidence, the theory must be supported by measurement. The purpose of the present chapter is to summarize relevant acoustic measurements and, where feasible, to place these in a theoretical framework.

No book on sonar would be complete without a chapter on underwater sound propagation, and this is it. The subject is central to sonar performance modeling because all sound, whether contributing to the signal, ambient noise, or reverberation, must propagate through the sea before arriving at the sonar. Thus, the scope includes not only propagation loss (PL), but also the effect of sound propagation on noise level (NL), and for active sonar the reverberation level (RL) and target echo level (EL). These terms were all introduced in Chapter 3, where they were applied to simplified sonar problems. The present chapter adds more realism by describing the effects of a reflecting seabed and a sound speed profile.

Before returning to the sonar equation in Chapter 11, there is one remaining piece to be fitted in the puzzle, namely the characteristics of the sonar itself. Some sonar properties, such as transmitter power through the source level and receiver directivity through the array gain, are incorporated explicitly in the sonar equations. Also important are the frequency, bandwidth, and pulse duration, which affect terms like processing gain, detection threshold, and propagation loss. In this chapter those properties that are intrinsic to sonar systems are collected and tabulated, with particular emphasis on the transmitter source level for active sonar, whether man-made or biological. Receiver sensitivity and self-noise are also considered, represented in the case of biological sonar by the animal)s audiogram. Finally, thresholds are given for possible impact on marine life in the form of behavioral effects and hearing threshold shifts. In the case of man-made equipment, the scope is extended to include all deliberate use of underwater sound. The directivity index of the receiving array is considered in Chapter 6.

The objective of this chapter is to reverse (or at least to mitigate) the preference in some previous chapters for simplicity over realism. The sonar equations and selected worked examples of Chapter 3 are revisited, with the aim of introducing the necessary realism to become not only didactic but also practical. To make this possible, use is made of a computer model for the calculation of propagation loss, noise level, and reverberation level. Selected sonar equation terms are redefined to establish a more rigorous basis for the revised worked examples.