3.1 Background

The propagation of sound in the sea has been studied intensely since the beginning of Second World War when it was recognized that an understanding of this phenomenon was essential to the successful conduct of anti-submarine warfare (ASW) operations. These early measurements were quickly transformed into effective, albeit primitive, prediction tools. Naval requirements continue to motivate advances in all aspects of underwater acoustic modeling, particularly propagation modeling.

The study of sound propagation in the sea is fundamental to the understanding and prediction of all other underwater acoustic phenomena. The essentiality of propagation models is inherent in the hierarchy of acoustic models illustrated previously in Figure 1.1.

Advances in propagation modeling have been achieved by both marine seismologists and underwater acousticians, although the motivating factors have been quite different. Marine seismologists have traditionally used earth-borne propagation of elastic waves to study the solid earth beneath the oceans. Underwater acousticians have concentrated on the study of waterborne, compressional-wave propagation phenomena in the ocean as well as in the shallow sub-bottom layers (Akal and Berkson, 1986). As research in underwater acoustics has extended to frequencies below several hundred hertz, it has overlapped with the spectral domain of marine seismologists. Moreover, marine seismologists have become more interested in exploring the velocity-depth structure of the uppermost layers of the sea floor using higher frequencies. This area of overlapping interests has been recognized as a sub-discipline of both communities and is referred to as "ocean seismo-acoustics."

The emphasis in this chapter is focused on applications in underwater acoustics. Developments in marine seismology will be discussed when the applications to sonar modeling are clearly evident. Much research has been performed in the marine seismology community that is theoretically and conceptually applicable to underwater acoustics. Such practical research includes the development of sophisticated, yet robust, mathematical methods.

Propagation models have continued to be used for the prediction of sonar performance. They have also found great utility in analyzing field measurements, in designing improved sonar systems and in designing complicated inverse-acoustic field experiments.

As modeling has continued to grow in prominence in many aspects of underwater acoustics, it is prudent to reassess the state-of-the-art in modeling techniques and the relationship to available measurements. Ideally, such an assessment should identify those areas requiring further measurement support as well as those that are firmly understood and hence properly modeled.

This chapter addresses the observations that have been made in the field and the physical (i.e. physics-based) models that have been developed. Aspects of propagation phenomena including ducts and channels, boundary interactions, volumetric effects and coherence are described. Chapter 4 addresses the mathematical models that have been developed for underwater acoustic propagation. Specialized aspects of surface ducts, shallow-water areas and Arctic regions are discussed in Chapter 5.

Field measurement programs are usually quite complex and typically involve multiple platforms (e.g. ships, buoys, towers, aircraft, submarines or satellites).

A wide variety of experimental field techniques have been used in underwater acoustic propagation studies. Some of the more typical types of measurement platforms and experimental geometries that have been utilized include (Urick, 1982: chapter 1):

1 Two ships - one a source ship and the other a receiving ship. The range between them is changed as transmission runs are made in order to yield level versus range.

2 Single ship - using a suspended transmitter and either sonobuoys or a hydrophone array for reception.

3 Ship and aircraft - where the aircraft drops explosive sound sources while flying toward or away from the ship.

4 Single aircraft - using sonobuoys for reception and recording on board the aircraft.

5 Bottomed hydrophone array - with a cable connected to shore, receives signals transmitted from a ship or the explosive shots dropped by an aircraft.

6 Two bottomed transducers - one acting as a source and the other as a receiver. This geometry is typically used in studies of the fluctuation of sound transmission between two fixed points in the sea.

6 Transmitter

Receiving array

6 Transmitter

Figure 3.1 Example of a simple experimental geometry (adapted from Ingenito et al., 1978).

A simple experimental geometry illustrating method (2) above is presented in Figure 3.1. Here, the transmitting ship is receiving signals via radio directly from the array. Fully integrated oceanographic and acoustic field experiments are required in order to obtain a comprehensive portraiture of the temporal, spatial and spectral scales necessary to characterize the marine environment for a full understanding of the governing acoustic phenomena.

The standard unit of measure of underwater acoustic propagation is acoustic intensity (I), which is sound pressure flow (power) per unit area (reported in units of watts per square meter): p2

P c where p is the instantaneous pressure amplitude of a plane wave, p the density of sea water and c the speed of sound in sea water. Sound intensity is actually a vector quantity, but in the far-field approximation it is represented as a scalar quantity based on sound pressure squared. The product Pc is commonly referred to as the characteristic acoustic impedance.

Transmission loss (TL) is defined as 10 times the log (base 10) of the ratio of the reference intensity (Iref), measured at a point 1 m from the source, to the intensity (I), measured at a distant point, and is expressed in units of decibels (dB):

Range (nm)

Figure 3.2 Example of standard TL curves generated by the FACT model for each combination of frequency, source depth and receiver depth. Here, the source and receiver depths are fixed at 150 and 90 m, respectively. The peaks (minimum TL values) correspond to convergence zones. Note the increase in TL with increasing frequency due to absorption.

Range (nm)

Figure 3.2 Example of standard TL curves generated by the FACT model for each combination of frequency, source depth and receiver depth. Here, the source and receiver depths are fixed at 150 and 90 m, respectively. The peaks (minimum TL values) correspond to convergence zones. Note the increase in TL with increasing frequency due to absorption.

The standard metric unit for pressure (force per unit area) is 1 |xPa, which is equivalent to 10-6 Nm-2.

Transmission loss has conventionally been plotted for each frequency, source depth and receiver depth as a function of range, as illustrated in Figure 3.2. This type of display is easily generated by all propagation models. Certain types of propagation models can also generate and display acoustic TL in the entire range-depth plane for all receiver depths and ranges, given a fixed source depth (Figure 3.3).

Sonar performance is commonly described in terms of a figure of merit (FOM). The FOM is a quantitative measure of sonar performance. Specifically, the larger the FOM value, the greater the performance potential of the sonar. Numerically, the FOM is equal to the allowable one-way TL in passive sonars. The FOM is further described in Chapter 10 within the context of the sonar equations.

The display method illustrated in Figure 3.2 is very useful in evaluating passive sonar performance. Specifically, once an FOM has been calculated for a particular sonar operating in a particular ocean environment against a particular target, a horizontal line can be drawn on the plot equating the numerical value of the FOM to TL. Then, any area below the TL curve, but above the FOM line, represents a sonar detection area. Figure 3.4 shows

a hypothetical relationship between the FOM and the sonar detection areas (upper panel), and the correspondence between the TL curve and the ray paths as propagated in the water column (lower panel). These ray paths are consistent with those resulting from a shallow source (target) and shallow receiver (sonar) positioned in a water column characterized by the soundspeed profile shown on the left side of the lower panel of Figure 3.4.

Sound propagates in the sea by way of a variety of paths. The particular paths traveled depend upon the sound-speed structure in the water column and the source-receiver geometry. The six basic paths include direct path, surface duct, bottom bounce, convergence zone, deep-sound channel and reliable acoustic path. These six paths are illustrated in Figure 3.5. Depending upon the ocean environment, propagation over combinations of paths may be possible for any given source-receiver geometry; this situation is referred to as multipath propagation. Four of these paths (surface duct, deep sound channel, convergence zone and reliable acoustic path) are strongly affected by the sound-speed structure in the water column and will be discussed in detail in Sections 3.7,3.8,3.9 and 3.10, respectively. The remaining two paths (direct path and bottom bounce) are relatively unaffected by the refractive properties of the sound-speed structure: direct paths span relatively short distances and bottom-bounce paths penetrate the refractive layers at steep angles.

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