
акустика / gan_ws_acoustical_imaging_techniques_and_applications_for_en
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11
Underwater Acoustical Imaging
11.1Introduction
Underwater acoustical imaging is a part of the field of acoustical imaging. Unlike most forms of acoustical imaging where the medium for sound propagation is solid, such as for nondestructive evaluation, medical ultrasound imaging and geophysical imaging, underwater acoustical imaging is concerned with sound propagation in water. Here it has its own uniqueness and peculiarities. Usually the size of an underwater acoustical imaging system is larger than that of other forms of acoustical imaging systems. Underwater acoustical imaging is useful for underwater inspection, differentiation and classification of sunken objects, be it garbage or treasures, and in the detection of military targets such as sonar.
Although optical imaging systems can be used for underwater inspection, they can be only used for very clear water. Most ocean waters are rather turbid. Deep ocean water (undisturbed) has 6–15 m visibility, while near-shore waters have typically only 1–6 m visibility. Within harbours and estuaries, where man disturbs or impacts the environment, the visibility is generally within range of 0–1 m only. Thus application of optical imaging is very limited in underwater inspection. On the other hand, sound waves can penetrate turbidity and mud. Unfortunately, resolution of underwater acoustical imaging system is usually significantly lower than optical image system. This is because optical wavelength used is shorter than sound wavelength.
Although sonar also has the capability of underwater acoustical imaging, it is different from underwater acoustical imaging system. Both sonar and underwater acoustical imaging system share many physical properties, hardware implementation and many techniques and provide similar kinds of information. They are different in the sense that sonar indicates where the target is located, while the underwater acoustical imaging system indicates what the target looks like. Generally, underwater acoustical imaging systems have higher resolution and shorter range than sonar and lower maximum resolution with longer range than underwater optical imaging systems. Hence, underwater acoustical imaging system fills the gap between sonar and underwater optics.
Acoustical Imaging: Techniques and Applications for Engineers, First Edition. Woon Siong Gan. © 2012 John Wiley & Sons, Ltd. Published 2012 by John Wiley & Sons, Ltd.

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11.2 Principles of Underwater Acoustical Imaging Systems
Underwater acoustics is concerned with sound propagations in sea. The sea, together with its boundaries, forms a very complex medium for sound propagation. To establish the basis for an underwater acoustical imaging system, one needs to understand the propagation or transmission of sound in the ocean. In travelling through the sea, an underwater sound signal will be delayed, distorted and weakened. When sound propagates in the ocean, there are many sources of loss, which includes sound wave spreading loss, attenuation loss, refraction loss in shadow zones and the convergence gain in sound channels.
Spreading loss is a geometrical effect representing the regular weakening of a sound signal as it spreads outwards from the source. Alternation loss includes the effects of absorption, scattering and leakage out of sound channels.
Sound transmission or propagation in ocean is a complex subject. It has been and continues to be the most active aspect of underwater sound from a research standpoint. Due to its complexities, the field has attracted experimentalists and theorists for many years and the number of papers published in this area has been increasing exponentially. Much of the trend recently has been towards theoretical modelling and computational works rather than at-sea experiments due to high costs and difficulties of performing experiments in the ocean.
11.2.1Spreading Loss
This can occur in two ways, (1) spherical spreading and (2) cylindrical spreading. Let a sound source be located in a homogenous, unbounded and lossless medium. For most simple propagation condition, the power generated by the source is radiated equally in all directions so as to be equally distributed over the surface of a sphere surrounding the source. Since there is no loss in the medium, the power P crossing all such spheres must be the same. This kind of spreading is called inverse-square spreading. The intensity decreases on the square of the range, and the transmission loss increases as the square of the range.
11.2.1.1Cylindrical Spreading
When the medium has plane–parallel upper and lower bounds, this spreading is no longer spherical because sound cannot cross the bounding planes. Beyond a certain range, the power radiated by the sound is distributed over the surface of a cylinder having a radius equal to the range and a height equal to the distance between the parallel planes. The spread is said to be inverse first power. In cylindrical spreading the product of the RMS power and the square root of the range is a constant. This type of spreading exists at moderate and long ranges wherever sound is trapped by a sound channel in the sea.
11.2.2Attenuation Loss
There are two main parts of attenuation loss: (1) absorption loss and (2) scattering loss. Absorption loss depends on the range of propagations. It involves conversion of acoustic energy into heat and represents a true loss of acoustic energy to the medium during sound propagation. The absorption of sound in the sea is high compared with that in pure water, and cannot be attributed to scattering, refraction or other anomalies attributed to propagation in the natural environment.

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11.2.3Propagation Theory
The underwater propagation of sound can be described mathematically by the homogeneous wave equation in the acoustic pressure P:
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There are two theoretical approaches to the solution of equation (11.1). One is the wave theory approach and the other is the ray tracing or geometrical approach. For the wave theory approach, the solution of the wave equation is described in terms of characteristic functions called normal modes, each of which is a solution of the equation.
The wave theory approach takes account of wave nature of sound propagation in the sea such as the phenomena of diffraction and multiple scattering. The normal modes are combined additively to satisfy the boundary and source conditions of interest. The wave theory gives a formally complete solution. The result will show a mathematical solution suitable for computational purpose. Only in limiting cases analytical solutions exist. It presents computational difficulties in all but simplest boundary condition. However it gives little insights on the distribution of energy of the source in space and time and the solution is difficult to interpret. Normal mode theory is particularly suitable for description of sound propagation in shallow water. It is valid for all frequencies but practically is useful for low frequencies (few modes). The source function can be easily inserted. But it cannot easily handle real boundary conditions.
The ray theory approach is also known as ray acoustics or geometrical acoustics. Like geometrical optics, it does not handle diffraction problems. It has the following properties:
The existence of rays that describe the paths of propagation of sound wave. Rays are easily drawn.
Sound distribution is easily visualized with the concept of wavefronts, along which the phase or time function of the solutions is constant.
Real boundary conditions are inserted easily, for example a sloping bottom. It is independent of the source.
Ray acoustics is analogous to geometrical optics and it presents a picture of the propagation of sound in the sea in the form of ray diagrams. Rays can be drawn by hand using Snell’s law. However, a ray-trace computer program is normally used. The ray theory does not provide an accurate solution when either (a) the radius of curvature of the rays or (b) the pressure amplitude changes appreciably over the distance of one wavelength. In practice, ray theory is therefore restricted to high frequencies or short wavelengths if radius of ray curvature is larger than the wavelength or the sound velocity does not change much in a wavelength. It cannot be used for predicting the intensities of sound in shadow zones or caustics. An important book on theory of sound propagation in the sea is that of Brekhovskikh [1]. Brekhovskikh’s book is based on the representation of the sea, or the medium of sound propagation, as a layered medium. (Figure 11.1).
Ray theory uses Snell’s law, which shows the analogies between sound waves and light waves. Snell’s law describes the refraction of sound rays in a medium of variable velocity.

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Velocity
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C1
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Figure 11.1 Refraction in a layered medium (Urick [2] © McGraw-Hill)
Snell’s law states that in a medium consisting of constant velocity layers (Figure 11.1), the grazing angles θ 1, θ 2, . . . of a ray at the layer boundaries are related to the sound velocities c1, c2, . . . of the layers by
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When θ = 0, the ray constant becomes the reciprocal of the sound velocity in the layer in which the ray becomes horizontal. This expression is the basis of ray computation used by most analogue and digital computers, since it enables a particular ray to be ‘traced out’ by following it through the successive layers into which the velocity profile may have been divided. In a layered medium having constant velocity, the rays consist of a series of straight-line segments joined together, in effect, by Snell’s law.
11.2.4Reflection and Scattering from the Sea Surface
The sea surface is both a reflector and a scatterer of sound and has a profound effect on sound propagation in the sea where the sound or receiver lies at shallow depth. If the sea surface were perfectly smooth, it would form an almost perfect reflector of sound. The intensity of sound reflected from the smooth sea surface would be very nearly equal to that incident upon it. The reflection loss, equal to 10 log (Ir/Ii ), where Ir and Ii are the reflected and incident intensities of an incident plane wave, would be closely equal to zero decibels. In real situations, the sea is somewhat rough, and the loss on reflection is found to be no longer zero. A criterion for the roughness or smoothness of the surface is given by the Rayleigh parameter, defined as R = kH sin θ where k = wave number = 2π /λ, H = RMS ‘wave height’ (crest to trough) and θ is the grazing angle. When R 1, the surface is primarily a reflector and produces a coherent reflection at the specular angle equal to the angle of incidence. When R 1, the surface acts as a scatterer, sending incoherent energy in all directions. With certain theoretical assumption, the amplitude reflection coefficient μ of an irregular surface defined as the ratio of the reflected or coherent amplitude of the return to the incident amplitude can be shown to be μ = exp (−R). When R 1, the return from the surface is incoherent scattering instead

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of coherent reflection with a distribution throughout space depending upon the nature of the surface roughness.
11.2.5Reflection and Scattering from the Sea Bottom
The sea bottom is a reflecting and scattering boundary of the sea having a number of characteristics similar to the sea surface. However, its effects are more complicated because of its diverse and multilayered composition. An example of this similar behaviour is the fact that the sea bottom casts a shadow or produces a shadow zone, in the upward-refracting water above it in the depths of the deep sea.
The reflection of sound from the seabed is vastly more complex than that from the sea surface. First, the bottom is more variable in its acoustic properties because it may vary in composition from hard rock to soft mud. Secondly, it is often layered, with a density and a sound velocity that change gradually or abruptly with depth. For these reasons, the reflection loss of the seabed is less easily predicted than that of the sea surface.
11.2.6Sea Bottom – Reflection Loss
The reflection loss of sound incident at an angle to a plane boundary between two fluids were worked out by Rayleigh [3]: If a plane wave is incident at grazing angle θ upon the boundary between fluids of density ρ1 and ρ2 and of sound velocity c1 and c2 as shown in Figure 11.2, then by the Rayleigh formula, the intensity of the reflected wave Ir is related to the intensity of the incident wave Ii by
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Figure 11.2 Reflected and transmission rays at a discontinuity between two media (Urick [2] © McGraw-Hill)

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Figure 11.3 Ratio of reflected to incident intensities for four combinations of conditions of sound velocities and densities in lossless media separated by a plane interface. The dashed curve in (c) shows the effect of an attenuating lower medium (Urick [2] © McGraw-Hill)
So far, absorption has not been brought into picture. All bottom materials are to some extent absorptive, and the effect of absorption is to smooth out the variation of loss with angle, so as to eliminate, or obscure, the sharp changes occurring at the critical angle θ 0 and the angle of intromission θ B. An example of the effect of absorption is the dashed curve in Figure 11.3(c).
Many measurements of sound attenuation in sediments have been made [4]. They show that the attenuation coefficient of compressional waves in marine sediments is related to frequency by
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where α is in decibels per metre, f is the frequency in kilohertz and k and n are empirical constants.
If the bottom in the most simple model is taken to be a homogeneous absorptive fluid with a plane interface, then the three bottom parameters that determine the reflections loss are its density, sound velocity and attenuation coefficient. If the bottom happens to be a sedimentary material, these quantities are related to and determined by the porosity of the sediment.
However, a number of complications to this simple model occur in the real world. First of all, the ocean flow is not a perfectly plane interface, so scattering as well as reflection takes place. In a very rough area, such as the Mid-Atlantis Ridge, scattered sound dominates the bottom return. As a result, some sound is sent by the bottom in all directions and the ‘beam pattern’ of the bottom return shows no appreciable lobe or peak in the specular direction.


270 Acoustical Imaging: Techniques and Applications for Engineers
argument (xl r) of the Hankel function is real; these are the modes for which kh > π /2 or h > λ/4, that is, those for which the water depth is greater than one-quarter wavelength. The frequency corresponding to h = λ/4 is termed the cut-off frequency; frequencies lower than the cut-off frequency are propagated in the channel only with attenuation and are not effectively trapped in the duct.
11.2.7.1Comparison of Ray and Mode Theory
Ray theory is more convenient to use at short ranges, where the higher-order images rapidly die out because of reflection losses and an increasingly great distance from the field point. Accordingly, only a few images ordinarily need to be summed at short ranges. Normal mode theory is more appropriate at long ranges because of the greater attenuation with distance of the higher-order modes; only a few modes need to be taken to describe the transmission. A ‘cross-over’ range between the regions of convenient usefulness of the two theories is given by r = Hλ2 [5] where H is water depth and λ is wavelength.
The usefulness of both theories for predicting the transmission loss in the real world depends upon the accuracy and validity of the input data such as the velocity profile, bathymetry, bottom loss, etc. In shallow water, where the bottom plays a large part in determining the transmission loss, this usefulness for prediction is limited, since bottom interaction effects on transmitted sound are largely unknown.
11.3 Principles of Some Underwater Acoustical Imaging Systems
The approach here is suitable for the beamforming and holographic systems.
The hydrophone array is used to detect the acoustic signals. The signal p arriving at a point (x, y, z) that was generated (or scattered) in a target plane (x0,y0,0) is given by
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ω = acoustic frequency in radian per second
n = vector normal to the illuminating wavefrontr = vector from (x0,y0,0) to (x,y,z)
c= acoustic velocity in water
√
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From the system’s geometric consideration, we make the following assumptions:
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2 |
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≈ |
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+ |
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+ |
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