# 5. ACOUSTIC PROPERTIES OF FISH

When an acoustic wave strikes a fish a proportion of the energy is reflected (the echo). For acoustic surveys we need to determine the amount.

Some discussions on the way that acoustic waves interact with fish-like objects and how fish as simple 'targets' fit into the acoustic equations took place in sections 2.8 and 4 respectively. Chapter 5 examines practical aspects of the characteristics of fish which affect the echoes so that the various factors involved can be assessed. These relate to fish size, morphology, physiology and orientation. The frequency of isonification has an effect on TS and is discussed in relation to fish size. Various methods of making TS measurements are described and published values of TS for some species are given. Work is continuing to improve the knowledge of fish TS and the factors which affect it.

## 5.1 Target Strength

Target strength (TS) is defined by equation 30 as 10 times the logarithm of the reflected intensity (IR) at one metre from the fish, divided by the intensity which strikes the fish, i.e. the incident intensity (I1), i.e. 10 log IR/I1.

The term target strength originates from Naval acoustics and the simplest object to consider as an acoustic 'target' is the sphere because it radiates its echo equally in all directions.

If an idealized perfectly reflecting sphere has a radius a, the amount of energy reflected depends on the acoustic cross-section s of the sphere which is p a2, i.e. the area of a circle of radius a. Acoustic cross-section is defined as, 'that plane area intercepting an amount of energy, which, if it were scattered equally in all directions would produce the observed echo'. In the case of the sphere the amount of energy intercepted will be p a2I1. At a distance of 1 m from the sphere, the reflected intensity IR will be equal to p a2I1 divided by the area of a 1 m radius sphere, 4p x 1 so that

IR = p a2I1/4p x 1 IR/I1 = a2/4
in decibel terms TS = 10 log a2/4(dB) (38)

If the reference TS is taken to be 0 dB then the target would have a radius of 2 metres, not a practical size.

The energy scattered by a target occupies 4p units of area at one metre from the target when the area corresponding to a is in the target position. Sigma is the 'scattering' cross-section of the sphere which gives the same TS as the specified target under given conditions. These are that the area corresponding to s is perpendicular to the incident plane waves of uniform intensity. For these conditions we can say that the scattered intensity is s /4p. In decibels the back-scattering coefficient is the target strength.

If s = scattering cross-section = p a2

a2 =s /p

so substituting in equation 38

TS = 10 log s /4p (39)

Fish are neither spherical, nor rigid so they do not scatter uniformly, the nearest that many of them approach to a uniform shape is the cylinder and it is interesting to consider this shape as a simple model. The TS of a small acoustically rigid cylinder of length L metres is given by Urick (1975) as

10 log aL2/2l (40)

a is the radius and l the wavelength, both in metres.

Equation 40 shows that the TS of a small cylinder is directly proportional to the square of the length and inversely to the wavelength. The ratio of length to acoustic wavelength L/l is important because it determines the wave 'interference' effects along the surface of the cylinder and these affect the number of 'lobes' appearing in the response pattern see 2.8. The longer the cylinder or the smaller the wavelength, the greater is the interference effect, resulting in more maxima and minima of acoustic energy, hence a directional response with more spikes, or lobes. Equation 40 is correct if the cylinder remains perpendicular to the acoustic waves.

Fish are composed mainly of flesh and bones which have an acoustic resistance (Impedance) quite similar to that of water, so the amount of reflected energy from these substances is small (Shibata, 1970). If we apply the TS formula for a cylinder of air, to fish, it is necessary to use a factor to correct for the difference in acoustic resistance of the materials. It is evident that the fish would have a TS lower than a cylinder of air of the same size. The factor (g 2) to correct for a cylinder of fish flesh instead of air, is derived from the relative impedance (Z) of seawater and fish flesh.

ZF = r c(F) where r is the density of the fish flesh (kg/m3)

c is the speed of acoustic waves through the fish flesh. m/s

ZW = r c(W) where r is the density of seawater (kg/m3)

c is the speed of acoustic waves in sea water. (m/s)

The factor g 2 = [(ZF-ZW)/(ZF+ZW)]2 (41)

TS of the cylinder of fish flesh becomes

10 log (aL2/2l) g 2 dB (42)

As an example, for Atlantic mackerel (Scomber scombrus)

ZF = 1.627 x 106
ZW = 1.54 x 106

giving a value of g 2 = 7.63 x 10-4

Assuming the effective fish length L is 0.4 m
Assuming the effective fish radius a is 0.025 m
Assuming the effective wavelength l is 0.039 m (f = 38 kHz) Generally the polar diagrams from fish are different to those from cylinders because the energy is more widely distributed from fish. This is attributed to the internal structures and impedances and their relative distribution within the body, e.g. the swim-bladder in relation to the backbone and the curvature of the body's outer surface.

Figure 36. Acoustic scattering from a fish is considered to fall into one of the following regions see Figure 36 from Lytle and Maxwell (1982). At any particular frequency not all parts of the fish may be in the same region.

1. Rayleigh scattering when the fish is small compared to l, i.e. L << l. In this case s µ to (Volume)2 and l -4. Transition between this and the intermediate region occurs when the dorsiventral dimension of the fish is close to l, (a maximum dorsiventral size is 0.2 of total length).

2. Resonant region where the swimbladder is caused to vibrate in sympathy with the frequency of the acoustic wave. It consequently absorbs and re-radiates more power than predicted by the Rayleigh approximation. In principle this effect can be used for sizing fish but in relation to present-day acoustic surveys the source of error in estimation due to resonance of small organisms is most important, see 9.6.4.

3. Transition or intermediate region where s µ L2 and is largely independent of l. The dorsiventral dimension is similar to l, this applies to some of the smaller fish e.g. at 38 kHz l = 39 mm.

4. Geometric, where the fish length L >> l. Half of the scattered power is reflected in various directions from curved surfaces of the dominant scattering parts. The other half is confined to a narrow angular region in the forward direction of the incident wave thus interfering with it below the fish.

Although in marine fish the volume of the swimbladder is only 5% of total fish volume (7% in freshwater fish) the fact that it is gasfilled, with a markedly different impedance to fish flesh, makes it a very significant acoustic reflector. The evidence seems to show (Foote, 1980) that often about 90% of the echo from a fish is due to the swimbladder alone, i.e. the TS of fish without a swimbladder is 10-15 dB lower than those of similar size with a swimbladder.

Gas filled swimbladders are used by fish to adjust their buoyancy when migrating up or down in the water column. They can tolerate sudden pressure increases of up to 400%, but decreases of only 50%, thus they can dive more easily than ascend. The state of the swimbladder at any given time depends on the extent of the last significant vertical movement and the rate at which it took place. This indicates that the swimbladder may cause changes of TS with time, but for example with the cod it has been shown that the maximum overall change is likely to be about 1 dB (Harden Jones and Scholes, 1979).

Midttun and Hoff (1962) measured the TS of a dead saithe with an intact swimbladder and found that the polar plot of TS around the dorsal aspect could be closely approximated by calculation using equation 40. An X-ray showed the angle of the near cylindrical swimbladder to the vertebral column of the fish. Many fish have swimbladders closer in shape to a prolate spheroid.

To sum up, the size of echo from a fish depends on the exact interaction of the fish with the acoustic waves striking it. The important factors are:

1. Dimensions shape and angle of the swimbladder
2. Dimensions shape and angle of the body
3. Acoustic impedance of 1 and 2
4. Acoustic wavelength.

## 5.2 Measurement of Fish Target Strength

In order to convert data collected on acoustic survey into population estimates it is essential to have precise estimates of fish target strength. The methods used to obtain these are by having single fish, or numbers of live fish in a cage, stunned individuals; or by measuring signals from wild fish in situ. In all cases the mean dorsal aspect TS is required.

### 5.2.1 Direct TS measurements

These have been performed on caged or tethered fish of various species in order to gain understanding of the effects on TS of variables such as the acoustic wavelength, size of fish, orientation and state of swimbladder. To make suitable observations requires carefully controlled conditions; but even so, there is great difficulty in knowing the physiological state of the fish and determining if their behaviour is 'normal'. Experiments on individual free-swimming fish in a cage at 10 m range were carried out by Goddard and Welsby (1975). The mean amplitude of the echoes from 1000 transmissions on each fish were converted into TS by reference to the system calibration. Four species were investigated, cod, haddock, saithe and dogfish. TS equations were produced from these data but echo-integration is the most commonly used technique for abundance surveys so it is the mean scattering cross section per fish, or mean echo intensity that is needed. A further analysis by Forbes (1975) used mean squared echo amplitude to convert results to mean echo intensity and some of the results are given below.

Table 3. Mean of individual target strengths

 Mean length Frequency (kHz) 10 30 100 Cod 0.491 m -39 -32.1 -33.9 dB Haddock 0.364 m -41.5 -38.9 -38.3 dB Saithe 0.401 m -41.2 -39.6 -35.6 dB

Table 4. Mean scattering cross section expressed as target strength

 Cod -35.5 -28.9 -31.9 dB Haddock -38.8 -35.7 -36.09 dB Saithe -40.3 -38.4 -34.8 dB

Table 5. Mean scattering cross section per kg expressed as TS

 TS/kg re mean fish length Cod -33.3 dB -36.5 -29.9 -32.8 dB Haddock -33.7 dB -35.7 -32.5 -32.9 dB Saithe -36.5 dB -40 -37.2 -33.5 dB

Another feature of the work by Goddard and Welsby was the measurements made with number of fish in the cage which showed that the TS increased by slightly more than the 3 dB expected per doubling of numbers.

Recently work has concentrated on integrating echoes from a number of fish, e.g. Dunn (1979), Edwards (1979). Fish were weighed so that the total biomass in the cage was known. After the fish had settled (sometimes this took more than 24 h) and steady mean values were obtained from the integrator, a mean TS for unit mass of a known size range for the particular species was derived. Calibration of the system in terms of integrated output per unit volume back-scattering coefficient (Sv) was achieved by substituting a standard target for the fish.

Methods of measuring TS on survey were examined by Ehrenberg (1972), most of them had drawbacks and he proposed the use of a new method, the dual beam, described in detail (Ehrenberg, 1974).

The dual beam measures the target strength of individual fish in-situ if the density is low enough, (a requirement for all in-situ measurements) whilst also recording the total back-scattered intensity.

As the name implies, the transducer forms a dual beam which comprises coaxial narrow and wide beams, the main lobe of the narrow beam covering approximately the same volume as the region of unity response in the centre of the wide beam. The ratio of received intensity for targets in the two beams is given by

In/Iw = kn/kw [bn (q, f)]

where

In = intensity in the narrow beam

kn = constant for the narrow beam

Iw = intensity in the wide beam

kw = constant for the wide beam

bn (q f) = directivity function for the narrow beam, defined as the distribution of acoustic power transmitted in different direction (q, f) relative to the acoustic axis of the transducer;

b is a quantity between 0 and 1.

Transmission occurs only on the narrow beam, but reception is on both wide and narrow. Signals are processed via amplifiers with 40 logR + 2a R characteristics for fish target strength analysis and 20 logR + 2a R for total biomass estimation. The narrow beam is 6° and the wide is 25°.

The scattering cross-section s of a fish at position (q, f) in the beam is s = In/kn [b2 (q f)]. From this the fish's mean scattering cross-section and its variance may be estimated. s is the effective-area of a fish which is normal to the incident acoustic energy when the fish has the properties of a spherical reflection pattern and total reflection.

Providing that fish densities are sufficiently low for the selection of individual echoes and at any time comprise one species only, target strength data may be collected and used during the progress of a survey. The intensity of back-scattered acoustic energy from fish concentrations received on either beam is proportional to fish density. By using the mean target strength extracted from the dual beam system, estimates of biomass can be obtained. There is no complex mathematical analysis involved in this process but a computer is necessary to perform the signal processing in real time. Fishing is necessary to identify the species and obtain length distributions (Traynor, 1975).

### 5.2.2 Indirect TS measurements

Craig and Forbes (1969) proposed a method of measuring fish target strength by removing the effects of the transducer beam pattern which was later considered by Ehrenberg (1971) and Traynor (1975). It statistically corrects an echo strength distribution to a TS distribution using beam pattern directivity measurements. The assumption is made that fish are distributed uniformly within the sampled volume, but in practice this is not always so. For small sample sizes the technique breaks down.

Another method which also uses a single beam transducer has been successfully exploited by Robinson (1979). In this the difficulty due to the unknown position of a fish in the beam is overcome by accepting the premise that, whilst the location of a particular fish in an acoustic beam cannot be known, or calculated, if a sufficient number of fish are taken into account, the probability that all positions will be occupied at some time can be described statistically. In order to use such a method the following conditions must be satisfied.

1. the directivity pattern of the transducer must be known.
2. a valid assumption of the likely distribution of fish in the beam is necessary.

A beam pattern density distribution results from these two factors, which when convoluted with the fish target strength distribution, results in an intensity distribution of received echoes. The fish target strength distribution has to be recovered from the other two distributions, of which the beam pattern density has already been discussed. In order to obtain a suitable distribution of received echo intensity it is necessary to collect sufficient echoes which are without doubt from single fish. To satisfy the statistical requirement about 104 echoes are needed although this depends on the distribution so a number of practical problems must be overcome.

3. the density of fish must be low in relation to the dimensions of the beam and the pulse length in order to provide a satisfactory number of single echoes.

4. echoes from single fish must be extracted without ambiguity.

5. there must be a positive means of species identification and size measurement, i.e. a good sample of the fish from which echoes are recorded must be captured.

6. the schools sampled should be predominantly of one species.

For 3 above to be satisfied, it is often necessary to work on the edge of a school, or to wait until it partially disperses. Even then a towed transducer may need to be lowered to with 20-30 m range of the fish. Then the beam is relatively narrow at the depth of the fish, giving a greater probability of receiving one fish echo per pulse volume.

To meet (4) the echo amplitudes must be accurately recorded from the calibrated echo-sounder with 40 logR + 2a R time-varied gain. Magnetic tape is suitable for the recording. After extraction from the tape the signals are digitised before going to an electronic processor which selects those from single fish on the following basis.

7. they do not exceed a certain time duration at the origin.
8. they do not exceed a given amplitude.
9. they are clearly separated by a specified amount from adjacent signals.

This method of in-situ measurement appears to be capable of achieving an accuracy of ± 0.5 dB if the distribution is unimodal and the standard deviation less than 2.5 dB. It needs a computer for the analysis. Although it is desirable to obtain a continuously updated record of target strength during survey, in practise a period sufficient to secure the 104 or so echoes is dedicated to the purpose when conditions are suitable, 30 minutes is often adequate. The ship drifts for this purpose. Indirect measurement of TS are described by Ehrenberg et al. (1981) and by Clay (1983).

## 5.3 Fish Size and Target Strength Dependence

It is clear from the previous parts of Chapter 5 that fish target strength is complex and far from being fully understood. There is a relationship between size of fish and TS but it varies widely with species. Certain classes appear to have similar TS/length characteristics within limits, e.g. gadoids, although there is limited agreement as to the TS to be used for particular species within this group. Love (1971), Figure 37, shows the results of dorsal-aspect measurements by nine workers including his own which covered many species and a wide range of frequencies. He gives a regression line equation of

TS = 19.1 logL + 0.9 logl - 23.9 (43)

where L and l are in metres which may be compared with

TS = 24.5 logL - 4.5 logl - 26.4 (44)

of McCartney and Stubbs (1971) from their own measurements on live fish. The technique of data reduction due to Love (1971) also used by Goddard and Welsby, was target strength expressed as an area and normalised by the square of the wavelength, is regressed on the fish length normalised by the wavelength.

Figure 37. Equations for three species were given by Forbes (1975) from the Goddard and Welsby data

Cod = 23.5 logL - 3.5 logl - 29.4 dB (45)
Haddock = 22.7 logL - 2.7 logl - 30.4 dB (46)
Saithe = 25.6 logL - 5.6 logl - 35.0 dB (47)

showing surprising differences between cod and haddock, fish reasonably similar in morphology and physiology.

At 38 kHz Nakken and Olsen (1977) obtained a relationship of TS against length for cod of

24.6 logL - 60.8 (48)

and for sprat at the same frequency

17.2 logL - 66.6 (49)

## 5.4 Fish Tilt Angle

Fish need to conserve energy as do other creatures so there is no reason to suppose that they are constantly executing sudden manoeuvres. Nevertheless, there is evidence to show that in certain circumstances their behaviour results in low TS, e.g. diving when under the passage of a ship as described in 9.5.

The directional patterns shown in Figure 38 are theoretically ideal but illustrate in principle the type of pattern possible for a given length of fish insonified by a frequency (f). Three frequencies are taken as the basis for these diagrams from which it is evident that the lower the frequency the broader the response pattern, hence there is less dependence on tilt.

Figure 38. (a) Figure 38. (b) Figure 38(a) shows the maximum response of the fish in the direction of the transducer but in practice this is not always perpendicular to the long axis of the fish. In Figure 38(b) a few degrees of tilt are very significant when f = 120 kHz. The larger the fish for a given wavelength, the narrower will be the lobes in its directional pattern, hence the greater will be the rate of change as the fish tilts up or down from its normal swimming state.

## 5.5 Acoustic Frequency and Fish Target Strength

There is little evidence to show a significant change of TS with frequency. If we use equation (44) which is valid for fish in the length range 0.8 < L/l < 20, the TS at 120 kHz would be about 2 dB greater than at 38 kHz and similar results would be obtained for (45) (46) and (47). Evidence from field observations that this is so and has practical significance is given by Saetersdal et al. (1982). Results from 38 kHz and 120 kHz calibrated systems were compared when surveying the same biomass concentrations and these indicate that for fish of the length studied (100-250 mm) the volume back scattering strength, hence by inference the TS of the individual fish is frequency dependent. It appears that the fish TS may be approximately 4 dB higher at 120 kHz than at 38 kHz. This difference has proved to be useful in helping to discriminate between fish and plankton for the 120 kHz system gave consistently higher readings of mean volume back scattering strength from fish whilst the 38 kHz system gave higher values for plankton.

## 5.6 Fish School Target Strength

Acoustic surveys of fish are mostly based on the assumption that total echo intensity from schools is equal to the arithmetic sum of echo contributions from individual fish, which is justified if the echoes are uncorrelated. In a uniform population therefore, doubling the number of fish should double the echo power, i.e. produce an increase of 3 dB in target strength. There was some evidence in work by Goddard and Welsby (1975) that a small but significantly greater increase than 3 dB actually occurred. Smith and Welsby (1979) examined this noting that the result for 32 fish was about 1.5 dB higher than predicted, an excess of about 40% in echo intensity from this group of fish.

Such an apparent increase in TS cannot be explained by coherence of the echoes from adjacent fish because for this to be significant the mean spacing of the fish must be similar to l. For the size of fish (300 mm) and l of 15 mm used in the experiment this clearly was not so.

Multiple scatter theory Was examined to see if the excess could be accounted for in this way. It is said that multiple scattering takes place when the incident intensity intercepted by one target is re-radiated in all directions and a portion is in turn intercepted by a second target, this portion also being re-radiated in all directions, some towards the transducer. If the second target had not been in position this fraction of the energy would not have reached the transducer. There is also the possibility that the re-radiation from the second target is further re-radiated from the first target and so on. Investigation has shown that generally the effects of multiple scattering are too small to be significant, although this is not certain for all situations.

Experimental data obtained from a large herring school have been analysed and compared to a theoretical multiple scatter model which is shown to adequately describe the school echo characteristics, Ertugrul and Smith (1982). They conclude that fish abundance measurements which employ echo-integration techniques could substantially underestimate the fish numbers. The smaller the school and the lower the density of fish the less likely it is that underestimation will occur.

Another effect in fish schools is the acoustic shadowing of fish low down in a school by those above them. Examination of this and other effects due to the schooling of fish is beyond the scope of this manual but readers are referred to Lytle and Maxwell (1982) and the Foote (1983).