© 2005 International Council for the Exploration of the Sea
Acoustic backscattering by Atlantic mackerel as being representative of fish that lack a swimbladder. Backscattering by individual fish
a Institute of Oceanology of Polish Academy of Sciences ul. Powsta
ców Warszawy 55, PL-81-712 Sopot, Poland
b Institute of Marine Research PO Box 1870, 5817 Bergen, Norway
*Correspondence to N. Gorska: tel: +48 58 551 72 81; fax: +48 58 551 21 30. e-mail: gorska{at}iopan.gda.pl.
Developing acoustic methods for the identification of fish remains a long-term objective of fisheries acoustics. The accuracy of abundance estimation may be increased when the acoustic-scattering characteristics of the fish are known, including their expected variability and uncertainty. The modelling approach is valuable during the process of interpreting multi-frequency echograms. This paper attempts to improve the understanding of sound backscattering of fish without a swimbladder, here represented by Atlantic mackerel (Scomber scombrus). Our approach includes results from modelling as well as comparisons with field data. There will be two papers. The first is a study of the non-averaged backscattering characteristics. This initial analysis is important for the understanding of the averaged backscattering cross-section, which will be considered in the second paper. In that paper the relative importance of bones in acoustic backscattering at higher frequencies will be verified.
Keywords: backbone, fish flesh, modelling, sound backscattering by mackerel
Received 30 May 2004; accepted 20 March 2005.
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Introduction |
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 Top Introduction Material and methodsResults and discussionConclusionsList of symbolsReferences |
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Acoustic surveys are widely used for the stock assessment of many pelagic fish species (MacLennan, 1990). A thorough understanding of the mechanisms of sound scattering by fish, including the understanding of the contribution of the various anatomical features to the overall backscattering, is required to improve present acoustic methods of fish species identification (Horne, 2000; Reeder et al., 2004). Numerical modelling of sound backscattering by fish (see the review presented by Horne and Clay, 1998; Reeder et al., 2004) and controlled accurate laboratory measurements (Sun et al., 1985; Nash et al., 1987; Barr, 2001; Reeder et al., 2004) have been carried out to gain more knowledge of the process by which sound is scattered by selected fish species.
The paper stems from the need for proper assessment from acoustic backscattering data of the abundance of the economically important fish species, Atlantic mackerel (Scomber scombrus). Multi-frequency measurements on mackerel made at 18, 38, 70, 120, 200, and 364 kHz demonstrated that backscatter intensities at different frequencies (i.e. frequency response) have a specific pattern. Korneliussen and Ona (2002) found that the frequency response for mackerel was flat at 18, 38, and 120 kHz and then increased in intensity towards 200 kHz. Unpublished backscatter measurements made in net pens and at sea confirmed frequency-independent backscatter at 18, 38, and 70 kHz, and stronger backscatter at 200 kHz. In the measurement series, backscatter intensities at 120 kHz were more variable. In some series it was similar to that at 38 kHz, and in others the increase in intensity lay anywhere in the range up to double the intensity at 38 kHz. To gain an understanding of this peculiar frequency response and to study its stability, we wanted to see if this particular frequency spectrum was consistent for Atlantic mackerel and could be used for acoustic identification.
In order to begin to answer this question the backscattering needed investigation. Most modelling to date has been done for fish with swimbladders where that organ is the source of most backscatter per se (Reeder et al., 2004). Backscattering by other anatomical features, which can be important for sound incidence, are not normal to the surface of swimbladder, as well as for fish without swimbladders, are still not well known. In this paper the need to understand the impact of the different anatomical components on total backscattering and the factors which could modify mackerel target strength is addressed. Furthermore, the contribution of mackerel body and backbone to the overall backscattering characteristics across a selected frequency range is examined. The effects of orientation and the morphological condition of the fish are also considered. The modelling was done using the Distorted Wave, Born-Approximation (DWBA) (Chu et al., 1993; Stanton et al., 1993, 1998; Stanton and Chu, 2000) and the Modal-Based, Deformed-Cylinder Model (MB-DCM) (Stanton, 1988a, b, 1989). A high-resolution morphology of flesh, based on measurements of the mackerel body, was considered. To study mackerel-backbone backscatter, straight and uniformly bent cylinders were used to describe its shape. The typical observed backscattering-frequency responses for mackerel are then explained in theoretical terms. The use of the frequency response in mackerel identification is justified.
The final outcome of the study should be to explain the frequency response of mackerel shoals. The frequency response is defined by the averaged backscattering cross-section of mackerel at different frequencies. However, for a better understanding of the averaged characteristics the modelling has to be done first at an individual level, i.e. for the backscattering cross-section before averaging takes place. The modelling section has, therefore, been divided into two aspects; first, backscattering by individual mackerel (this paper), and second, average backscattering by mackerel (in a second paper).
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Material and methods |
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TopIntroductionMaterial and methodsResults and discussionConclusionsList of symbolsReferences |
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Main backscattering equation: backscattering by fish flesh
The DWBA-based, deformed-cylinder model (Chu et al., 1993; Stanton et al., 1993, 1998; Stanton and Chu, 2000) has been used to describe backscatter by mackerel flesh. This model is assumed to be applicable because: (i) mackerel flesh has material properties that are similar, within a few per cent, to those of the surrounding water, so mackerel can be referred to as a weak scattering target; and (ii) the mackerel body has a cross-section that can be described, at first order, as circular.
Using the analytical solution (Equation (6) from Stanton and Chu, 2000), some derivations have been made to apply it to mackerel. A solution has been obtained for mackerel backscattering length, fbscfl, normalized by length, lfl.
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| (1) |
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| (2) |
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| (3) |
is expressed as = 2(kfla0). Ratio values of f(u) = a(u)/a0 describe the variability of the cross-sectional radius of mackerel body a(u), normalized by the maximum radius a0, along the longitudinal axis of the fish (see Figure 1a). The variable u denotes the x-variable along the axis, normalized by fish length lfl (u = x/lfl). The symbol a(x) in the argument of the F function in Equation (1) refers to the sensitivity of the function to the shape of the mackerel body, or more precisely, to the dependence of the normalized radius f(u) on u.
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Equations (1), (2), (3) incorporate the fact that the cross-sectional radius varies only along the axis of the body. Although fat content is known to differ from dorsal to anterior (i.e. back to stomach), sufficient data on the properties of mackerel-body components are not available and have been treated as being homogeneous.
Backscatter from the backbone
The Modal-Based, Deformed-Cylinder Model (Stanton, 1988a, b, 1989) was used to study backscattering by the backbone. This model is applicable to elongated deformed cylinders with large aspect ratios and where the direction of incidence and scattering is normal or near-normal to the tangent of the axis of the cylinder. The measurements, made on the mackerel cruise by RV "G. O. Sars", October 2002, demonstrated the near-circularity of backbone cross-section and the large backbone elongation: the aspect ratio of backbone, i.e. the length/radius ratio of the backbone, can reach values of 140–160, so justifying the use of the model.
The backbone was modelled in two different ways: (i) as an elastic, solid, straight cylinder of uniform composition (see Figure 1b); and (ii) as an elastic, solid, uniformly bent cylinder of constant radius of curvature of its axis, constant cross-section radius, and constant composition (see Figure 1c).
These simple geometric shapes were chosen because approximate analytical–numerical MB-DCM solutions have been obtained in similar cases (cf. Stanton, 1988b, 1989).
Equation (7) of Stanton (1988b) was used to model the backscattering length of a straight cylinder. Equation (8) of Stanton (1989) was employed to derive solutions for the backscattering length of a bent cylinder. The modal coefficients, defined by Equation (1) of Stanton (1988b) or by Equations (22)–(25) of Faran (1951), were used in both cases.
The backscattering length of the backbone can be expressed by
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| (4) |
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| (5) |
The scattering phase angles 
m, 
m, 
m, 
m, ßm, 
m involved in modal sum coefficients are functions of acoustic frequency, cylinder cross-section radius, sound-speed contrasts for compressional (hcom) and shear (hsh) waves (i.e. parameters x, x1, x2), and the density contrast (g) inside the backbone. They can be expressed as:
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| (6) |
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| (7) |
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| (8) |
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| (9) |
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| (10) |
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| (11) |
Modelling parameters
Acoustic backscattering by fish is a complex function of the geometrical shape of various body components, the properties of their materials, the orientation of the fish in space, and the acoustic frequency (Horne, 2003). In the modelling process, we considered the following factors.
Size and frequency
To include a full range of frequencies and lengths of mackerel bodies and backbones, ka0 values from 0 to 40 were used for fish body and ka values from 0 to 2.5 for fish backbones. These ranges were based on the results of a large number of body-size measurements (Korneliussen et al., 2003) and mackerel-morphology studies conducted during October 2002 on the RV "G. O. Sars" (2) and October 2003 on the RV "G.O. Sars" (3).
Animal morphology
The digitizing of fish-body morphology needs to include the acoustic properties of the flesh and backbone (the spatial, three-dimensional distribution of the contrasts gfl, g and hfl, hcom, hsh) and the three-dimensional shape. Two classes of mackerel, differing in body shape, were chosen for analysis – thick and lean mackerel. Examples of these classes are presented in Figure 2a, b. In Figure 2c, the digitizing of the outer boundary of mackerel bodies is shown using light and dark grey lines. The radius of the mackerel body and the x coordinate, both normalized by the fish length lfl, are indicated in the vertical and horizontal axes. Aspect-ratio values for fish flesh were efl= 10.54 for lean fish and efl= 8.5 for thick fish. We assumed independence of the aspect ratio of the fish length for the two classes.
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Simple geometric shapes (e.g. straight and uniformly bent cylinders) were considered when modelling the backbone. Backbone dimensions (a and l) and the aspect ratio eb, obtained in mackerel morphology studies conducted during October 2002 on the RV "G. O. Sars" (2) were used in the computations. The information on the change in angle between the main axis of the body and the backbone may be important for the study. A 3° angle was measured between the sagittal axis of the body and the backbone.
There are few data on sound-speed and density contrasts for Atlantic mackerel. According to Lockwood (1988), the fat content of mackerel varies from 10% in June to 25–30% in October, which is in agreement with a typical fat content of 5.5% for mackerel landed in Norway in June 2002, increasing to 20% in July–September (personal communication with the Norwegian Directorate of Fisheries). Accounting for the fat content varying from 5% to 30%, and the empirical relationship between mackerel fat content Ff and the density contrast gfl, gfl = 1.03 – 0.094Ff, found in our own measurements, a range of variability in density contrast of 1.002–1.025 is considered appropriate for mackerel flesh. According to Sigfusson et al. (2001), the contrast varies between 1.002 and 1.025. The measured sound-speed contrast in mackerel flesh hfl varied around 1.025 both in our own measurements and in Sigfusson et al. (2001), where it was found to be hfl = 1.034 – 0.125Ff at 25°C. The measured density contrast of backbone 1.10 ± 0.05 was used in the computations. Sound-speed contrast measurements for shear and compressional waves were not performed. Given the lack of available information on these two parameters, we assumed sound-speed contrasts of 0.1–1.0 for shear waves and 1.3–2.0 for compressional waves.
Length and orientation statistical distributions
Based on samples from trawl and purse-seine catches, mean total body lengths of 30–40 cm with a standard deviation of 10% were used in the analysis. Given the lack of mackerel tilt-angle measurements, we assumed a narrow distribution of orientations, based on visual observations of behaviour in net pens.
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Results and discussion |
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TopIntroductionMaterial and methodsResults and discussionConclusionsList of symbolsReferences |
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Sensitivity analysis for mackerel flesh
The possible effect of changes in mackerel morphology on backscattering was analysed using expressions for the normalized backscattering length, fbscfl/lfl (Equations (1), (2), (3)).
The ka0-dependencies of reduced target strength, RTS = 10 log(
bscfl/lfl2), are presented in Figure 3 by grey and black lines for lean and thick mackerel, respectively. The density contrast gfl = 1.03 was used in both calculations at normal incidence (i.e. ß = 0). Comparison of the two curves in the figure demonstrates that the reduced target strength is slightly dependent on the geometrical shape of the mackerel body. The reduced target strength is sensitive to the sound-speed contrast, which influences both the amplitude of the oscillations and their period. The period of oscillations over ka0 is defined mainly by the difference in speed of sound (hfl), and it is proportional to hfl. The density contrast influences only the value of the RTS, not the periodicity of its oscillations. For the density contrast variation from 1 to 1.03, the reduced target strength increases 6–12 dB, depending on the value of the sound-speed contrast.
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Sensitivity analysis of the orientation dependence (Figure 4) shows that the shape of the directivity pattern depends strongly on the value of ka0. There is a minimum in the pattern for both curves at ß = 0 (Figure 4a). While the minimum in the mackerel-directivity pattern at ß = 0 is surprising, it is consistent with the shape (minimum) of the ka0-dependence, as indicated by solid arrows in Figure 3, at ka0 = 2.5 and ka0 = 12.15, at which the calculations were made. The possibility of the minimum in the directivity pattern at normal dorsal incidence is also supported by the results of earlier measurements (Foote and Nakken, 1978). A maximum and local minimum at ß = 0 for curves in Figure 4b are explained by the shape of the ka0-dependence at ka0 = 1.5 (ka0 of the first maximum of RTS) and ka0 = 11.45 (ka0 is close to the ka0 of seventh maximum of RTS), indicated by dotted arrows in Figure 3. Comparison between dotted and solid curves in Figure 4 demonstrates that the width of the lobes of the directivity pattern is controlled by the ka0 parameter. For the larger ka0, the individual lobe width is smaller and number of lobes is larger.
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The calculations of the orientation dependence of the target strength of mackerel flesh TS = 10 log(
bscfl) (Figure 5) show that the dependence is more complex for higher frequencies. The number of the directivity-pattern lobes increases and the width of an individual lobe decreases with frequency.
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Sensitivity analysis for mackerel backbone
The analysis demonstrates (Figure 6) that the resonance and anti-resonance structure (the ka of maxima (resonances) and minima (anti-resonances) of the target strength, the frequency of the occurrence of resonances and anti-resonances, the width of the resonance and anti-resonance peaks and their amplitudes) are all extremely sensitive to the sound-speed contrast of shear waves in backbone. For the larger contrast the resonances and anti-resonances are more frequent and narrow, and their amplitude is higher. The similar qualitative dependences are observed for sound backscattering by elastic solid spheres (Hickling, 1962).
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The dependence of the reduced target strength on ka is illustrated for various sound-speed contrasts of compressional waves in Figure 7. Individual plots refer to different sound-speed contrasts of shear waves: 0.3, 0.5, and 0.9 – from top to bottom. The sound-speed contrast of compressional waves does not impact the width of the peaks of resonances and anti-resonances and their positions over ka-axis, but influences the value of the reduced target strength of backbone. The value increases with the contrast. The impact depends on the ka parameter.
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Figure 8 illustrates the sensitivity of the reduced target strength of backbone to the backbone-density contrast. The density contrast does not influence the resonance and anti-resonance structure of the curves and defines only the magnitude of the reduced target strength. The magnitude increases with increasing density contrast.
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The sensitivity of backscatter to the backbone shape is demonstrated in Figure 9. The three curves shown refer to various backbone geometries viz. from top to bottom, straight cylinder and bent cylinders with ratios of l/(2
c) 0.1 and 0.2, respectively. Only the magnitude of the reduced target strength is sensitive to the shape of the backbone. The more curved the backbone, the smaller the level.
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Conclusions |
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TopIntroductionMaterial and methodsResults and discussionConclusionsList of symbolsReferences |
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A model has been developed to describe sound backscattering by Atlantic mackerel flesh and backbone. It has been shown that:
- in the case of normal sound incidence, the value of RTS is defined mainly by the sound-speed and density contrasts, and to a lesser extent by the geometrical shape of the body, while the periodicity of its oscillations over ka0 depends only on the sound-speed contrast: period is proportional to hfl.
- the features of the directivity pattern of a fish body are highly dependent on the ka0 parameter: the ka0-value in regard to the ka0 of maxima and minima of the ka0-dependence of RTS is important. Minimum (maximum) of the directivity pattern is observed for the normal incidence at the ka0 of minima (maxima).
- the ka of maxima (resonances) and minima (anti-resonances) of the backbone target strength, the frequency of the occurrence of resonances and anti-resonances, the width of the resonance and anti-resonance peaks, and their amplitudes are mainly defined by the sound-speed contrast of shear waves. Sound-speed contrasts of compressional waves and density contrast influence the value of the target strength of fish backbone. The value is also sensitive to the degree of curvature of the cylinder backbone.
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List of symbols |
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TopIntroductionMaterial and methodsResults and discussionConclusionsList of symbolsReferences |
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Backscattering cross-section of flesh
Backscattering cross-section of backbone
Backscattering length of flesh
Backscattering length of backbone
- lfl Length of body (from the top of the head to the start of tail) Figure 1a
- l Length of backbone
- a(x) Cross-sectional radius of body, variable along the longitudinal axis Figure 1a
- a0 Maximum of a(x)
- a Radius of backbone cylinder
- efl = lfl/a0 Aspect ratio of body of fish
- eb = l/a Aspect ratio of backbone cylinder
c Radius of curvature of the axis of backbone bent cylinder
max l/(2c)
- hfl = cfl/c Sound-speed contrast in fish flesh
- hcom = ccom/c Sound-speed contrast of compressional wave in backbone
- hsh = csh/c Sound-speed contrast of shear wave in backbone
- c Speed of sound in surrounding seawater
- cfl Speed of sound in flesh
- ccom Speed of compressional sound wave in backbone
- csh Speed of shear sound wave in backbone
- gfl =
fl/ Density contrast of fish flesh
Density of surrounding water
fl Density of fish flesh
- g =
1/ Density contrast of backbone
1 Density of backbone
- f Carrier frequency of sound
- k = 2
f/c Acoustic wavenumber in surrounding seawater
- kfl = 2
f/cfl Acoustic wavenumber in flesh
- kcom = 2
f/ccom Acoustic wavenumber of compressional wave in backbone
- ksh =2
f/csh Acoustic wavenumber of shear wave in backbone
- x ka cos
- x1 kcoma
- x2 ksha
m Neumann's number: 0 = 1, m>0 = 2
m, m, m, m, ßm, m Scattering phase angles
- Jm( ) Bessel function of the first kind of order m
- Nm( ) Bessel function of the second kind of order m
- Jm'( ), Nm'( ) Derivative with respect to argument of Jm( ) or Nm( )
- ß Angle between the direction of incidence and the normal to the longitudinal axis of the fish Figure 1a
Angle between the direction of incidence and the normal to the backbone longitudinal axis of the fish Figure 1b
kl sin
- Ff Fat fraction of total weight
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Acknowledgements |
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This work has been partially supported by the Institute of Oceanology, Polish Academy of Sciences (sponsor programme 2.7), the Research Council of Norway (Grant No. 133657/120), and the European project SIMFAMI (Grant No. Q5RS-2001-02054).
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References |
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TopIntroductionMaterial and methodsResults and discussionConclusionsList of symbolsReferences |
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