ICES Journal of Marine Science: Journal du Conseil Advance Access originally published online on June 29, 2007
ICES Journal of Marine Science: Journal du Conseil 2007 64(6):1145-1151; doi:10.1093/icesjms/fsm094
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Acoustic backscatter by schools of adult Atlantic mackerel
1 Institute of Oceanology of Polish Academy of Sciences, ul. Powsta
ców Warszawy 55, PL–81–712 Sopot, Poland
2 Institute of Marine Research, PO Box 1870, Nordnes, N-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
Gorska, N., Korneliussen, R. J., and Ona, E. 2007. Acoustic backscatter by schools of adult Atlantic mackerel. – ICES Journal of Marine Science, 64: 1145–1151.The extent of acoustic backscatter by schools of adult Atlantic mackerel (Scomber scombrus) is investigated to improve biomass estimates. Previous studies involving modelled scattering from individual mackerel showed that backscattering at high frequencies is dominated by the contribution from the backbone. Accurate predictions of the scattering spectra require consideration of backscattering from the entire skeleton, including details of the bone shapes and their acoustic properties. Here, the backscattering cross-sections from mackerel flesh and backbone are estimated theoretically from 18 to 364 kHz and averaged over fish size and tilt angle, then compared with in situ measurements of volume backscattering from mackerel schools. Based on the comparisons, some gross features of the observed relative frequency response are explained, and recommendations for further studies suggested.
Keywords: backbone, fish flesh, mean backscattering cross-section, modelling, sound backscattering by mackerel
Received 3 October 2005; accepted 30 March 2007; advance access publication 29 June 2007.
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Introduction |
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The extent of acoustic backscatter by schools of Atlantic mackerel (Scomber scombrus) is used to improve biomass estimates in fisheries research. Acoustic methods make it possible to measure mackerel abundance annually, and at the same time to map the geographical distribution far more efficiently than the labour-intensive, egg-fertility method (Anon., 2003) used every third year to estimate mackerel stock abundance.
For fish with well-developed swimbladders, the gas-filled chambers are responsible for 90–95% of the backscattered energy (Foote, 1980), and determine their relative frequency responses, r(f) 
sv(f)/sv(38 kHz) (Korneliussen and Ona, 2002), values that are commonly used to identify species (Korneliussen and Ona, 2002, 2004; Anon., 2006). To improve existing acoustic methods of fish species identification, the various anatomical features contributing to the overall backscattering by fish must be better understood (Horne, 2000; Reeder et al., 2004). Many theoretical studies [see reviews of Horne and Clay (1998), and Reeder et al. (2004)] and laboratory studies (Sun et al., 1985; Nash et al., 1987; Barr, 2001; Reeder et al., 2004) of backscattering mechanisms still fail to elucidate clearly the role of anatomical features other than the swimbladder in backscattering. Atlantic mackerel do not have swimbladders and therefore provide a more complex acoustic target to model.
Annual multifrequency surveys targeting mackerel started at Norway's Institute of Marine Research (IMR) in 1999 and both species identification and target-strength estimation methods are supported by controlled measurements of captured mackerel. The investigations showed that the backscatter at 200 kHz was four times stronger than that at 38 kHz, r(200 kHz) 
4 ± 1, and that the backscatter at 120 kHz relative to 38 kHz, r(120 kHz), varied between being equal and twice as strong during the period 1999–2005.
There was no significant variation in the average mackerel length (33.5 ± 1 cm) or weight (325 ± 25 g) in the trawl catches during the surveys in that time, but there was a jump in r(120 kHz) from 1 in the years 1999–2002 to 1.5–2 in the years 2003–2005. Therefore, the hypothesis of change in fish size being the reason for the change in r(120 kHz) between the two periods is not supported by the catches. However, change in mackerel size between the two periods cannot be completely ruled out as the cause of the change in r(120 kHz), because the trawl catches may not be representative of the stock as a result of the difficulties in catching the mackerel. An increase in r(120 kHz) for large mackerel as compared with that of small mackerel in captivity, where the sizes of the fish were controllable, could indicate that the dominating scattering part of the fish at 120 kHz had moved from, for example, flesh to backbone, at least for the sizes of mackerel investigated. The value of r(120 kHz) was closer to 2 for large mackerel in captivity and closer to 1 for small mackerel in captivity. Around 120 kHz, mackerel flesh is a geometric scatterer, i.e. essentially frequency independent, whereas backbone is a Rayleigh scatterer, i.e. it increases rapidly with frequency. Therefore, based on measurements and this argument, 120 kHz should not be used in acoustically estimating mackerel abundance.
The annual IMR surveys have shown that mackerel and herring (Clupea harengus) often occur together. Because backscatter intensity for adult mackerel is greater at 200 kHz than at 38 kHz, but lower at 200 kHz than at 38 kHz for schooling fish with swimbladders (e.g. herring; Anon., 2006), 200 kHz may be better than 38 kHz as a frequency for acoustically estimating mackerel abundance. Therefore, the error introduced by mistakenly using backscatter from, for example, herring rather than mackerel in estimating mackerel abundance is less when 200 kHz rather than 38 kHz data are used. However, in such a case, a reliable relationship between target strength (TS) and fish size is needed. A TS model can be used to judge whether or not TS can be measured accurately at 200 kHz.
Before changing the frequency used in the acoustic estimation of mackerel abundance, we need to know whether the differential backscattering by mackerel flesh and backbone can explain existing measurement differences, and also how the measurements may change if other factors such as the environment, the size of fish, or the fat content change. The results of this study document the reliability of calculating mackerel abundance from acoustic data.
Gorska et al. (2004) showed that the measured relative frequency response, r(f), of mackerel cannot be modelled accurately as simply as the backscattering by fish flesh. This result encouraged further studies of backscattering by Atlantic mackerel that considered backscattering by both mackerel body and backbone (Gorska et al., 2005). As a first step, backscattering characteristics of individual fish were analysed. The backscattering characteristics presented by Gorska et al. (2005) fluctuate and are difficult to compare with measurements. However, their average values are more stable and comparable with in situ measurements. Here, we present an analysis of the averaged backscattering cross-sections of backbone and fish body.
Using the results obtained for non-averaged characteristics (Gorska et al., 2005), a sensitivity analysis of the mean backscattering cross-section of mackerel flesh and backbone is made at frequencies of 18, 38, 70, 120, 200, and 364 kHz. The backscattering mechanisms are investigated, including a study of the role of the various anatomical features in the total backscattering, and an analysis is made of the biological and acoustic parameters that control backscattering. The r(f) of mackerel is explained.
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Methods |
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A list of the symbols, their definitions and the units is given in Table 1.
The mean total backscattering cross-section of mackerel can be modelled as a sum of the mean backscattering cross-sections of the mackerel parts:
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| (1) |
flbsc
, bbsc, bscsk, and bscob describe the mean backscattering cross-sections of mackerel flesh, backbone, skull, and other bones, respectively. Here, only the backscattering by the mackerel flesh and backbone is considered. The brackets ... denote the average over the ensemble of aggregation realizations differing in lengths and orientations:
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| (2) |
bsc is substituted by flbsc or bbsc for backscattering by flesh and backbone, respectively. The function fbsc corresponds to the respective scattering length of mackerel flesh or backbone, i.e. to fbscfl andfbscb. The functions Wß (ß) and Wl(ltot) represent probability density functions (PDFs) of fish orientation, ß (see Figure 1a of Gorska et al., 2005), and fish total length, ltot, respectively. Gaussian distributions are assumed for Wß (ß) and Wl(ltot):
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| (3) |
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| (4) |
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The TSs of mackerel flesh TSfl = 10 log (
bscfl) and backbone TSb = 10log( bscb) will be considered here. The backscattering cross-section used to estimate fish-stock abundance is averaged over fish lengths and tilt angles. This is similar to estimating the average TS of individual fish in schools, but obviously different from calculating the TS of individual fish given tilt, fat, etc., as done by Gorska et al. (2005). The numerical analysis in the following sections is based on Equations (1)–(4) and the expressions for the backscattering lengths of mackerel flesh and backbone from Gorska et al. (2005) (their Equations (1)–(3) and (4)–(10), respectively). The results are compared with the relative frequency response r(f) of schools identified as mackerel from trawl samples taken during the 2003 and 2004 acoustic surveys (Korneliussen and Ona, 2004).
The modelling parameters are as discussed by Gorska et al. (2005). The range of density contrast, i.e. the density of mackerel flesh relative to that of the surrounding seawater, 1.002 
gfl 1.025 is based on the measurements made during a study of the acoustic properties of mackerel flesh. The sound-speed contrast of flesh, hfl,, has been measured as 1.025. A backbone-density contrast of g = 1.1 was chosen based on the results of the measurements. Given the lack of available information in the averaging process, {
Sß} are set to 0° and 5° (N(0°, 5°)), respectively. Further, the values of the sound-speed contrasts of bone are uncertain and difficult to measure, so 0.1 hsh 1.0 are used for shear waves and 1.3 hcom 2.0 for compressional waves, to analyse backscatter sensitivity for these parameters. The standard deviations of the normal length distribution [Equation (4)] is set to 10% of the mean of the fish caught in the schools, because this is the variability typically observed. The measured length and radius of backbones are given later.
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Results |
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The modelled TS of flesh, TSfl, from thick mackerel (see Figure 2a of Gorska et al., 2005, for an illustration of "thick") is plotted against fish total length, ltot, and density contrast gfl at 18 kHz and 70 kHz in Figure 1a and b, respectively. The plots show the sensitivity of flesh TS to the density contrast and fish total length, i.e. TSfl = TSfl(gfl, ltot). At 70 kHz, TSfl increases monotonically with ltot and gfl. At 18 kHz, the length dependence is more complicated: for smaller fish, the TSfl first decreases, then increases with increasing ltot. For larger fish, TSfl increases with ltot, over the entire range of fish total lengths. The greater the density contrast, gfl, the larger is the TS. In contrast to the 70 kHz case where backscatter is always geometric, the more complicated length dependence can be explained by the fact that the k
0 parameter at the lower frequency, i.e. at 18 kHz, varies in the transition zone between the Rayleigh- and geometric–scattering regions where the k0 dependence of mean backscattering cross-section is oscillatory. The regions corresponding to geometric and Rayleigh scattering are indicated in Figure 1. The figure shows that for a given value of gfl (density of mackerel relative to seawater shown along the x-axis), TSfl ranges between 
7.5 dB at 18 kHz and 3.5 dB at 70 kHz, for lengths from 28 to 42 cm. The variability of the TSfl attributable to the changes in gfl for a fixed fish total length is 5.2 dB at both 18 kHz and 70 kHz. Accepting the frequency independence of TSfl at frequencies >38 kHz, where scattering from flesh is in the geometric region (Gorska et al., 2004), the sensitivity of TSfl to fish length and density contrast at the frequencies used in hydroacoustically surveying mackerel (38, 120, 200, and 364 kHz) is the same as presented in Figure 1b for 70 kHz.
In Figure 2, the modelled backbone target strength TSb =10log bscb is plotted against frequency for two different backbone sizes for the shear-wave, sound-speed contrast 0.1 (Figure 2a) and 0.5 (Figure 2b). In Figure 3, TSb for a single backbone is plotted against frequency for three different shear-wave, sound-speed contrasts. The backbones were modelled as straight cylinders with the sound-speed contrast of the compressional wave in the backbone hcom = 1.3. Further, the tilt angle of the backbone varies around 3° from horizontal, because the angle between the main axis of the mackerel body and the backbone was 3°, as measured from a dissected mackerel. Figure 2 shows that the frequency dependence of TSb is sensitive to the backbone size. Note that for small sound-speed contrast, e.g. hsh= 0.1, as in Figure 2a, the impact of backbone size is generally less than at higher contrast, e.g. hsh= 0.5, as in Figure 2b. Figure 3 shows that at lower frequencies, TSb decreases with increasing sound-speed contrast of the shear wave, hsh, but at higher frequencies (200 and 364 kHz), it increases under the same conditions. This is easily seen in Figure 3, where the curve for hsh = 0.9 crosses the curves for hsh= 0.1 and hsh= 0.5 around 100 kHz. The variability attributable to the contrast can be up to 30 dB. The sensitivity of the sound-speed contrast of shear waves in backbones, hsh, is explained by the sensitivity of the resonance structure of the ka dependence in the non-averaged case to this parameter (see Figure 6 of Gorska et al., 2005).
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The mean backscattering cross-section is also sensitive to the density and the sound-speed contrasts of the compressional waves. However, unlike the sound-speed contrast of the shear waves, for which the impact on the shape of frequency dependence of TSb is strong, these two parameters have only a slight influence on the level of the curve. Varying these parameters does not affect the shape of the curve, because of the insensitivity of the resonance structure in the non-averaged case to them (Gorska et al., 2005).
In Figure 4, the modelled backscatter from several backbone sizes with different shear-wave, sound-speed contrasts is plotted against the frequency. Also, modelled backscatter from mackerel flesh is plotted against the frequency, for comparison. The backscattering cross-sections were modelled for ltot = 42 cm, gfl = hfl = 1.025, hsh= 0.1 and 0.3, and for measured backbones of lengths and radii of 248 mm and 2.3 mm, 191 mm and 1.4 mm, 220 mm and 1.35 mm, and 282 mm and 1.75 mm. The calculations demonstrate that the dominant backscattering mechanism is flesh at 18 kHz and 38 kHz, both flesh and bone at 70 kHz, and bone at 120, 200, and 364 kHz.
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In Figures 3 and 4 of Gorska et al. (2004), the mean backscattering cross-section of mackerel flesh,
bscfl, is clearly fairly flat over the entire frequency range, even when varying all simulation parameters for the flesh. The increase in backscattering at higher frequencies (Korneliussen and Ona, 2002, 2004) is therefore not flesh-dependent, but caused by other reflecting tissues within the fish. The result presented in Figure 4 suggests that the increase of the measured relative frequency response, r(f), at higher frequencies is a result of the dominance of backscattering from backbone. In Figure 5, the combined backscatter, r(f), from both flesh and backbone at each frequency is normalized by the respective backscattering at 38 kHz for both measured and modelled data. The stippled lines in Figure 5 show the modelled r(f) curves and may be compared with the solid curves that show different measurement series of r(f). Using the same parameters as in Figure 4, theoretical curves are presented that best fit the measurements.
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Discussion |
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In order to understand the stability of the measurements, the impact of fish shape and morphology on the relative frequency response, r(f), of mackerel has been analysed, and there is variability with mackerel size and seasonal variations in condition factor and fat content. Generally, adult mackerel wintering in the North Sea are from the length range 28–42 cm (Korneliussen et al., 2005), and with the shear-wave contrasts used in the simulations for most of these sizes (and shear-wave contrasts), the maximum backscatter is predicted to be at 200 kHz, as seen in Figures 4 and 5. Figure 4 also shows that the backscatter from the flesh is essentially frequency independent, at least at 38 kHz and above, although the level of backscatter from flesh may vary slightly from one year to another. Using the results presented in Figure 1, for the entire range of mackerel lengths from 28 to 42 cm, the relative frequency response, r(f), varies by up to 4.5 dB at 18 kHz and by up to 3.5 dB at high frequencies (120 kHz and higher). This variation represents the maximum possible change of frequency response attributable to the possible variation in mackerel length. In reality, annual variations in mean mackerel size from trawl catches are slight, although the extent to which trawl catches are representative of a stock is uncertain, as stated above. Even more important is that the backbone thickness increases as the size of the fish increases, so r(200 kHz) does not vary much with fish size.
Computations were also done to explore sensitivity to other parameters. Mackerel are thought to be ectotherms, the temperatures of the fish body and the ambient water differing by less than 1–2°C (Block et al., 1993). The speed of sound in oil decreases with temperature (Sigfusson et al., 2001), but the actual sound speed is not easy to estimate exactly, because it also varies with oil composition (unpublished measurements of oil from caged mackerel by RJK in 2000, sound-speed measurements in Korneliussen et. al., 2005), which depends on the mackerel feed. Variation in the surrounding temperature results in changes in the sound-speed contrast of fish flesh, hfl. The survey data were recorded in the North Sea at temperatures of 8–12°C. Over this temperature range, the computed variability of r(f) is no more than 0.3 dB at 18 kHz, and less at higher frequencies.
The expected variability in the fat content of fish muscle, causing a change in the tissue-density contrast, will affect r(f) only at higher frequencies. This is because the backscatter at high frequencies is mainly attributable to bone, which is independent of the fat content of the fish flesh, but when normalized to the backscatter at 38 kHz, the normalizing parameter sv(38 kHz) refers to flesh and is fat-sensitive. The maximum observed seasonal variability in fat content in mackerel (5–30%) may therefore lead to changes of no more than 4 dB in r(f) at high frequencies. Such changes depend on the actual value of the sound-speed contrast in the mackerel tissue. Acoustic investigations of mackerel in the North Sea are carried out in September and October, when the fat content of mackerel has attained its maximum, so r(f) is unlikely to vary by as much as 4 dB at that time of year.
Figure 5 reveals some disagreements between theoretical and measured curves. This may be explained by the use of a low-resolution model for the skeleton (i.e. a straight-cylinder model of the backbone, ignoring the skull and minor bones) in the simulations. Attempts to model backscatter from the skull have so far been unsuccessful because of its complex morphology. The length and width of a skull of a 35 cm mackerel is near 5 cm and 0.5–1.5 cm, respectively, so it should contribute to total backscattering. As mackerel are weak scatterers relative to fish with swimbladders, it is also worthwhile considering the contribution of the scattering from mackerel stomach contents, which are sometimes hard-shelled zooplankton. Moreover, the correct value of shear-wave, sound-speed contrast in the backbone, to which r(f) is highly sensitive, is unknown. It is of note that the best fit between simulated and measured data was obtained with a contrast between 0.1 and 0.3, the most likely range within which the actual contrast will lie.
Qualitatively judging multifrequency echograms of mackerel schools, the measured r(f) seemed to be stable throughout the vertical extent of the school and density-independent, so the effects of frequency-dependent acoustic extinction are likely to be negligible.
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Conclusions |
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Modelling has shown that the backscatter of schooling mackerel is closely related to the averaged backscattering from mackerel flesh only (Gorska et al., 2004) and to the backscattering from flesh and bone of individual mackerel (Gorska et al., 2005).
Here, we studied the theoretical mean backscattering cross-sections of mackerel flesh and backbone numerically and compared them with the measured backscattering data. The analysis demonstrated that the mean backscattering cross-section of adult Atlantic mackerel is dominated by backscattering from the fish flesh at the lower frequencies (18 and 38 kHz), and by the backbone at higher frequencies (120, 200, and 364 kHz). The main parameters dominating the r(f) are: fish size, fat content of the body tissue, temperature of the surrounding water, and the sound-speed contrast of shear waves in the backbone and other large bone structures of the fish.
In summary:
- measured r(f) can be explained by backscatter from flesh and bone;
- backscatter at low frequencies, e.g. 38 kHz, is dominated by flesh;
- backscatter at higher frequencies, e.g. 200 kHz, is dominated by bone;
- backscatter at 200 kHz is stronger than that at 38 kHz. This is in contrast to the situation in fish with swimbladders, such as herring (Foote et al., 1993; Anon., 2006);
- backscatter of flesh may vary with environment and fat content, and the backscatter of bone is stable but may vary with an average tilt; and
- r(200 kHz) may change with the environment and fat content because r(200 kHz) = sv(200 kHz)/sv(38 kHz), but computations demonstrated that it is quite stable.
Residual discrepancies between modelled and measured backscattering patterns may be from artefacts related to the simple geometrical shape used to describe the skeleton, and the lack of data on the density and the sound-speed contrasts in mackerel flesh and backbone. Therefore, to take forward this investigation, a combined approach is needed. First, the model should account for other fish parts (e.g. the skull and stomach contents). Second, the relevant material properties should be measured and used in the model. Finally, target-strength measurements should be made of individual mackerel, their flesh, and their bones, over a wide acoustic bandwidth. Additionally, future analyses should consider the impact of changes in the oil composition of mackerel flesh.
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Acknowledgements |
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The work was partially sponsored by the Institute of Oceanology, Polish Academy of Sciences (under sponsor programme 2.7), by the Research Council of Norway (Grant 143249/140), and by the European project SIMFAMI (Grant No. Q5RS-2001-02054).
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References |
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Anon. (2003) ICES Report of the Working Group on Mackerel and Horse Mackerel Egg Surveys. ICES Document CM 2003/G: 07.
Anon. Species identification methods from acoustic multi-frequency information (SIMFAMI). (2006) 486. Final Report EU Contract Q5RS-2001-02054.
Barr R. A design study of an acoustic system suitable for differentiating between orange roughy and other New Zealand deep-water species. Journal of the Acoustical Society of America (2001) 109:164–178.[CrossRef][Web of Science]
Block B. A., Finnerly J. R., Stewart A. F. K., Kidd J. Evolution of endothermy in fish; mapping physiological traits on molecular phylogeny. Science (1993) 260:210–214.
Foote K. G. Importance of the swimbladder in acoustic scattering by fish: a comparison of gadoid and mackerel target strengths. Journal of the Acoustical Society of America (1980) 67:2084–2089.[CrossRef][Web of Science]
Foote K. G., Hansen K. A., Ona E. More on the frequency dependence of target strength of mature herring. (1993) 30. ICES Document CM 1993/B.
Gorska N., Ona E., Korneliussen R. On backscattering mechanism for fish without swimbladder. Simons R. G., ed. (2004) 7;1. Proceedings of the Seventh European Conference on Underwater Acoustics, ECUA 2004: Delft, The Netherlands. The Hague, Netherlands: TNO Physics and Electronics Laboratory. 367–372. (ISBN: 90-5986-080-2) 2004.
Gorska N., Ona E., Korneliussen R. Acoustic backscattering by Atlantic mackerel as being representative of fish that lack a swimbladder. Backscattering by individual fish. ICES Journal of Marine Science (2005) 62:984–995.
Horne J. K. Acoustic approaches to remote species identification: a review. Fisheries Oceanography (2000) 9:356–371.[CrossRef][Web of Science]
Horne J. K., Clay C. S. Sonar systems and aquatic organisms: matching equipment and model parameters. Canadian Journal of Fisheries and Aquatic Sciences (1998) 55:1296–1306.
Korneliussen R. J., Ona E. An operational system for processing and visualizing multi-frequency acoustic data. ICES Journal of Marine Science (2002) 59:293–313.
Korneliussen R. J., Ona E. Verified acoustic identification of Atlantic mackerel. ICES Document CM2004/R (2004) 20:14.
Korneliussen R., Skagen D. W., Slotte A. (2005) Bergen, Norway: Institute of Marine Research. 18. Cruise summary report 2004113 ISSN 1503-6294/Nr. 3 2005 mackerel http://www.imr.no/produkter/publikasjoner/toktrapporter/toktrapporter_2005. Document: Nr. 3_CruiseSummaryReport_2004113_mackerel.pdf).
Nash R. D. M., Sun Y., Clay C. S. High-resolution acoustic structure of fish. Journal du Conseil International pour l'Exploration de la Mer (1987) 43:23–37.
Reeder D. B., Jech J. M., Stanton T. K. Broadband acoustic backscatter and high-resolution morphology of fish: measurement and modelling. Journal of the Acoustical Society of America (2004) 116:747–761.[CrossRef][Web of Science][Medline]
Sigfusson H., Decker E. A., McClements D. J. Ultrasonic characterisation of Atlantic mackerel. Scomber scombrus. Food Research International (2001) 34:15–23.[CrossRef]
Sun Y., Nash R., Clay C. S. Acoustic measurements of the anatomy of fish at 220 kHz. Journal of the Acoustical Society of America (1985) 78:1772–1776.[CrossRef][Web of Science]
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