Acoustic density estimation of dense fish shoals
AAcoustic density estimation of dense fish shoals
Benoit Tallon and Philippe Roux ∗ Univ. Grenoble Alpes, CNRS, ISTerre, 38000 Grenoble, France
Guillaume Matte iXblue, Sonar division, 13600 la Ciotat, France
Jean Guillard
Univ. Savoie Mont Blanc, INRA, CARRTEL, 74200 Thonon-les-Bains, France
Sergey E. Skipetrov
Univ. Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France (Dated: August 21, 2020)Multiple scattering of acoustic waves offers a noninvasive method for density estimation of a denseshoal of fish where traditional techniques such as echo-counting or echo-integration fail. Throughacoustic experiments with a multi-beam sonar system in open sea cages, multiple scattering of soundin a fish shoal, and in particular the coherent backscattering effect, can be observed and interpretedquantitatively. Furthermore, a volumetric scan of the fish shoal allows isolation of a few individualfish from which target strength estimations are possible. The combination of those two methodsallows for fish density estimation in the challenging case of dense shoals.
INTRODUCTION
Fish density estimation using acoustic waves has beenunder investigation for almost 70 years [1, 2]. This inter-est comes from the strong scattering of acoustic waves byfish, and in particular due to the great acoustic contrastbetween the fish swim bladder and the surrounding wa-ter. Hence, when the fish spacing is large compared tothe acoustic wavelength, fish density estimation is rela-tively straightforward, through the counting of hot spotson echograms [2]. For convenience, the echo-integrationmethod [3] can be used for large shoals. Furthermore,acoustic scans provide the target strength (TS; dB) [2]of the fish, which depends on their size, species, physi-ology, and position. However, these traditional acousticcounting methods are only valid under the single scat-tering assumption: during its propagation, the backscat-tered signal received on the probe should be scattered atmost by one fish. For large or dense shoals (density (cid:38) ), this assumption does not hold [4], as part of,and indeed most of, the backscattered intensity comesfrom wave paths that are scattered by several fish be-tween emission and reception. The so-called multiplescattering regime is then reached when the wave prop-agates over distances greater than the scattering meanfree path (cid:96) s , which is defined as the average distance be-tween two scattering events [5]. Therefore, fishery acous-tic methods are ineffective, although they remain widelysought after for density estimation in the aquaculture in-dustry due to their nonintrusive aspect. This means thatto obtain the main parameters needed (i.e., number offish, total biomass and/or individual mean size), aqua-culture uses manipulation of the fish, with large impacton individuals. In this Letter, we propose an original method for non-invasive fish-density estimation in open-sea cages. Thisapproach is based on a combination of fishery acousticsand multiple scattering concepts. Multiple scattering ofwaves in random media is a widely studied phenomenonin optics [6], acoustics [7], and geophysics [8]. It has ap-plications for medical [9] and wave control [10] purposes.In particular, it has been shown that wave propagation inrandom media can result in remarkable mesoscopic phe-nomena [5], such as the coherent backscattering (CBS)effect [11]. CBS is a wave interference phenomenon thatmanifests as an enhancement (by a factor of 2) of theaverage backscattered intensity measured in the direc-tion opposite to the direction of the incident wave. Thisphenomenon occurs in multiple scattering regimes due toconstructive interference of partial waves scattered alongreciprocal paths [5]. From the dynamic point of view [7],CBS develops gradually as a wave propagates inside thefish aggregate, and becomes significant for wave propaga-tion distances greater than (cid:96) s . In this way, CBS measure-ments in fish cages can provide useful information aboutshoals. In particular, we show below that simultaneousknowledge of the fish TS and the shoal (cid:96) s allows estima-tion of the fish density even in the challenging cases ofdense shoals. EXPERIMENTS
Experiments were performed with dense salmon shoalsthat were contained in large open-sea cages on a salmonfarm in the North Sea (Eide Fjordbruk, Rosendal, Nor-way). The cubic cages are 30 m in both width and depth.In this area, the sea depth is about 50 m. The cage a r X i v : . [ phy s i c s . a pp - ph ] A ug for the experiments contained approximately 200,000 At-lantic salmon ( Salmo salar ) with an average weight of 6kg (total length, about 80 cm).The sonar probe used here was a reversible multi-beam antenna (Mills Cross; based on Seapix technolog-ical brick [12], iXblue La Ciotat) that can be used forthree-dimensional (3D) volumetric scanning. This probeis made of two perpendicular arrays, each of 64 ultra-sonic transducers (see Fig. 1a) with a central frequency f = 150 kHz and an inter-element spacing of half awavelength in water. Each of the 128 transducers canbe controlled independently, for precise manipulation ofthe emission/reception direction of the acoustic waves. Avolumetric scan of the whole cage (Fig. 1b) is possiblefrom successive shots in about 1 s, which is sufficientlyfast to approximate the fish shoal as ’frozen’ between twoscans. Target strength measurement
To determine the fish density inside the cage, an esti-mation of the individual fish TS is required. To achievethis, we perform a large number of acoustic 3D volumet-ric scans of the shoal, from which we select a collection ofindividual targets with propagation distances below (cid:96) s ,i.e., in the single-scattering regime. The volumetric scanis constructed as follows: a series of 21 plane waves[13]is sent with array 1 by varying the incidence angle from α = − ◦ to α = 10 ◦ (see Fig.1b). The backscatteredacoustic field is recorded with array 2 (perpendicular toarray 1) and beamformed after post-processing over an-gles β = α : for each of the 21 incident angle α , beam-forming is applied on the perpendicular array over the21 angles β . This process was repeated to obtain 550independent 3D scans of the fish shoal from which 3,800individual targets were isolated.From the literature, the TS of an 80-cm salmon isTS th = −
26 dB [14]. This TS is used to set a detec-tion threshold on the acoustic scan: a spot with TS th − < TS < TS th + 5 dB is identified as a salmon.The TS is calculated from the backscattered acousticintensity I , through the relation:TS = 10log ( I ) − SL + 40log ( r ) + 2 ar + NF + ψ, (1)where SL is the source level (intensity of the incidentpulse), a = 0 .
051 dB/m is the absorption coefficient ofsound in sea water, and 40log ( r ) is a range correction.Furthermore, NF and ψ are the near-field and inter-beamcorrections, respectively, which are calculated and mea-sured during the sonar factory calibration.A (shallow) image of a single 3D scan above the fishshoal is shown in Fig. 1c. This image allows the detectionof several individual targets. The collection of individualtargets provides the TS distribution (Fig. 2a), which is fitted with a Gaussian law to obtain (cid:104) TS (cid:105) = ( − ± ( σ bs ) , (2)where σ bs is the backscattering cross-section; i.e., the nor-malized scattered intensity in the backward direction. Inthe present case where the salmon size is much largerthan the wavelength, the measured σ bs corresponds tothe acoustic intensity scattered mainly by the swimblad-der (the most reflective organ in the fish body).As an additional tool, if the scanning process is fastenough (the 3D image acquisition takes 1.02 s here), thefish movement can be observed for two or more successivescans. A histogram of fish velocities can be constructedby measuring the distance traveled by each fish betweenthese two images [16]. Figure 2b shows the velocity his-togram for the salmon cage that follows a Rayleigh lawwith mean (cid:104) v (cid:105) = 0 .
19 m/s. This means that during theduration of a 3D scan, each fish might have moved over adistance greater than the wavelength, but much smallerthan the individual fish size. Furthermore, the Rayleighvelocity distribution confirms the visual observation thatthe dynamics individual fish are random inside the shoal.On the time scale of this experiment ( ∼
10 min), no vari-ation in the mean velocity was observed. However, themean velocity estimation can be used over a longer timescale to monitor the fish activity for feeding optimization,for example.
Scattering mean free path measurements
Coherent backscattering is a wave interference phe-nomenon that is manifested as a pronounced angular de-pendence of the average backscattered acoustic intensityin the multiple scattering regime. More precisely, the in-tensity in the exact backscattering direction ( θ = 0 ◦ )is twice that for large scattering angles θ [11]. Thebackscattered intensity shows a cone that narrows withtime t (or depth z = v t/ v =1500 m/s, the speedof sound in sea water) [7]. Figure 3a shows the mea-surement of CBS in the salmon cage by the beamform-ing method [17] with the Seapix probe [18]: the incidentplane wave is generated using all of the 128 transducers -12-10-8-6-4-20 z ( m ) -202x (m) -2 0 2y (m) I ( d B ) -20-25-30-35(b)(a) x z yk α β array 1array 2 -0.5-1 0-2 y (m)-0.5 0.5-1.5 x (m) 0 z ( m ) -1 0.5-0.510(c) αβ Open sea cage
FIG. 1. (a) Scheme of the Seapix sonar probe positionned at the surface of the open sea cage. (b) Snapshot of a volumetricscan of a cage (backscattered acoustic intensity I ). (c) Isosurface representation of the shallow scan ( z < > -31 dB. P r ob a b ilit y d e n s it y ExperimentRayleigh law-32 -30 -28 -26 -24TS (dB)050100150200 N t a r g e t s ExperimentGaussian law (b)(a)
FIG. 2. (a) Gaussian fit of the measured distribution of the target strength. (b) Histogram of salmon velocity measured fromthe acoustic scan. and spatial Fourier transform is performed over the arrayafter reception in order to probe the angular dependenceof backscattered acoustic intensity. The CBS is measuredwith a depth resolution dz = 0 . z . When the acousticwave propagates deeper into the fish shoal, it undergoesmore scattering events and gets closer to the multiplescattering regime. The peak in the intensity at θ = 0 ◦ increases gradually with depth.The rise of the CBS peak can be characterized bythe intensity enhancement factor EF( z ) = I ( θ =0 , z ) /I ( θ max , z ), where θ max is the angle for which theintensity profile becomes flat. In this case, the maximumangle of observation θ max = 6 ◦ appears to be sufficientsince the intensity I ( θ max , z ) seems to be independent of the depth z . In the single scattering regime, the in-tensity profile shows no fine structure and EF( z ) = 1.Once the multiple scattering regime is reached, the in-tensity is halved for large angles, and EF( z ) tends to2. Finally, single and multiple scattering contributionsare equivalent for EF( z ) ≈ /
3, which corresponds to apropagation distance equal to the scattering mean freepath (cid:96) s [9]. Measurement of the enhancement factor isshown in Figure 3b. From Figure 3b, it is clear thatthe multiple scattering regime is not fully reached fordepths z <
10 m, as the enhancement factor grows with z . A linear fit EF( z ) = Az + 1 to the ’transitionalregime’ together with the condition EF( (cid:96) s ) = 4 /
3, yieldsan accurate estimation of the scattering mean free path (cid:96) s = (4 / − /A = (4 ± .
3) m. z (m) E F ( z ) ExperimentLinear fit-6 -4 -2 0 2 4 6 (°)
I() z = 10 mz = 5 mz = 1 m(a) (b)
FIG. 3. (a) Angular dependence of the intensity for three different depths z (b) Depth dependance of the enhancement factor EF ( z ). The dashed line represents the linear fit used to measure the scattering mean free path (cid:96) s . RESULTS AND DISCUSSION
During these experiments, there were no currents inthe fjord, and therefore no fish polarisation[19] was ob-served, as can be seen for other at-sea cages under strongcurrents from tidal effects. Thus, we can reasonably as-sume that the fish are randomly oriented in the azimuthalplane, and we do not expect complex effects, such asthe anisotropic light diffusion that occurs in liquid crys-tals [20]. Furthermore, the reasonable fish density ( ∼ ) allows us to neglect correlations between scat-terers [21] and to use the relation [22]: η = 1 σ(cid:96) s , (3)where η is the fish density and σ is the total scatter-ing cross-section σ = σ bs /φ ( γ = π ). The phase func-tion φ ( γ ) reflects the anisotropy of sound scattering by afish [22]. For isotropic scattering by an infinite cylinder, φ ( γ ) = 1 / π . In the present case, considering the length L of the fish, we approximate its swimbladder as an im-mersed air cylinder with radius [23] R = 0 . L . Bynumerically solving the scattering problem [24] for sucha scatterer, this gives (cid:104) φ ( γ = π ) (cid:105) δγ = 9 × − , where (cid:104) φ ( γ = π ) (cid:105) δγ is the phase function averaged over a smallangular range δγ = 10 ◦ around the backscattering direc-tion γ = π , to take into account the angular spectrumof emission of our ultrasonic probe. Thus, the simulta-neous knowledge of the backscattering cross-section andthe mean free path gives a straightforward estimationof the fish number density η = (14 ±
3) fish/m . How-ever, this estimation corresponds to the fish density in theshoal and not in the cage. Indeed, because of its sphericalshape, the shoal does not occupy the whole volume of thecubic cage (see Fig. 1). Thus, the measured fish densityhas to be corrected by the volume ratio between the cu-bic cage and its inscribed sphere: π/
6. The effective fishdensity in the cage is then η × π/ . , which agrees with the farmer estimations ( ∼ ). Notethat during a feeding sequence, the shape of the shoalcan change rapidly and approaches a torus. Thereforefeeding sequences were excluded from the data analysis. CONCLUSION
The combination of fishery acoustics and mesoscopicphysics provides new opportunities for fish density esti-mation, by taking advantage of the multiple scatteringof sound. Experiments were performed in salmon cages,although the method is a priori not limited to any par-ticular fish size or species. By taking into account theavoidance phenomena [25], this CBS density estimationapproach can also be applied to fish shoals in their natu-ral environment. For example, CBS can be used for den-sity estimation of dense herring shoals ( η ∼
60 fish/m ),which is at present a key challenge [2] for fishing re-sources monitoring. However, for such high densities,one has to be careful about strong mesoscopic interfer-ence effects that can impact the CBS temporal evolution[18]. Such effects appear when the scattering mean freepath is so low that k(cid:96) s ∼ k is the wave num-ber). Thus, high shoal density can be probed with CBSprovided that fish average T S is low enough to fulfill thecondition k(cid:96) s (cid:29) ∗ To whom correspondence should be addressed; E-mail:[email protected][1] I. D. R. G. C. Trout, A. J. Lee and F. R. H. Jones, Nature , 71 (1952).[2] J. Simmonds and D. N. MacLennan,
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