Near resonance acoustic scattering from organized schools of juvenile Atlantic bluefin tuna (Thunnus thynnus).
Summary (3 min read)
I. INTRODUCTION
- Near swimbladder resonance) has been examined both theoretically and experimentally for at least the last half century (e.g., Weston, 1967; Holliday, 1972) , the relative positioning of fish within an aggregation is often considered in a mostly ad hoc manner due to the difficulty in experimentally observing, or accurately modeling, the locations of individual fish.
- One of the earliest investigators of the acoustic effects of the spatial organization of fish was Weston (1966 Weston ( , 1967)) , who considered line and plane arrays of fish the swimbladders of which were the dominant scattering mechanism.
- Using aerial imagery, individual fish are identified and the spatial organization of the ABFT within the school for up to 6 nearest neighbors is examined (Sec. II).
- These school models are used to seed an acoustic simulation that examines the continuous wave (CW) backscatter from the schools at frequencies between 10 and 2000 Hz (Sec. V).
II. AERIAL PHOTOGRAPHY
- Aerial photography was collected from schools of juvenile ABFT using a hand-held Canon EOS Rebel T1j on a commercial spotter plane in similar fashion to previous ABFT aerial surveys (e.g., Lutcavage and Kraus, 1995; Lutcavage et al., 1997b) , during a flight conducted on 16 August 2009 over Cape Cod Bay, MA.
- To examine the combined dependence of nearest neighbor distance and relative bearing for multiple neighbors, twodimensional histograms were generated for the closest near neighbor, the second closest near neighbor, and so on (Fig. 4 , upper row).
- The aerial photographs are also used to estimate the horizontal shape of the school.
- Within the school, the observed number of fish in each of the 11 photographs varied from 215 to 263 individuals with the variation attributed to an unknown combination of occlusion, optical clarity of the water, and relative position of the plane to the fish.
III. SIDE-LOOKING MBES DATA
- The aerial imagery provides a useful synoptic view of the juvenile ABFT schools but collapses the three dimensional school onto a two-dimensional surface.
- After thresholding, both the obvious outliers and "image" fish (reflections arriving via the sea surface) were manually removed, and the final result was considered to be a representation of a school cross section.
- Four parameters were derived from the convex hull and are shown as a function of ping number in Fig. 6 , corresponding to MBES data collected from the same school shown in Fig. 2 .
- The school area and maximum length steadily increase from ping 10 to 100 with the latter increasing from slightly more than 10 m to approximately 30 m and then begin to steadily decrease for the duration of the record.
- The increasing school area and length suggest that the orientation between the vessel and the school changed so that by pings 95-100, the long axis of the school was being imaged.
IV. SCHOOL MODELS
- The aerial imagery and the MBES data are consistent with an ellipsoid shaped school the horizontal major and minor axes of which are 31 and 13 m, respectively, and the vertical axis of which is 9 m.
- This task is somewhat complicated by the lack of accurate knowledge of the orientation of the school with respect to the MBES, and so the authors assume a simple shape consistent with the MBES and aerial observations, acknowledging that it is only an approximate school shape.
- When accounting only for nearest neighbor distance and not relative bearing, the location of each fish was found by repeated draws from a uniform distribution of locations within the school, with retention of the first fish whose distance (in the horizontal plane) from each other previously drawn fish was at least one-half body length.
- In addition to uncertainty about the distribution of swimbladder sizes for the tuna observed within the school, there is also an unknown depth dependency in the swim bladder size and acoustic response for the fish distributed over the observed depths (1-10 m).
- It is possible that this underrepresents the true variability in swimbladder resonance, but information describing the true variable is not available for the ABFT studied here.
V. ACOUSTIC SIMULATION
- The simulated schools are used to seed an ideal environment with monopole scattering centers with the assumption that the boundaries are sufficiently far away to be negligible and in an isovelocity water column.
- Hz are examined, covering the range of an individual swimbladder resonance.
- For reference, the school target strength is also calculated assuming that the scattered contributions add incoherently at the receiver EQUATION.
- In total, seven different school target strength models are considered.
- For both single [Eq. ( 1)] and multiple scattering models [Eq. ( 4)], fish are distributed with three different degrees of spatial organization (Poisson distributed, a nearest neighbor criterion in range, and a nearest neighbor criterion in both range and bearing).
VI. SIMULATION RESULTS
- The difference between single and multiple scattering at the school resonance is most evident when comparing model results corresponding to ensonification along the short axis [Fig. 8 (a) vs Fig. 8(b) ].
- The lower frequency resonance behavior is consistent with the type of school collective resonance described by Hahn (2007) , who examined this phenomenon for spherically shaped schools.
- Below resonance, the incoherent target strength model deviates substantially from the other models and also does not predict a second low-frequency school resonance.
VII. DISCUSSION
- This work is constrained by not having low frequency scattering data from the school with which to compare.
- To interpret the results, it is assumed that the multiple scattering model [Eq. ( 4)] more accurately represents the scattering process from the school than the single scattering model [Eq. ( 1)].
- It is worth noting that ABFT exhibit multiple schooling behaviors and that the modeled results shown here might have differed if, for example, the fish were found in a cartwheel or parabolic school formation frequently exhibited by adult ABFT (Lutcavage and Kraus, 1995) .
- The largest difference between single and multiple scattering models is the presence of a second resonance below the swim bladder resonance, a result that is consistent with Hahn's results (Hahn, 2007) from multiple scattering from fish schools with high packing densities.
- In that sense, the results shown here may represent an end-member case for similarly organized fish with smaller differences associated with spatial organization appearing for smaller fish the swimbladders of which do not radiate as strongly.
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1,337 citations
"Near resonance acoustic scattering ..." refers methods in this paper
...The second model incorporates multiple scattering in the manner first described by Foldy (1945) pms ¼ X263 i¼1 sip i o;iGðrr; riÞ; (4) where the incident pressure accounts both for the incident pressure from the source as well as the contributions from the other tuna within the school pio;i ¼ po;i…...
[...]
929 citations
"Near resonance acoustic scattering ..." refers methods in this paper
...The second model incorporates multiple scattering in the manner first described by Foldy (1945) pms ¼ X263 i¼1 sip i o;iGðrr; riÞ; (4) where the incident pressure accounts both for the incident pressure from the source as well as the contributions from the other tuna within the school pio;i ¼ po;i…...
[...]
806 citations
"Near resonance acoustic scattering ..." refers background in this paper
...ABFT are physoclists (they have a closed swimbladder), and as such have a swimbladder resonance frequency that is expected to vary as the square root of the ambient pressure, about a 40% variation over the depth variation observed in the school (Simmonds and Maclennan, 2005)....
[...]
525 citations
"Near resonance acoustic scattering ..." refers background in this paper
...The complex scattering amplitude of the swimbladder is assumed to be the same for a gas bubble acting as a monopole radiator (Clay and Medwin, 1977) si ¼ a expð jkaÞ x2o=x 2 1 jd ; (3) where a ¼ ð3vsb=4pÞ1...
[...]
258 citations
"Near resonance acoustic scattering ..." refers background in this paper
...…Weston’s early work, simulating acoustic scattering from fish arranged in “basic school units” with average fish locations at the corners and center of a cube of variable size and with deviations from the average fish location being drawn from a normal distribution of variable standard deviation....
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Frequently Asked Questions (9)
Q2. How long did the distance between the vessel and the school decrease?
2. Between pings 8 and 135 (approximately 0.5 min), the distance between the vessel and the school (as imaged by MBES) decreased nearly linearly from 65 to 30 m.
Q3. How many beams did the MBES use?
This MBES uses a Mills cross array topology to form 256 beams between 664 with a nominal angular resolution of 1 0.5 (horizontal and vertical 3 dB beamwidths) and was oriented so that its center beam was pointed horizontally in the vertical plane and approximately 45 off the starboard bow.
Q4. What is the angular dependence in the modeled school target strength?
There is also a strong angular dependence in the modeled school target strength with increased backscatter when the school is ensonified along its short axis compared to the model outputs for ensonification along the long axis.
Q5. What is the depth dependence of the swimbladder?
This depth dependence is expected for fish that have adapted to depth, however, and if the tuna are rapidly changing depth within the school, the swimbladder resonance frequency is expected to vary more widely, following a (1þz/10)5/6 relationship with depth, z, or about a 75% variation for the ABFT observed here.
Q6. What is the acoustic response of the swimbladder of the tuna?
The resulting swimbladder resonance frequencies very between approximately 45 and 65 Hz with a standard deviation slightly greater than 3 Hz.
Q7. What is the acoustic amplitude of the swimbladder?
The complex scattering amplitude of the swimbladder is assumed to be the same for a gas bubble acting as a monopole radiator (Clay and Medwin, 1977)si ¼ a expð jkaÞx2o=x 2 1 jd ; (3)where a ¼ ð3vsb=4pÞ1=3 is assumed to be the effective swimbladder radius based on its volume vsb, xo is the resonance frequency of the fish in radians per second, and d is a3808 J. Acoust.
Q8. How many different school target strength models are considered?
For reference, the school target strength is also calculated assuming that the scattered contributions add incoherently at the receiverTSinc ¼ 10 log10X263 i¼1 jpj2A2 r4 : (7)In total, seven different school target strength models are considered.
Q9. What is the acoustic frequency of the swimbladder?
Both the resonance frequency and damping constant are calculated following the formulation given by Love (1978) assuming the swimbladder to be filled with air with a density of 1.3 kg/m3 and a sound speed of 340 m/s, sea water and fish flesh densities of 1000 kg/m3 and 1050 kg/ m3, respectively, a viscosity parameter of 50 Pa s, and a surface tension of 1000 N/m.