Near resonance acoustic scattering from organized schools of juvenile Atlantic bluefin tuna (Thunnus thynnus).

TL;DR: Results suggest that both multiple scattering and spatial organization within the school should be considered when estimating the target strength of schools similar to the ones considered here.

Abstract: Schools of Atlantic bluefin tuna (Thunnus thynnus) can exhibit highly organized spatial structure within the school. This structure was quantified for dome shaped schools using both aerial imagery collected from a commercial spotter plane and 400 kHz multibeam echo sounder data collected on a fishing vessel in 2009 in Cape Cod Bay, MA. Observations from one school, containing an estimated 263 fish within an approximately ellipsoidal volume of 1900 m(3), were used to seed an acoustic model that estimated the school target strength at frequencies between 10 and 2000 Hz. The fish's swimbladder resonance was estimated to occur at approximately 50 Hz. The acoustic model examined single and multiple scattering solutions and also a completely incoherent summation of scattering responses from the fish. Three levels of structure within the school were examined, starting with fish locations that were constrained by the school boundaries but placed according to a Poisson process, then incorporating a constraint on the distance to the nearest neighbor, and finally adding a constraint on the bearing to the nearest neighbor. Results suggest that both multiple scattering and spatial organization within the school should be considered when estimating the target strength of schools similar to the ones considered here.

Summary

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.

Figures

FIG. 5. Data collected from a single ping of a side-looking 400 kHz MBES, showing a vertical cross-section of a juvenile ABFT school. The “image” school due to acoustic paths reflected from the sea surface were excluded from this work.

FIG. 6. Parameters describing the juvenile ABFT school derived from the MBES data, including (a) maximum length of the school; (b) school height; (c) vertical cross sectional area; (d) shape parameter.

FIG. 8. Target strength as a function of kRe for single scattering (left) and multiple scattering (right) solutions) and for ensonification along the short axis (top) and long axis (bottom). Model outputs for the Poisson distributed fish (dotted line) and for the nearest neighbor criterion accounting for both range and bearing (solid line) are shown. The incoherent summation (dashed line) is shown for reference.

FIG. 1. (a) Raw aerial imagery showing a school of ABFT; (b) manually classified individual ABFT with randomly assigned colors indicating unique fish.

FIG. 2. Eleven consecutive aerial images of a juvenile Atlantic bluefin school. In each image. the tuna have been enhanced by using the manual classification as a mask.

FIG. 7. School target strengths [Eq. (6)] for both the single scattering (top row) and multiple scattering solutions (bottom row) and for the three school types: Poisson distributed (left-most column), nearest neighbor in range only (center column), and nearest neighbor criterion accounting for both range and bearing (right column). In each figure, red indicates higher target strength and blue indicates lower target strength with a variation from 22 to þ22 dB. Frequency increases logarithmically from the center. The angular coordinate indicates the angle of ensonification in the horizontal plane; black dots in the center of each image represent simulated fish locations for one realization of the school to provide a frame of reference.

FIG. 4. Two-dimensional histograms describing the positional dependency of the nearest neighbors of an individual tuna, plotted as a function of NND in body lengths and NNRB in degrees. The first column represents the closest near neighbor, the second column represents the next closest near neighbor, and so on. The top row shows the raw histograms, and the bottom row shows low-pass filtered versions of the histograms. Color represents the amplitude of the pdf with red being the highest and blue being the lowest, ranging from 0 to 0.008 deg 1m 1 in the top row and 0 to 0.005 deg 1m 1 in the bottom row.

FIG. 3. Pdf of nearest neighbor distance, NND, calculated in terms of body lengths (BL) (left) and pdf of nearest neighbor relative bearings, NNRB, in degrees (right). Observations of 2586 individual ABFT from 11 consecutive images were used to generate these empirical pdfs.

Full text

University of New Hampshire University of New Hampshire
University of New Hampshire Scholars' Repository University of New Hampshire Scholars' Repository
Center for Coastal and Ocean Mapping Center for Coastal and Ocean Mapping
6-2013
Near resonance acoustic scattering from organized schools of Near resonance acoustic scattering from organized schools of
juvenile Atlantic blue=n tuna (Thunnus thynnus) juvenile Atlantic blue=n tuna (Thunnus thynnus)
Thomas C. Weber
University of New Hampshire, Durham
, thomas.weber@unh.edu
Molly Lutcavage
University of Massachusetts - Amherst
Madeline L. Schroth-Miller
University of New Hampshire, Durham
Follow this and additional works at: https://scholars.unh.edu/ccom
Part of the Oceanography and Atmospheric Sciences and Meteorology Commons
Recommended Citation Recommended Citation
T. C. Weber, M. E. Lutcavage, and M. L. Schroth-Miller, ‘Near resonance acoustic scattering from organized
schools of juvenile Atlantic blue=n tuna (Thunnus thynnus)’, The Journal of the Acoustical Society of
America, vol. 133, no. 6, p. 3802, 2013.
This Journal Article is brought to you for free and open access by the Center for Coastal and Ocean Mapping at
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information, please contact Scholarly.Communication@unh.edu.

Near resonance acoustic scattering from organized schools
of juvenile Atlantic bluefin tuna (Thunnus thynnus)
Thomas C. Weber
a)
Center for Coastal and Ocean Mapping, University of New Hampshire, Durham, New Hampshire 03824
Molly E. Lutcavage
Large Pelagics Research Center, Department of Environmental Conservation, University of Massachusetts
Amherst, Gloucester, Massachusetts 01931
Madeline L. Schroth-Miller
Center for Coastal and Ocean Mapping, University of New Hampshire, Durham, New Hampshire 03824
(Received 30 July 2012; revised 23 March 2013; accepted 26 Mar ch 2013)
Schools of Atlantic bluefin tuna (Thunnus thynnus) can exhibit highly organized spatial structure
within the school. This structure was quantified for dome shaped schools using both aerial imagery
collected from a commercial spotter plane and 400 kHz multibeam echo sounder data collected on
a fishing vessel in 2009 in Cape Cod Bay, MA. Observations from one school, containing an
estimated 263 fish within an approximately ellipsoidal volume of 1900 m
3
, were used to seed an
acoustic model that estimated the school target strength at frequencies between 10 and 2000 Hz.
The fish’s swimbladder resonance was estimated to occur at approximately 50 Hz. The acoustic
model examined single and multiple scattering solutions and also a completely incoherent
summation of scattering responses from the fish. Three levels of structure within the school were
examined, starting with fish locations that were constrained by the school boundaries but placed
according to a Poisson process, then incorporating a constraint on the distance to the nearest
neighbor, and finally adding a constraint on the bearing to the nearest neighbor. Results suggest
that both multiple scattering and spatial organization within the school should be considered when
estimating the target strength of schools similar to the ones considered here.
V
C
2013 Acoustical Society of America. [http://dx.doi.org/10.1121/1.4802646]
PACS number(s): 43.30.Ft, 43.30.Sf [APL] Pages: 3802–3812
I. INTRODUCTION
Although acoust ic scattering from aggregations of fish
containing swimbladders at low- to mid-frequencies (i.e.,
near swimbladder resonance) has been examined both theo-
retically 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 individ-
ual fish. In this work, we examine the modeled acoustic
backscatter from a school of juvenile Atlantic bluefin tuna
(Thunnus thynnus) for which the spatial organization of fish
and the school shape are well known, having been empiri-
cally derived from measurements made using aerial imagery
and a high frequency multibeam echosounder (MBES). The
term school is used to describe a specific type of aggregation
where, according to the definition used by Pitcher and Parish
(1993), an aggregation is simply a group of fish, whereas in
a school, the fish are closely spaced, polarized, of similar
size, and act with some sort of synchronicity. Of particular
interest in this work is whether the spatial organization of
fish within the school has any non-negligible effect on the
acoustic backscatter from the school and if the school target
strength is adequately considered as an incoherent summa-
tion of the scattered waves from individual fish or whether a
higher fidelity model that includes either singly or multiply
scattered waves is important to consider.
One of the earliest investigators of the acoustic effects
of the spatial organization of fish was Weston (1966, 1967),
who considered line and plane arrays of fish the swimblad-
ders of which were the dominant scattering mechanism.
Feuillade et al. (1996) followed up on 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 distri-
bution of variable stand ard deviation. Diacho k (1999) con-
sidered the attenuation through an aggregation of sardines,
examining school resonances in the context of an average
spacing between fish as well as multiple resonances due to
changes in fishing spacing according to whether the fish
were located within a densely populated school nucleus or
on the more sparsely populated periphery. Hahn (2007)
examined hypothetical aggregations of randomly distributed
fish, constraining the average spacing between fish with a
wide range of packing densities. Andrews et al. (2011) com-
pared the modeled backscatter from aggregations of Atlantic
herring arranged with either fully randomized fish positions
or with a similar lattice structure to that used by Feuillade
et al. (1996). Collectively, these authors suggest that group
a)
Author to whom correspondence should be addressed. Electronic mail:
weber@ccom.unh.edu
3802 J. Acoust. Soc. Am. 133 (6), June 2013 0001-4966/2013/133(6)/3802/11/$30.00
V
C
2013 Acoustical Society of America
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resonances may exist for sufficiently dense aggregations of
fish where the resonance frequency for an aggregation of fish
is lower than that which would be predicted by incoherent
fish scattering models, analogous to the collective bubble
plume oscillations identified as a source of low frequency
ambient noise in the ocean (Carey and Bradley, 1985; Carey
and Fitzgerald, 1987; Prosperetti, 1988). However, these
types of coherent scattering effects are not expected to be an
important consideration for all types of schools. For exam-
ple, Andrews et al. (2011) concluded that these effects were
negligible for a long-range acoustic experiment (see Gong
et al. 2010) with aggregations of herring in the Gulf of
Maine for which the average volumetric fish density was
estimated to be 0.05 fish/m
3
, providing a bound on what
“sufficiently dense” means at least in the context of the
Atlantic herring considered in that study. The work of
Weber et al. [2007, Eq. (39)] suggests that in addition to
considering the density of scatters, it is also important to
consider both the average scattering strength of an individual
as well as the size of the aggregation under the premise that
coherent scattering effects will be more pronounced when
multiple scattering effects are non-negligible.
If the spatial organization of fish (i.e., schooling behav-
iors) within an aggregation is important for acoustic scatter-
ing predictions, then Atlantic bluefin tuna (ABFT) are an
interesting species to consider. ABFT have been observed to
exhibit schooling behaviors (Lutcavage and Kraus, 1995;
Lutcavage et al., 1997a; Lutcavag e et al., 1997b), perhaps
for increased hydrody namic efficiency, for feeding benefits,
or for some other unknown benefit (Partridge et al., 1983).
They exhibit a variety of schooling geometries at the sea sur-
face including parabolic or straight line formations, cart-
wheels (swimming in a circle), surface sheets, and dome
shapes (Lutcavage and Kraus, 1995). ABFT are also slightly
denser than seawater and utilize a gas-filled swimbladder to
maintain swimming depths at slow speeds ( Magnuson,
1973).
ABFT are found in much of the North Atlantic at depths
between the surface and 1000 m. For the size of fish exam-
ined in this paper (approximately 1.5 m), ABFT travel with
an average speed of approximately 3–4 knots on feeding
grounds and 8 knots durin g migration (Mather et al., 1995;
Lutcavage et al., 2000; Brill et al., 2002). Electronic data
loggers and sonic tracking have provided extensive fishery-
independent information on vertical behavior of ABFT.
Juvenile and adult ABFT spend >80%–90% of their time in
the top 10–20 m, especially in the Gulf of Maine, their forag-
ing grounds (Lutcavage et al., 2000;Galuardi et al., 2010,
Brill et al., 2002). Although juveniles have been observed to
occasionally dive mo re deeply, to hundreds of meters, on the
continental shelf, they are usually located between the sur-
face and thermocline (Galuardi and Lutcavage, 2012), con-
sistent with our sonar observations. Although the explicit
behavior of individuals in schools of different sizes/behav-
iors is not completely documented, schooling behavior has
been described from aerial surveys and direct observations
of juveniles and adults in the Gulf of Maine, VA, and the
Bahamas (e.g., Lutcavage and Kraus, 1995; Lutcavage et al.,
1997a; Lutcavage et al., 1997b). Packing density (e.g.,
nearest neighbor distance) appears to be related to fish size
not behavior or number of individuals in a school. The con-
formation and number of individuals in schools change, but
packing density or nearest neighbor distances do not change
to any extent. Partridge et al. (1983) examined aerial photo-
graphs of schools containing between 2 and 79 large
(2.4–2.9 m) ABFT in what they considered to be two-
dimensional schools at the sea surface. Within these schools,
they found nearest neighbor distances (estimated from the
distance between one nose and another) to be between 1.5
and 2 body lengths, and for schools containing 15 or more
fish that were not arranged in a parabola or line, they
observed the most common bearing to a nearest neighbor to
be either 45

or 135

.
In the work described in this paper, we examine a
dome-shaped school containing an estimated 263 juvenile
ABFT, in which each individual fish is an estimated 1.5 m
long. 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). The aerial
imagery collapses the school onto a two dimensional plane,
possibly missing fish that are deeper than a few meters water
depth (depending on the optical clarity of the water) or fish
that are obscured by other fish. The nearest neighbor distance
for the fish collapsed onto a two-dimensional plane is esti-
mated to be 0.5 body lengths. To determine the average ver-
tical cross-section of the school, side-looking 400 kHz
MBES data that were collected concurrently with the aerial
imagery are examined (Sec. III). Together, the empirically
derived school characteristics from the aerial imagery and
the MBES are used to generate simulated schools of ABFT
(Sec. IV). Schools with varying levels of spatial organization
are simulated: A Poisson distributed (i.e., no spatial organi-
zation) group of fish located within the school boundaries,
schools, where a nearest neighbor distance derived from the
empirical observations is imposed on the spatial organization
of fish, and schools where both a nearest neighbor distance
and a relative bearing are imposed. These school models are
used to seed an acoustic simulation that examines the contin-
uous wave (CW) backscatter from the schools at frequencies
between 10 and 2000 Hz (Sec. V ). The acoustic scatter from
individual fish is considered only in terms of the swimblad-
der response. To isolate the effects of spatial organization
within the school on acoustic backscatter, the acoustic simu-
lation is performed in an idealized setting: Far from the
ocean surface or bottom boundaries and in an isovelocity
environment with results shown in Sec. VI. The acoustic
model examines both the single scattering and a full multiple
scattering solution.
II. AERIAL PHOTOGRAPHY
Aerial photography was col lected from schools of juve-
nile 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. A typical altitude
for collecting the aerial imagery was 213 m (700 ft), and at
J. Acoust. Soc. Am., Vol. 133, No. 6, June 2013 Weber et al.: Scattering from schools of bluefin tuna 3803
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this altitude, individual ABFT can be identified in the aerial
photographs [Fig. 1(a)]. These data were collected near
42.0

N/70.3

W in a water depth of approximately 40 m.
Each image was classified manually by tracing the outlines
of each fish [Fig. 1(b)] to estimate the approximate horizon-
tal shape of the visible portion of the school (an ellipse with
major and minor axes of 31 and 13 m, respectively, as will
be discussed), and to determine whether any spatial organi-
zation between individual ABFT was apparent within the
school. The aerial imagery data used in this paper, which are
considered to be typical of the dome shaped juvenile ABFT
schools that were present during several days of ABFT sur-
veying in Cape Cod Bay over the course of the experiment,
consist of 11 consecutive images collected between 19:21:31
and 19:21:35 GMT (Fig. 2) under calm surface conditions.
The fish imaged in this school were estimated to weigh
between 57 and 79 kg (125–175 lb) by the commercial spot-
ter pilot. Using the length-weight relationship given by
Restrepo et al. (2010) this corresponds to a body length
between 1.4 and 1.6 m.
For each classified fish, both a “center of mass” (assum-
ing equal weighting within the outlined representation of the
fish) and a fish orientation (the orientation of the longest axis
of the fish) within the local coordinates of the image are cal-
culated. The distance and bearing (relative to the fish orien-
tation) to the nearest neighbor is calculated with lengths
measured in fish body lengths. Because these fish are
assumed to be approximately the same length, based on
observations from the commercial spotter pilot as well as
sizes of individuals in bluefin schools caught by purse seine
(Lutcavage, unpublished data), the body length is taken to be
the longest observed length within the school, with shorter
observed lengths attributed to limited optical clarity in the
water. For the purposes of this work, any bias error in the av-
erage fish length is thought to be small compared with the
unknown error in estimates of swimbladder size.
Both neares t neighbor distances (NND) and nearest
neighbor relative bearings (NNRB) were estimated for all
observed individuals in 11 sequential photographs of the
same school (Fig. 2) with a total 2586 observed individuals.
Probability density function (pdf) estimates (Fig. 3) of NND
shows that the preferential distance between fish observed in
the aerial imagery is 0.48 body lengths. It is important to
note that the aerial imagery projects any three-dimensional
structure within the school onto a two-dimensional plane,
and so the nearest neighbor distance in three dimensions is
likely to be greater. The pdf representing the NNRB show
that the nearest neighbor is unlikely to be located either
FIG. 1. (a) Raw aerial imagery showing a school of ABFT; (b) manually
classified individual ABFT with randomly assigned colors indicating unique
fish.
FIG. 2. Eleven consecutive aerial images of a juvenile Atlantic bluefin school. In each image. the tuna have been enhanced by using the manual classification
as a mask.
3804 J. Acoust. Soc. Am., Vol. 133, No. 6, June 2013 Weber et al.: Scattering from schools of bluefin tuna
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directly in front or behind a juvenile ABFT, and that there
may be some preference for nearest neighbors located near
645

and 6135

.
To examine the combined dependence of nearest neigh-
bor distance and relative bearing for multiple neighbors, two-
dimensional histograms were generated for the closest near
neighbor, the second closest near neighbor, and so on (Fig. 4,
upper row). A two-dimensional (2D) sliding mean (a 2D uni-
formly weighted window that was 30

by 0.15 body lengths)
was used to smooth the data (Fig. 4, lower row) to help eluci-
date any structure within the school. The results of the nearest
neighbors analysis show that it is not uncommon to have six
or more fish within one body length of each other (as pro-
jected onto a two-dimensional plane; the average number of
neighbors within one body length is estimated from these
data to be 6.5) with the nearest neighbor most often located
at a distance of 0.48 body lengths and at a relative bearing of
either 645

or 6135. The pdf’s describing the second to
sixth nearest neighbors also appear to show some increased
probability at localized bearings as well. To determine
whether the apparent preferred bearings to neighboring fish
are statistically significant (or, conversely, are artifacts of the
low-pass filtering), a Kolmogorov–Smirnov test was used to
examine the hypothesis that the bearings for each of the near-
est neighbors (first through sixth) fit a uniform distribution.
This hypothesis was rejected at the 5% significance level for
the nearest neighbor, as expected, and also, unexpectedly and
for unknown reasons, for the sixth neighbor. The hypothesis
FIG. 3. Pdf of nearest neighbor dis-
tance, NND, calculated in terms of
body lengths (BL) (left) and pdf of
nearest neighbor relative bearings,
NNRB, in degrees (right). Observations
of 2586 individual ABFT from 11 con-
secutive images were used to generate
these empirical pdfs.
FIG. 4. Two-dimensional histograms describing the positional dependency of the nearest neighbors of an individual tuna, plotted as a function of NND in
body lengths and NNRB in degrees. The first column represents the closest near neighbor, the second column represents the next closest near neighbor, and so
on. The top row shows the raw histograms, and the bottom row shows low-pass filtered versions of the histograms. Color represents the amplitude of the pdf
with red being the highest and blue being the lowest, ranging from 0 to 0.008 deg
1
m
1
in the top row and 0 to 0.005 deg
1
m
1
in the bottom row.
J. Acoust. Soc. Am., Vol. 133, No. 6, June 2013 Weber et al.: Scattering from schools of bluefin tuna 3805
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Frequently asked questions

Q1. How many cc of swimbladder is a typical ABFT?

The ABFT are assumed to have a length variation following a Gaussian distribution with a 7.5 cm standard deviation, resulting in a standard deviation in swimbladder volume of 200 cc. 

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.