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Measuring the o-axis angle and the rotational
movements of phonating sperm whales using a single
hydrophone
Christophe Laplanche, Olivier Adam, Maciej Lopatka, Jean-François Motsch
To cite this version:
Christophe Laplanche, Olivier Adam, Maciej Lopatka, Jean-François Motsch. Measuring the o-axis
angle and the rotational movements of phonating sperm whales using a single hydrophone. Journal
of the Acoustical Society of America, Acoustical Society of America, 2006, Vol. 119, pp. 4074-4082.
�10.1121/1.2184987�. �hal-00797701�
To link to this article: DOI: 10.1121/1.2184987
http://dx.doi.org/10.1121/1.2184987
This is an author-deposited ver sion p ublished in: http://oatao.univ-toulouse.fr/
Eprints ID: 5606
To cite this version: Laplanche, Christophe and Adam, Olivier and Lopatka,
Maciej and Motsch, Jean -François Measuring the off-axis angle and the
rotational movements of phonating sperm whales using a single hydrophone.
(2006) The Journal of the Acoustical Society of America (JASA), Vol. 119 (n°6).
pp. 4074-4082. ISSN 0001-4966
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Measuring the off-axis angle and the rotational movements
of phonating sperm whales using a single hydrophone
Christophe Laplanche,
a兲
Olivier Adam, Maciej Lopatka, and Jean-François Motsch
Laboratoire Images, Signaux et Systèmes Intelligents, Groupe Ingénierie des Signaux Neuro-Sensoriels,
Université Paris XII, France
The common use of the bent-horn model of the sperm whale sound generator describes sperm whale
clicks as the pulse series 兵 p0,p1,p2,p3, ...其. Clicks, however, deviate from this standard when
recorded using off-axis hydrophones. The existence of additional pulses within the
兵p0,p1,p2,p3,...其 series can be explained still using the bent-horn model. Multiple reflections on
the whale’s frontal and distal sacs of the p0 pulse lead to additional sets of pulses detectable using
a farfield, off-axis hydrophone. The travel times of some of these additional pulses depend on the
whale’s orientation. The authors propose a method to estimate the off-axis angle of sperm whale
clicks. They also propose a method to determine the nature of the movement 共if it is pitch, yaw, or
roll兲 of phonating sperm whales. The application of both methods requires the measurement of the
travel time differences between pulses composing a sperm whale click. They lead, using a simple
apparatus consisting of a single hydrophone at an unknown depth, to new measurements of the
underwater movements of sperm whales. Using these methods shows that sperm whales would
methodically scan seawater while searching for prey, by making periodic pitch and yaw movements
in sync with their acoustic activity.
关DOI: 10.1121/1.2184987兴
I. INTRODUCTION
Sperm whales 共Physeter macrocephalus兲 mostly feed on
meso- and bathypelagic squid and fish of various sizes and
physical constitution 共Kawakami, 1980; Whitehead, 2003兲.A
15-ton adult sperm whale would need to catch around half a
ton of pelagic food in a day, assuming a daily consumption
of 3% of its body weight 共Lockyer, 1981兲. Sperm whales
spend most of their time underwater and undertake long,
deep dives to catch such an amount of prey 共Miller et al.,
2004; Watkins et al., 1999兲. However, the low-light, high-
pressure conditions reigning at these great depths make dif-
ficult the visual observation of foraging sperm whales. Con-
sequently, one does not know precisely the technique共s兲
sperm whales would use to successfully seek and catch their
food.
Nevertheless, scientists have developed many methods
of studying the underwater behavior of deep-diving marine
mammals 共e.g., sperm whales兲, notably electronic tagging
and passive acoustics. By using such methods, scientists
have been collecting over the last decades many clues re-
garding the foraging behavior of sperm whales.
Sperm whales have a sound generator located in their
snout 共Madsen et al., 2002兲. The snout represents one quarter
to one third the length of the whale 共Clarke, 1978b; Nishi-
waki et al., 1963兲, and the whale uses it primarily for bioso-
nar purposes 共Jaquet et al., 2001兲; Møhl et al., 2000; White-
head and Weilgart, 1990兲. Sperm whales are indeed the most
acoustically active toothed whales. They emit a series of
transient sounds 共clicks兲 when undertaking foraging dives
共Backus and Schevill, 1966兲. Such clicks would be of a du-
ration, frequency content, source level, and directionality
suited to echolocate their prey 共Møhl et al., 2003, 2000兲.
Sperm whale dives are composed of a vertical descent, a
hunt in a prey layer at depth, and a reascent 共Miller et al.,
2004兲. Sperm whales emit a long series of clicks at a slow
rate 共usual clicks, 0.45艋ICI⬍ 2 s, ICI denoting the inter-
click interval兲 during the descent. At depth, sperm whales
emit
usual
clicks followed by clicks of increasing rate
共creaks, ICI⬍0.45 s兲 and/or silences 共Mullins et al., 1988;
Zimmer et al., 2005b兲. It has been advanced that sperm
whales emit usual clicks when searching for prey 共denoted
searching phase兲 and creaks when closing in on prey 共de-
noted approach and terminal phases兲. They repeat this
searching/approach/terminal pattern at depth 共Laplanche et
al., 2005; Madsen et al., 2005兲. According to Miller et al.
共2004兲, sperm whales would keep crossing the prey layer
during the searching phase and actively swim during the
approach/terminal phases.
The sperm whale movements and precise use of their
biosonar during these searching/approach/terminal phases
are not perfectly understood yet. Laplanche et al. 共2005兲
have proposed a model describing the sperm whale vertical
movements and biosonar use during the searching phase.
This model is, however, only partially correct and the authors
offer some clarifications below. They propose a passive
acoustic technique, requiring a single hydrophone, to deter-
mine the nature of the movements of diving sperm whales
共i.e., if it is a pitch, yaw, or roll movement兲. They also
present a new technique to estimate the off-axis angle of
sperm whale clicks. The application of both techniques is
grounded on a close description of the waveform of sperm
a兲
Electronic mail: laplanche@univ-paris12.fr
whale clicks, as predicted by the standard model of the
sperm whale sound generator. The authors show that sperm
whales synchronize their movements with their clicking ac-
tivity. The authors then propose a more accurate model de-
scribing how sperm whales move and use their biosonar
while searching for prey.
II. METHODS
A. The leaky bent-horn model
Today’s hypothesis is that sperm whales generate their
clicks with their snout 共Norris and Harvey, 1972兲 according
to the bent-horn model. This model, proposed by Møhl et al.
共2003兲 and later confirmed by Zimmer et al. 共2005b兲, suc-
cessfully predicts the function and location of the various
organs composing the sperm whale’s snout. The sperm
whale’s snout is composed of the nasal circuitry 共left and
right nares兲, a connective organ 共phonic lips兲, two air sacs
共distal and frontal sacs兲, two spermaceti compartments 共sper-
maceti case and junk兲, muscles, and blubber, as described by
Clarke 共1978b兲 and illustrated in Fig. 1. According to the
bent-horn model, and in the notation of Møhl et al. 共2003兲,
clicks are generated by the phonic lips 共leading to the p0
pulse兲, roughly directed backward by the distal sac, focused
by the spermaceti case, and reflected by the frontal sac. The
frontal reflected pulse 共labeled p1/2兲 is channeled and pro-
jected forward by the spermaceti junk, leading to the outgo-
ing p1 pulse.
The use of this model also predicts that the sperm whale
click waveform is multipulsed, i.e., composed of a series of
pulses, 兵p0,p1,p2, ...其共Fig. 2, top兲. Indeed, the frontal re-
flection p1 / 2 travels back in the spermaceti case and reflects
on the distal sac 共leading to a p1
⬘
pulse兲. The distal reflection
p1
⬘
follows an acoustic path inside the snout of the whale
similar to the one followed by p0, leading to a frontal reflec-
tion p3/2, the junk pulse p2, and a distal reflection p2
⬘
, the
distal reflection p2
⬘
itself leading to the triplet
兵p5/2,p3,p3
⬘
其, and so on. The standard use of the bent-horn
model predicts that the initial p0 and the junk
兵p1,p2,p3,...其 pulses exit from the sperm whale’s snout,
explaining the observed multipulse structure of sperm whale
clicks. The bent-horn model also successfully predicts the
measured variations of the apparent source level of the
兵p0,p1其 pulses with the orientation of the hydrophone rela-
tive to the whale 共Møhl et al., 2003; Zimmer et al., 2005b兲.
Using this model 共or its Norris and Harvey ancestor兲,
some researchers have described the 兵p0,p1,p2, ...其 series
as regular, the time of arrival difference between successive
pulses 兵pi, pi+1其共i艌 0兲 being a function of the whale’s
length 共Goold, 1996; Gordon, 1991; Rhinelander and Daw-
son, 2004兲. However, the irregularity of the multipulse struc-
ture 共i.e., variations of such time of arrival differences as
well as the existence of additional pulses within the
兵p0,p1,p2,...其 frame兲 has been underlined by different re-
FIG. 1. The initial pulse p0 is generated by the phonic
lips, transmits through the spermaceti case, and reflects
on the frontal sac into the p1/2 pulse. The p1 / 2 pulse
transmits 共1兲 through the junk and leads to the echolo-
cation pulse p1, 共2兲 back through the spermaceti case,
reflects on the distal sac, and leads to the distal pulse
p1
⬘
, and 共3兲 through the whale’s body to the receiver.
The pi
⬘
pulses 共i 艌1兲 then recursively lead to the p共2i
+1兲/2, p共i+1兲, and p共i+1兲
⬘
pulses.
FIG. 2. Both clicks were emitted by the same sperm whale. Sperm whale
clicks are often described as a series of regularly spaced pulses
兵p0,p1,p2,...其共top兲. Clicks recorded in the farfield rarely fit to this model
and are composed of a more complicate set of pulses 兵p0,p1/2,p1, ...其
共bottom兲.
searchers 关see Bahl et al. 共2002兲; Goold 共1996兲; Møhl et al.
共2003兲 for instance兴 without being elucidated.
The standard multipulse series 兵p0,p1,p2,...其 does not
actually fully represent the waveform of sperm whale clicks.
Clicks, when recorded off axis, deviate from this standard
共Fig. 2, bottom兲. The authors propose a new and more com-
plete description of the multipulse structure of sperm whale
clicks, however, maintaining the standard bent-horn model,
and describe what one could call the leaky bent-horn model.
This description clarifies the discrepancies between the mul-
tipulse structure of clicks predicted by the standard model
共兵p0,p1,p2, ...其兲 and what is actually observed in practice.
Different researchers have reached similar conclusions 共Zim-
mer et al., 2005a兲. The authors of the present work then do
not reillustrate the soundness of the new model, as it has
been convincingly done by Zimmer et al. 共2005a兲. However,
they briefly redefine it as a basis for the application described
below. They also supplement the description of the sperm
whale click multipulse structure proposed by Zimmer et al.
共2005a兲, as it is not complete. For the sake of clarity, the
authors of the present work use a notation similar to the
notation that Zimmer et al. 共2005a兲 introduced.
The standard use of the bent-horn model stipulates that
only the initial and the junk pulses 兵p0,p1,p2,p3,...其 exit
from the sperm whale’s snout. The leaky bent-horn model
stipulates that 共1兲 the above mentioned frontal
兵p1/2,p3/2,p5/2,...其 and distal 兵p1
⬘
, p2
⬘
, p3
⬘
, ...其 reflec-
tions also leak, and that 共2兲兵p0,p1,p2,p3,...其,
兵p1/2,p3/2,p5/2,...其, and 兵p1
⬘
, p2
⬘
, p3
⬘
, ...其 form distinct
sets of pulses that can be separated using an off-axis hydro-
phone in the farfield. Zimmer et al. 共2005a兲 demonstrated
that the frontal p1/ 2 pulse indeed leaks from the sperm
whale’s snout and that the p1 pulse exits at the flat anterior
surface of its junk. Zimmer et al. 共2005a兲 also demonstrated
that the travel time differences of the p1/2 and p1 pulses to
the p0 pulse depend on the orientation of the whale to the
hydrophone. The authors of the present work do not reillus-
trate the soundness of such statements. They supplement the
description of the waveform of a sperm whale click proposed
by Zimmer et al. 共2005a兲, asserting that it is also composed
of the distal reflection p1
⬘
and the additional sets of pulses
兵p3/2,p5/2, ...其, 兵p2,p3...其, and 兵p2
⬘
, p3
⬘
, ...其,asde-
scribed above. Such a description is discussed below.
B. Definition of pulse delays and angles
The delay of the py pulse on the px pulse is noted
xy
,
simplified into
y
if px= p0. The delays 兵
1
⬘
,
1
⬘
2
⬘
,
2
⬘
3
⬘
, ...其
are all equal to the travel time required by a pulse to travel
twice between the distal and frontal sacs through the sper-
maceti case. Such a travel time is still denoted IPI by the
authors, being the interpulse interval used in the literature
regarding the sperm whale length estimation process men-
tioned above.
The delays 兵
1/2
,
3/2
, ...其 of the frontal pulses
兵p1/2,p3/2, ...其 to the initial p0 pulse, and the delays
兵
1
⬘
1
,
2
⬘
2
, ...其 of the junk pulses 兵p1,p2,p3, ...其 to the dis-
tal pulses 兵p1
⬘
, p2
⬘
, p3
⬘
, ...其 depend on the orientation of the
whale to the hydrophone, as proven by Zimmer et al.
共2005a兲 regarding
1/2
and
1
⬘
1
. Using a hydrophone at a
fixed location in the farfield, 兵
1/2
,
3/2
, ...其 and
兵
1
⬘
1
,
2
⬘
2
, ...其, delays will change while the sperm whale
moves underwater. Our aim in this work is to determine the
nature of the whale’s movements using the measurement of
these delays. As described below, in the recordings used to
illustrate this work, most of the time only pulses from the set
兵p0,p1/2,p1,p1
⬘
其 are clearly detected. In the study of the
whale’s movements that follows, the authors have considered
such pulses and used the delays 兵
1/2
,IPI,
1
⬘
1
其 only.
The authors consider in the following the reference
frame of the whale. They define the pitch, yaw, and roll
movements of the whale as rotations on its left-right, up-
down, and dorsorostral axes. As a difference, Zimmer et al.
共2005b兲 and Laplanche et al. 共2005兲 have both considered
the sperm whale movements in the terrestrial reference
frame. The off-axis angle of the whale 共labeled
␦
苸 关0,
兴,
and estimated when the whale is emitting a click兲 is defined
as the angle separating the whale dorso-rostral axis to the
line joining the whale to the hydrophone 共Fig. 3兲.
C. Estimation of the off-axis angle of a click
The off-axis angle of a whale represents its orientation
to a reference point 共e.g., the hydrophone兲. This angle varies
with the whale’s underwater movements, and, inversely, the
variations of the off-axis angle of a whale provide informa-
tion on the whale’s underwater movements. The knowledge
of this angle is critical in the following study, and the authors
propose a simple method to carry out the estimation of the
off-axis angle of a sperm whale click.
FIG. 3. The off-axis angle of the whale is defined as the angle between the
whale dorsorostral axis and the line joining the whale to the hydrophone H.
The point D is at the center of the phonic lips 共point of emission of the p0
pulse兲. F is the point of frontal reflection p0→ p1/2. K is the orthogonal
projection of F on the line 共DH兲.
