1021
Variations in echosounder – transducer performance
with water temperature
David A. Demer and Josiah S. Renfree
Demer, D. A., and Renfree, J. S. 2008. Variations in echosounder– transducer performance with water temperature. – ICES Journal of Marine
Science, 65: 1021 – 1035.
Electro-acoustic transducers are central components of multifrequency echosounders used in remote-target identification and acoustic surveys for fish and zooplankton. Appreciable changes in echosounder system gains can result from shifts in transducer frequency
responses with water temperature. Because it is standard practice to calibrate echosounder systems for fisheries surveys in one environment and apply the resulting gains to interpret data collected over the range of sea temperatures encountered during a survey, the
results may be biased. Such biases may be different for estimates derived from each echosounder frequency. In moving to quantify and
mitigate these effects, the performances have been measured for ten commonly used survey transducers in water temperatures
ranging from 18C to 188C, using three techniques. Results show that the transducer impedances all change with temperature, potentially changing the signal-to-noise ratio from 5 to .20 dB. The resonance frequencies and quality factors also change with temperature, ranging from 0.2% to 2.8% and 2.5% to .130%, respectively. Corresponding directly to changes in the echosounder gains, the
transmitting-current and receiver-voltage responses changed 1 dB or less with temperature, except for the Simrad ES120-7, which
showed a 2 dB increase. Generally, the magnitudes of frequency-dependent biases in echosounder-system gains depend primarily
on the temperature-dependent performances of the survey transducers, the range of temperatures encountered, and whether the
operational frequencies are less or greater than the resonance frequency.
Keywords: impedance, quality factor, resonance frequency, temperature, transducer.
Received 2 October 2007; accepted 6 February 2008; advance access publication 25 April 2008.
D. A. Demer and J. S. Renfree: Southwest Fisheries Science Center, 8604 La Jolla Shores Drive, La Jolla, CA 92037, USA. Correspondence to
D. A. Demer: tel: þ1 858 546 5603; fax: þ1 858 546 5656; e-mail: [email protected].
Introduction
Scientific echosounders used for fisheries-resource surveys generally use resonant transducers and transmit and receive near their
resonance frequencies. Their construction from multiple materials
such as piezo-electric ceramics, polyurethanes, and metals makes
them likely to change performance characteristics with changes
in temperature and pressure (Blue, 1984). Many researchers have
characterized the performances of standard hydrophones against
temperature and pressure (e.g. Van Buren et al., 1999; Beamiss
et al., 2002; Ablitt et al., 2006), and have highlighted the need to
account for these influences when making measurements in
dynamic environmental conditions. In fisheries applications,
however, the echosounder systems are typically calibrated in a
static environment, then used to acquire data over the range of
water temperatures encountered during a survey. The reasons
for this are practical: standard sphere calibrations (Foote et al.,
1987) consume expensive ship-time and are best conducted in
sheltered areas before and after each survey; and the performances
of commercial echosounder transducers have not, in general, been
characterized against temperature. Moreover, the range of water
temperatures encountered during a survey may not be significantly
different from that during the calibration. In areas such as the
Arctic or Southern Oceans, however, the range of temperature
can be large, and compensation for the temperature-dependence
of system calibrations may be warranted.
For a 120 kHz echosounder transducer made up of 76 piezoceramic elements and a polyurethane window (Simrad model
ES120-7), Demer and Hewitt (1993) showed that an appreciable
change in on-axis system gain (g0; dimensionless) results from a
shift in seawater temperature. Researchers from the British
Antarctic Survey and the Alaska Fisheries Science Center have confirmed this phenomenon for other echosounder transducers and
frequencies (Brierley et al., 1998; N. Williamson, pers. comm.,
respectively). Therefore, because the material, electrical, and
hence acoustic properties of transducers are dependent on water
temperature, data collected without taking these changes into consideration may be biased. Here, the changes in ten commonly used
echosounder transducers are characterized precisely, and a method
is proposed to account for these changes and therefore to minimize this component of uncertainty in acoustic surveys of
aquatic life.
Note that all symbols used herein, their descriptions and their
units are listed in the Appendix, for ease of reference.
Transducer materials and performance
Many Simrad transducers are made from PZT4 or PZT8 ceramics
and with PRC or Durotong window material (H. Bodholt, Simrad,
pers. comm.), effectively creating a coupled resonance system. The
properties of these materials vary with acoustic frequency f (kHz)
and temperature T (8C; Blue, 1984). Simrad– Kongsberg also uses
# US Government/Department of Commerce/National Oceanic and Atmospheric Administration/National Marine Fisheries Service
2008
1022
D. A. Demer and J. S. Renfree
polyurethane (Durotong) in the fabrication of their EM series
multibeam transducers and reports a relationship between its
sound speed c (m s21) and T (Kongsberg, 2006), indicating a
change in c of 5.1% when T declines from 178C to 18C. For a
similar polyurethane rubber (DeSoto PR1547) and change in T
from 17.28C to 3.98C, c changes by 6.1%, and possibly more
importantly, the absorption coefficient changes 57.9% at f =
70 kHz (Mott et al., 2002).
In addition to changes in the properties of the transducer
materials with T, the transmitting current response (S0; mPa A21
at 1 m), the receiver free-field voltage response (M0; V mPa21),
and the mechanical resonance frequency ( fr; kHz) can vary with
temperature (Blue, 1984; Van Buren et al., 1999). These changes
can be characterized using a self-reciprocity calibration
(Carstensen, 1947), where a transducer projects a pulse of sound
at a near-perfect reflector (e.g. an air–water interface; Patterson,
1967). Both S0 and M0 can be determined from separate measurements of the transmitter current (It, A), and the open-circuit
voltage (Vr, V), through the received reflected sound:
S0 ¼
Vr
2r J
It
Sabin (1956) showed that Equations (1) and (2) can be solved
with measurements of J, r, and the reflectional impedance:
Vr jZref j ¼ ¼ Z 0 Z ;
It
where Z is measured using Equation (3) during transmission into
a free-field, and Z0 is measured when the transmitted signal overlaps with that from a total reflection (e.g. using a self-reciprocity
calibration configuration, during the superposition of a transmitted pulse and its echo from an air– water interface). The subtraction in Equation (6) is a vector difference, and k designates
an amplitude operator for the complex argument.
Echosounder performance
Principal measurements of echosounders are the backscattering
cross-sectional area of an individual target (s; m2):
s¼
1=2
;
ð1Þ
sv ¼
Vr
2rJ
It
1=2
;
ð2Þ
where r (m) is the range from the transducer to the air–water
interface, J ¼ (2l/rc)(10212) (W mPa22) the reciprocity parameter at 1 m, l (m) the wavelength of sound, and rc
(kg m22 s21) the characteristic impedance of water, the product
of its density r (kg m23) and c (Rosen et al., 1992, p. 377). Both
Equations (1) and (2) contain the ratio of V and I, which has
units of electrical impedance (Z; V). Both Z and the electrical
admittance (Y; S) are derived from measurements of voltage (V;
V) and current (I; A):
V
Z ¼ ¼ R þ jX;
I
Pr 64p3 r 4 10ar=5
;
Pt g02 l2
ð7Þ
and the volume-backscattering coefficient (sv; m – 1):
and
M0 ¼
ð6Þ
Pr 32p2 r 2 10ar=5
;
Pt g02 r02 l2 ctc
ð8Þ
which is the backscattering area (m2) per unit volume of seawater
(m3), following Simrad (1993), but with a correction to the a
term, Pt is the transmitted electrical power (W), Pr the received
electrical power (W), g0 the on-axis system gain (dimensionless),
r0 the reference range (1 m), and c the equivalent two-way solid
beam-angle (sr). Both Pt and Pr are functions of the transmitted
voltage Vt, received voltage Vr, and the impedance:
Pt ¼
Vt2
;
ZðTÞ
ð9Þ
Pr ¼
Vr2
:
ZðTÞ
ð10Þ
and
ð3Þ
If impedance depends on temperature Z(T ), so does power
P(T), and changes in Z(T ) correspond to changes in P(T):
Y¼
I
¼ G þ jB;
V
where R is the resistance (V), X the reactance (V), G the conducp
tance (mS), B the susceptance (S), and j = 21. G is maximum
(Gmax) at fr (Wilson, 1988). The quality factor Q (unitless) is a
measure of the width of the resonance peak relative to its
maximum:
Q¼
fr
;
f2 f1
dPðTÞ
d V2
V 2 dZðTÞ
¼
;
¼
dT
dT ZðTÞ
ZðTÞ2 dT
ð4Þ
ð5Þ
where f2 and f1 are the closest frequencies above and below fr where
p
G( f1) ¼ G( f2) ¼ Gmax/ 2.
ð11Þ
or
DPðTÞ ¼ V 2
ZðTÞ ZðT0 Þ
;
ZðTÞ2
ð12Þ
where T0 is a reference temperature. Assuming the transmitter and
receiver impedances are equivalent (Simrad– Kongsberg, 2003)
and the transducer is reciprocal, the changes in Pt and Pr are
equal, and their effects are cancelled in the quotients defining s
and sv [see Equations (7) and (8)]. However, if Z(T) and hence
Pt change, and both Vt and the ambient acoustic noise remain constant against T (assuming a constant-voltage transmit amplifier
1023
Variations in echosounder–transducer performance with water temperature
Table 1. Electrical characteristics for ten commonly used Simrad transducers.
Simrad model
Nominal
Measured in this experiment
h (%)
fEK500 (kHz) jZj (V)
u (88 )
fEK60 (kHz) jZj (V)
u (88 )
fr (kHz)
Q
h (%)
jZj (V) u (88 )
ES18
11–20
+30
60
+
20
17.986
13.5
6.79
18.000
13.4
5.30
18.057
27.9
77
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . .
ES38-B
11–20
+30
60+20
37.878
13.6
29.59
38.000
15.5
26.04
36.817
24.0
–
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . .
ES38-12
11–20
+30
70
+
20
37.878
13.6
5.86
38.000
14.9
6.45
36.947
12.3
68
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . .
ES70-7C
19
–
75
70.422
20.9
27.78
70.000
20.6
26.30
67.347
4.8 75
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . .
ES120-7
11-20
+30
70
+
20
119.047
20.0
13.20
120.000
20.2
7.57
120.120
9.2
–
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . .
ES120-7C
19
–
75
119.047
17.6
214.79
120.000
18.0
215.54
111.767
3.4
74
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . .
ES200-7C
19
–
75 200.000
23.0
26.59 200.000
23.0
26.59 178.899
11.6 73
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . .
ES200-28E
45–80
+30
70
+
20
200.000
46.2
31.59
200.000
46.2
31.59
221.729
19.8
–
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . .
Combi
D-50
75
–
50
49.020
88.0
19.33
50.000
79.7
22.82
52.345
6.8
–
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . .
Combi D-200
75
–
60 200.000
84.3
28.13 200.000
84.3
–8.13 203.820
10.4
–
Summarized are the nominal transducer-impedance values (jZj, and phase u), and those measured during this experiment at the operational frequency of
the Simrad EK500 and EK60 echosounders fEK500 and fEK60, respectively, at a temperature of 178C; and the resonant frequencies fr, quality factors Q, and
efficiencies (h) at 178C. Measurements were made with 10 m of cable factory-attached to each transducer, and a connector set (Amphenol
97-3106A-24-19P and 97-3102A-24-19S). The four quadrants of the split-beam transducers were connected in parallel, except for the ES120-7, which had only
three quadrants connected in parallel: a connection to quadrant IV was broken.
and thermal noise is not dominant (Urick, 1983)), the
signal-to-noise ratio will change with T (snr(T ); dimensionless):
dsnrðTÞ
d Pr ðTÞ
d CðTÞ
CðTÞ dZðTÞ
¼
;
¼
dT
dT Pn
dT ZðTÞ Pn ZðTÞ2 dT
ð13Þ
where Pr(T ) = C(T )/Z(T ) is determined from a combination of
either Equation (7) or (8) and Equation (9), Pn is noise power,
and C(T) is substituted for all non-Z(T ) parameters. The
Simrad EK60 transmit voltage is designed to be constant for
small changes in Z(T ). However, the transmitter is
current-limited, and the output impedance and Vt will change
for large changes in Z(T ), e.g. from 80 to 40 V (L. Andersen,
Simrad, pers. comm.). The characteristics of the current-limiter
are the same for all transmit powers, but different for each frequency. The receiver impedance is constant (A. Johansen,
Simrad, pers. comm.). Note that changes in the transducer impedance, and efficiency and directivity, have equivalent effects on the
reception of the volume-scatter signal and the incoherently additive acoustic noise. To evaluate the effects of D Z(T ) on D
snr(T ), let dC(T)/dT = 0:
DsnrðTÞ ¼ CðTÞ ZðTÞ ZðT0 Þ
:
Pn
ZðTÞ2
ð14Þ
Therefore, changes in SNR(T) = 10 log(snr(T )) are proportional to changes in the transducer impedance divided by the
square of the impedance. Changes in SNR(T ) will change the
effective precisions (Demer et al., 1999), biases, and maximum
detection ranges of the echosounder measurements (Demer,
2004).
The accuracy of s and sv will be affected by changes in g0(T )22
[see Equations (7) and (8)]. The on-axis system gain is proportional to both M0 and S0, and is defined (Simrad –
Kongsberg, 2003) as the product of the temperature-dependent,
transducer directivity [d(T ); unitless], and electro-acoustic transducer efficiency [(h(T ); unitless]:
g0 ðTÞ ¼ dðTÞhðTÞ:
ð15Þ
A change in the d(T ) through a change in T is approximately
equal to the change in sound speed (e.g. 4.0% or 0.17 dB for a
168C change in T ), because the effective aperture is proportional
to l (see Foote, 1991). Changes in h(T) can be more appreciable
(Blue, 1984).
The self-reciprocity technique can also yield accurate measurements of h from the reciprocity-voltage ratio, the
Thevenin-equivalent resistance, and the transducer-directivity
index (Widener, 1980). Therefore, taking account of changes in
Z(T) and d(T ), changes in h(T) should mimic changes observed
in M0(T ) and S0(T ). It is desirable, however, to have explicit and
independent estimates of h(T ).
At the transducer-resonance frequency, h(T ) can be determined from measurements of Y(T) made with the transducer
loaded and unloaded (Wilson, 1988):
h¼
DW ðDA DW Þ
;
DA ðGmin þ DW Þ
ð16Þ
where DA and DW are the widths of the unloaded (in air) and
loaded (in water) admittance circles (G vs. B as a function of f ),
respectively; and Gmin is the minimum conductance in the admittance circle. Formulation (16) assumes that the difference in resistance in the motional impedance is attributable to acoustic
radiation into air vs. water, and that the losses (e.g. lossy resistances in the transducer-equivalent circuit) are the same in both
measurement conditions. However, different losses may arise
from, for example, the heating of the transducer. Although this
method can be prone to error for some transducers, it is included
here for completeness.
Multifrequency target identification
Fish-number densities (fish m22 of sea surface) are estimated
acoustically by apportioning sv (m2 backscatter m23 seawater) to
the various sound-scatterers contributing to the reverberation,
integrating that from the targeted type, resulting in units of m2
backscatter m22 of sea surface, and dividing by the representative
s (m2 fish21). Generally, the largest sources of error in this process
1024
D. A. Demer and J. S. Renfree
Stanton et al. (1996). To be useful, the models must be validated
with measurements. To elucidate these spectra independent of
animal density, the sv measured at multiple frequencies can be normalized to that at a reference frequency, typically 38 kHz
(Korneliussen and Ona, 2002). Probabilistic comparisons
between the shapes of the measured spectra and those predicted
by the models may identify the targets (Demer, 1994). However,
the effectiveness of these methods for remote-target identification
depends on both the accuracies of the scattering spectra predictions and the accuracies and precisions of the measurements at
each f. Moreover, if changes in SNR(T ) are different from each frequency, the detection ranges at each frequency will be dependent
on water temperature. One aim of this study is to reduce uncertainty in measurements of scattering spectra and the acoustic
identification of targets.
Figure 1. An array of ten commonly used Simrad transducers being
lowered into Deep Tank. From left to right and top to bottom the
transducers are the Simrad ES120-7, ES38-12, 200-28E, ES18, ES38-B,
ES120-7C, ES200-7C, ES70-7C, Combi D-50, and Combi D-200.
are associated with identifying backscatter from the target, and
estimating its s (Furusawa, 1991; Demer, 2004; Simmonds and
MacLennan, 2005). As the echo from an object depends on l
and its material properties, size (L), shape, and orientation, the
sound-scattering spectra can be used to measure some of its biophysical characteristics (Holliday, 1977). For example, animal
sizes can be acoustically estimated by solving one or more scattering models with multifrequency measurements of sv (Greenlaw
and Johnson, 1983). The effectiveness of the inversion technique
depends on the accuracy of both the model(s) and the measurements. Because of the challenges in studying complex aquatic ecosystems, a large number of models, both physics-based and
empirical, have been developed to predict the frequencydependent backscatter from a variety of targeted species, e.g.
Methods
The performance characteristics of ten commonly used survey
transducers (Table 1) were measured with T ranging from 18C
to 188C. All are split-beam, except for the single-beam
ES200-28E and the Combi D-50 and Combi D-200.
Measurements of the split-beam transducers were made with the
four quadrants in parallel. Three of the transducers (ES70-7C,
ES120-7C, and ES200-7C) are made from composite materials,
of which the details are unavailable from the manufacturer.
Three experiments were conducted:
(i) Z(T ), fr(T ), and Q(T ) were determined from measurements
of V(T) and I(T ), using Equations (3) and (4); the corresponding Dsnr(T ) were estimated from changes in Z(T)
[using Equation (14)];
(ii) M0(T ) and S0(T) were measured from the vector differences
in Z(T ) and Zref(T ), using Equations (1), (2), and (6); and
(iii) h(T ) were estimated from measurements of Y(T) when the
transducer was loaded and unloaded, using Equation (16).
Figure 2. Measurement instrumentation and wiring. The main instrumentation included an arbitrary waveform generator (Hewlett Packard
HP33120A), a current probe (Pearson Electronics, Model 410), a digital storage oscilloscope (Agilent 54624A), a custom multiplexer, and a
laptop computer.
Variations in echosounder–transducer performance with water temperature
1025
Tablep 2. Coefficients for third-order polynomial fits to the impedance (Z; V) plotted vs. temperature (T) for ten Simrad transducers
( j = 21).
Simrad model
Z = AT 3 + BT 2 + CT + D
A
B
C
D
20.0008
+
0.0011j
0.0138
–0.0379j
0.0479
+
0.2361j
12.6586 + 0.3103j
f. .EK500
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.0008
+
0.0011j
0.0126
–0.0374j
0.0561
+
0.2297j
12.5330 + 0.6727j
f. . EK60
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.0005
+
0.0003j
0.0049
–0.0116j
0.1033
+
0.0681j
12.3600 + 1.3278j
f
r
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0.0001– 0.0000j
0.0010 + 0.0004j
0.0525 + 0.0745j
11.8484 + 1.1061j
ES38-B
fEK500
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0.0000–
0.0001j
0.0029
+
0.0009j
0.0519
+
0.0567j
13.5995 + 0.8389j
f. . EK60
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.0001–
0.0002j
0.0025
–0.0059j
20.0436
+
0.0942j
6.3874 –2.7853j
f
r
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0.0007
+
0.0000j
20.0174
+
0.0036j
20.0143
+
0.0108j
15.1850
–2.7242j
ES38-12
f. .EK500
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0.0008–
0.0001j
20.0186+0.0070j
20.0049–0.0033j
16.3856
–3.0476j
f. . EK60
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.0049–
0.0047j
0.1057
+
0.1151j
–
0.5039–0.6108j
10.7026
–4.7634j
f
r
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.0003 + 0.0000j
0.0059 + 0.0015j
20.1658–0.0547j
23.1687 + 3.3368j
ES70-7C
f. .EK500
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.0003
+
0.0001j
0.0055
–0.0012j
20.1527–0.0348j
22.8979
+ 2.7594j
f. . EK60
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.0003
+
0.0014j
0.0057
–0.0426j
20.1642
+
0.3437j
22.0256
–1.9985j
f
r
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ES120-7
fEK500
0.0002 + 0.0005j
20.0130 –0.0219j
0.4049 + 0.0724j
15.2558 –1.6158j
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0.0003
+
0.0002j
20.0157
–0.0111j
0.3691–0.1004j
16.9575 + 1.4755j
f. . EK60
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0.0009
+
0.0028j
20.0165
–0.0592j
0.3375
+
0.1755j
14.6381 –3.0457j
f
r
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.0004–
0.0006j
0.0106
+
0.0197j
20.0166–0.2538j
16.3358
+ 6.2809j
ES120-7C
f. .EK500
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.0004–
0.0006j
0.0088
+
0.0198j
–
0.0057–0.2720j
16.7465+6.8770j
f. . EK60
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.0004– 0.0005j
0.0126 + 0.0144j
20.0670–0.1244j
14.9444 + 0.0020j
fr
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.0002
+
0.0002j
0.0024
–0.0021j
20.1594–0.1379j
25.7382
+ 4.6383j
ES200-7C
f. .EK500
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.0002 + 0.0002j
0.0024 –0.0021j
20.1594–0.1379j
25.7382 + 4.6383j
fEK60
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0.0004
+
0.0006j
20.0092
–0.0133j
0.0836
+
0.0566j
8.1946 –2.5116j
f
r
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.0002
+
0.0004j
0.0014
–0.0066j
0.2103–0.0397j
36.2900
–23.7616j
ES200-28E
f. .EK500
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.0002
+
0.0004j
0.0014
–0.0066j
0.2103–0.0397j
36.2900
–23.7616j
f. . EK60
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.0002
+
0.0002j
0.0058
–0.0023j
20.0335–0.0263j
12.0943
+ 0.4901j
f
r
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.0019
+
0.0020j
0.0323
–0.0464j
21.2822–0.5660j
104.9815
–15.8744j
Combi D-50
f. .EK500
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
fEK60
0.0005– 0.0032j
0.0037 + 0.1086j
21.4286–1.2456j
94.6220 –25.3273j
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.0034–
0.0008j
0.0812
–0.0030j
20.6151
+
0.3777j
62.9419
–25.4864j
f
r
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0.0047–
0.0014j
20.1302
+
0.0528j
1.3645–1.4487j
74.9270
+ 28.7277j
Combi D-200
f. .EK500
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0.0047–
0.0014j
20.1302
+
0.0528j
1.3645–1.4487j
74.9270
+ 28.7277j
f. . EK60
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0.0110– 0.0036j
20.2750 –0.1057j
1.1218 + 3.3855j
72.8872 + 4.5647j
fr
ES18
Least-squares fits were made to the data at the operational frequencies of the Simrad EK500 and EK60 echosounders ( fEK500 and fEK60) and the transducer
resonance frequencies ( fr). Measurements were made with 10 m of cable factory attached to each transducer, and a connector set (Amphenol
97-3106A-24-19P and 97-3102A-24-19S). The four quadrants of the split-beam transducers were connected in parallel, except for the ES120-7, which had only
three quadrants connected in parallel: a connection to quadrant IV was broken.
Estimating Z(T ), fr(T ), and Q(T)
Measurements of V(T ) and I(T ) were made of each transducer
mounted inside a large insulated tank (Deep Tank, Hydraulics
Lab, Scripps Institution of Oceanography). The tank is 10 m
deep and 3 m diameter, and contains filtered seawater that was
chilled from the local ocean T (178C in May and June) to 18C.
The transducers and a CTD (Seabird SBE 19+) were mounted
on a 12-mm thick aluminium plate (Figure 1). A surfactant was
applied to the transducer faces to shed bubbles. The transducer
array was suspended inside the tank by a four-point harness
attached to the corners of the array and to a gantry crane. The
faces of the transducers were thus positioned at a depth of
1.1 m, orientated with their acoustic beams directed down.
Measurements of water T, salinity (s; dimensionless), r,
pressure (p; dbar), and c were recorded at the depth of the transducers using the CTD. Additionally, T was monitored with a chain
of temperature loggers (Onset HoboTemps) at five depths (0.1,
1.7, 3.3, 6.5, and 8.1 m), and a thermocouple profiler. A vertically
mixing pump was used to maintain a uniform water temperature
between 0.5 and 10 m.
Data acquisition was with a digital storage oscilloscope (Agilent
54624A), an arbitrary waveform generator (Hewlett Packard
33120A), a current probe (Pearson 410), and a custom multiplexer
(Figure 2). A laptop computer (Sony Vaio) and custom program
(The Mathworks Matlab) were used to configure the instruments,
to automate their functions, and to record the data, and a multiplexer to connect sequentially each transducer to the measurement
apparatus.
The excitation signal was a 2-ms broad-bandwidth chirp
(Vp-p = 10 V). The frequency bandwidth was fEK60 + 20%, where
fEK60 is the operational frequency of the Simrad EK60 echosounder
for that transducer model (Table 1). The V and I signals were
recorded by the oscilloscope (2000 samples each), converted to
analytical signals using the Hilbert transform, digitally filtered
1026
D. A. Demer and J. S. Renfree
Figure 3. Magnitude of impedance (jZj; V) with temperature (T; 8C) for the ten transducers. Measurements (dots) are plotted at the
operational frequencies of the EK60 ( fEK60; kHz; black), and EK500 ( fEK500; kHz; dark grey) echosounders, and the transducer resonance
frequency ( fr; kHz; light grey), and each dataset was fitted with third-order polynomials (lines; see Table 2).
into 400 narrow-frequency bands, and used in Equations (3) and
(4) to estimate Z and Y at f and T. These measurements were made
three times for each transducer before proceeding to the next in
the multiplexer sequence. Each electrical measurement was temporally matched with CTD measurements of T, s, p, r, and c.
This process was continually repeated while T in the tank
warmed from 18C to 178C. The Z(T) were modelled by
third-order polynomials using the method of least-squares:
ZðTÞ ¼ AZ T 3 þ BZ T 2 þ CZ T þ DZ ðVÞ;
ð17Þ
and changes in snr(T ) for each transducer were estimated from
changes in Z(T ), using Equation (14).
Estimating M0(T) and S0(T)
For the second set of tank experiments, the transducer faces were
orientated with their acoustic beams perpendicular to the air–
water interface (self-reciprocity configuration), at a range of
1.8 m (Table 1). The inverted transducer array was suspended
inside the tank by adjustable lines attached to each of the four
corners, and to a frame secured to the tank top. Accurate
Variations in echosounder–transducer performance with water temperature
1027
Figure 4. Changes in transducer impedance divided by the square of the impedance [proportional to changes in the signal-to-noise ratio
(snr); see Equation (14)], plotted against temperature (T; 8C) for the ten Simrad transducers. The y-axes are labelled with both linear and
logarithmic scales because the SNR is alternatively considered in each domain. Measurements (dots) are plotted at the operational frequencies
of the EK60 ( fEK60; kHz; black), and EK500 ( fEK500; kHz; dark grey) echosounders, and the transducer resonance frequency ( fr; kHz; light grey).
Datasets were fitted with fifth-order polynomials (lines).
alignment of the array was facilitated first by centring bubbles
inside levels affixed to the plate at five locations, then by minimizing the electrical phase angles measured between the quadrants of
the split-beam transducers (ES18, ES38-B, ES70-7C, ES120-7C,
and ES200-7C). Ultimately, the acoustic beams were made perpendicular to the air– water interface +0.28 mechanical.
Measurements of water T, s, r, p, and c were recorded by the
CTD at the depth of the transducers (1.85 m). Additionally, T
was measured with the temperature loggers at five depths
between the transducers and the water surface (0.1, 0.5, 0.9, 1.3,
and 1.7 m). The vertically mixing pump was employed to maintain a uniform T from depths between 0.2 and 10 m. This
time, to minimize thermal transfer and ripples on the water
surface, the top of the outdoor tank was completely covered
with wood and plastic wrapping, leaving a gap of still air
(0.3 m) between the water surface and the cover.
The first of two excitation signals was a 2-ms broad-bandwidth,
linearly-sweeping chirp (Vp-p = 10 V). To measure complete
1028
D. A. Demer and J. S. Renfree
Figure 5. Resonance frequency ( fr; kHz) plotted against temperature (T; 8C) for the ten Simrad transducers. The measurements (dots) are
fitted with fifth-order polynomials (solid) and bounded by 95% confidence intervals (+2 s.d.; dashed).
admittance circles for the transducers with lowest Q, the frequency
bandwidth for all was fEK60 + 50%. As in experiment (i), the V and
I signals were recorded by the oscilloscope (2000 samples each),
converted to analytical signals using the Hilbert transform, digitally filtered into 400 narrow-frequency bands, and used in
Equations (3) and (4) to estimate Z and Y at f and T. These
loaded admittance circles were used to estimate h(T ); see experiment (iii) below.
After each of the 2-ms broad-bandwidth chirps, but before
switching to the next transducer in the multiplexed array, a
4.0-ms CW pulse at fEK60 (see Table 1) was transmitted. This
second excitation signal was used to measure Z during a free-field
period of 1 –2 ms after beginning the transmission, and Z 0 during
a period of 3 –4 ms when the transmitted signal overlapped with
an echo from an air–water interface. The estimations of Zref(T )
and of M0(T ) and S0(T) were made from Equations (6), (1),
and (2), respectively. This process was continually repeated while
T in the tank warmed from 0.88C to 16.78C.
Estimating h(T)
The transducer array was repositioned a third time, in a
temperature-controlled room. The array was placed on its side so
that the transducer faces did not touch their surroundings.
Measurements of air T were recorded by the CTD. Additionally,
Variations in echosounder–transducer performance with water temperature
1029
Figure 6. Quality factor (Q; unitless) plotted against temperature (T; 8C) for the ten Simrad transducers. The measurements (dots) are fitted
with fifth-order polynomials (solid) and bounded by 95% confidence intervals (+2 s.d.; dashed).
T was monitored with an indoor and outdoor digital thermometer.
Two fans inside the room maintained a well-mixed environment.
The excitation signal was a 2-ms broad-bandwidth chirp
(Vp-p = 1 V; and fEK60 + 50%). As in experiments (i) and (ii)
above, the V and I signals were recorded by the oscilloscope
(2000 samples each), converted to analytical signals using the
Hilbert transform, digitally filtered into 400 narrow-frequency
bands, and used in Equations (3) and (4) to estimate Z and Y at
f and T. This process was repeated continually while T in the
room cycled between 08C and 198C several times over a
4-day period. Each temperature cycle took 3 h. These unloaded
admittance circles were used in conjunction with the loaded
measurements [see experiment (ii)] to estimate h(T ) from
measurements of DW, DA, and Gmin, using Equation (16).
For the loaded state, the 400 point estimates of G( f ) and B( f )
at each T were smoothed with a low-pass filter and interpolated to
2000 points. The fr was then estimated as the frequency of
maximum conductance within the frequency range fEK60 + 20%.
The admittance circles for each transducer required a different frequency range, because some transducers have multiple conductance peaks and the variability in the measurements differed
between transducers.
To determine Gmin of the admittance circles, B( f,fr) were
pairwise subtracted from B( f.fr), beginning at fr, and Gmin
1030
D. A. Demer and J. S. Renfree
Figure 7. M0 (dB re V mPa21) and S0 (dB re mPa A21) plotted against temperature (T; 8C) at the EK60 operational frequency ( fEK60; kHz) for
the ten Simrad transducers. The measurements (dots) are fitted with fifth-order polynomials (solid) and bounded by 95% confidence intervals
(+2 s.d.; dashed).
was evaluated at the frequencies where differences changed
polarity (i.e. where the two functions crossed). DW and DA
were estimated from G( fr) 2 Gmin, in the loaded and unloaded
conditions.
Results
Estimating Z(T ), fr(T ), and Q(T)
Measurements of transducer performance were made of ten
commonly used survey transducers (Table 1). The magnitude
of the impedance (jZj; V) was plotted against T from 1.58C
to 17.28C at the operational frequencies of the Simrad EK500
and EK60 echosounders ( fEK500 and fEK60, respectively) and fr,
and each dataseries was fitted with a third-order polynomial
[Equation (17); Table 2; Figure 3]. jZj changes appreciably
and smoothly with T for all ten transducers, but most pronounced for the ES70-7C, ES120-7, and the Combi D-50 transducers. When the operational frequency is away from resonance
(notably for the ES38-B, ES38-12, ES120-7C, ES200-7C,
200-28E, Combi D-50, and Combi D-200), jZj were different
at fEK500 and fEK60 vs. fr. Moreover, jZj did not systematically
Variations in echosounder–transducer performance with water temperature
1031
Figure 8. Admittance circles [susceptance (B; mS) plotted against conductance (G; mS) as a function of frequency] ( fEK60 + 50%) for nine
Simrad transducers listed in Table 1, at 178C. The measurements were fitted with fifth-order polynomials (lines); they were made with the
transducer loaded (in water; solid) and unloaded (in air; dashed). Results for the Combi D-50 transducer are not shown because the fr was
appreciably different when loaded and unloaded, and the admittance circles did not overlap. Note also that the unloaded admittance circle
for the ES18 is malformed because the frequency resolution was too low, and that those for the ES38-B, ES120-7, 200-28E, and Combi D-200
transducers are very small.
increase or decrease with T; five transducers increased, and five
decreased, depending on whether the operational frequency was
less than or greater than fr.
Following Equations (12) and (14), the changes in SNR attributable to changes in Z(T) were evaluated at T0, and plotted at
jZjmin=Z(T0), and plotted at fEK500, fEK60, and fr for each transducer (Figure 4). Changes in Z(T) can cause changes in SNR from 5
to .20 dB (ES120-7C and ES70-7C, respectively).
Plots were made of fr(T ) for each of the ten transducers
(Figure 5). Gaps in the data were caused by instability in the automated data acquisition (Matlab). Despite the gaps, the trends are
reasonably clear (i.e. increasing with T for the ES18, ES38-12,
ES70-7C, ES120-7, and Combi D-200; and decreasing with T for
the ES38-B, ES120-7C, ES200-7C, 200-28E, and Combi D-50).
The changes in fr(T ) range from 0.2% for the ES200-28E to
2.8% for the Combi D-50. The composite transducers (ES70-7C,
1032
D. A. Demer and J. S. Renfree
Figure 9. Transducer efficiencies (h; %) at resonance frequency ( fr; kHz) plotted against temperature (T; 8C) for nine Simrad transducers. The
measurements (dots) are fitted with fifth-order polynomials (solid) and bounded by 95% confidence intervals (dashed). The estimate of h(T )
for the ES18 may be slightly low, and those for the ES38-B, ES120-7, 200-28E, and Combi D-200 transducers are dubious.
ES120-7C, and ES200-7C) showed changes in fr(T) of 0.3%,
0.4%, and 0.5%, respectively. The Combi D-50 and Combi
D-200 transducers both exceeded 2%. Other than the two
Combi D transducers, the ES120-7 exhibited the largest change
in fr(T ).
Plots were also made of Q(T ) (Figure 6). The results varied: Q
decreased with T (ES18, ES120-7, ES120-7C, and ES200-7C);
increased with T (ES38-B, ES70-7C, and 200-28E); and both
decreased and increased with T (ES38-12, Combi D-50, and
Combi D-200). Changes in Q(T ) ranged from 2.5% for the
200-28E to .130% for the ES120-7 and ES120-7C. Of the splitbeam transducers, the ES70-7C and ES38-B exhibited the smallest
changes in Q(T ), 4% and 7%, respectively.
Estimating M0(T) and S0(T)
Estimates of M0(T ) and S0(T ) were plotted for fEK60 (Figure 7).
Changes in these parameters with T should correspond directly
to changes in g0. Generally, M0(T) and S0(T ) changed 1 dB or
less, either decreasing or remaining fairly stable. A notable
Variations in echosounder–transducer performance with water temperature
exception was the ES120-7, which exhibited an increase of 2 dB
in M0(T) and S0(T ).
Estimating h(T)
Admittance circles [susceptance (B; mS) plotted against conductance (G; mS) as a function of frequency] were plotted for nine
of the ten transducers (Figure 8). Measurements were made with
the transducers loaded (in water) and unloaded (in air). Because
Simrad transducers are equipped with a window, effectively creating a coupled-resonance system, G( f ) exhibits two separate peaks
when operating in air, and one broad peak in water. Also, for the
Combi D-50, fr was appreciably different when loaded and
unloaded, and the admittance circles did not overlap. The
unloaded admittance circles for the ES18 were malformed
because the frequency resolution was too low for a transducer
with such a high Q. This meant that the DA had to be estimated
from an estimated Gmax, which may be slightly less than the
actual Gmax. Consequently, the h(T) estimated for the ES18
(Figure 9) is less precise than that for the other transducers, and
possibly biased a little low. The unloaded admittance circles for
the ES38B, ES120-7, 200-28E, and Combi D-200 transducers
were also very small, so the resulting estimates of their h(T ) are
of dubious accuracy.
For a fixed Vp-p, Pt is higher for the unloaded than for the
loaded transducers because of the decrease in Z. When an
unloaded transducer is driven with high power, there is a risk
that the ceramics stretch too much and break, or the sound
window separates from the elements, or both such developments
occur (L. N. Andersen, Simrad, pers. comm.). Following the
in-air measurements, impedance measurements were made of
the ES38-B, ES120-7, and 200-28E transducers in water, to
confirm that the transducers had not been damaged.
Discussion
The variations in ES120-7 performance were pronounced relative
to the other transducers tested. For example, M0 and S0 changed
by 2 dB with T ranging from 18C to 178C. Such large variations in the performance of this transducer model with T inspired
these investigations (Demer and Hewitt, 1993; Demer, 1994).
Although most of the transducers we tested were more stable
against T, even the newest materials and designs are susceptible
to the problem. For example, the ES200-7C exhibited a 1-dB
change in M0 and S0 with T ranging from 18C to 178C
(Figure 7). Because the performance of each transducer is different
against T, changes in SNR(T), and in M0(T) and S0(T) and hence
g0(T ) are different for each frequency, and multiple-frequency
methods for target identification can be compromised.
Substantial changes in Q(T) were evident for all the transducers
tested (Figure 6). These changes may be inconsequential for short
pulses at a single frequency, but may become important when
using these transducers for broad-bandwidth applications.
Simrad has recently begun marketing new multibeam echosounders (ME70) and multibeam sonars (MS70) that use composite
materials and a design similar to the ES70-7C. The Q of the
ES70-7C changes 5% with changes in T from 18C to 178C.
Employed as both a transmitter and receiver, the effects of the
change could be doubled.
Variations in the performances of echosounder transducers
with temperature can be characterized precisely using the
methods employed here. Each method provides additional
insight into the transducer performance against T. Note,
1033
however, that the results of these experiments are probably only
valid for the transducers tested, and should not be generalized to
other transducers of the same models. Variations in transducer
materials and manufacturing tolerances will probably yield variations in the temperature-dependence of transducer performance
within any transducer model. Therefore, the results of these experiments should only be used to gauge the magnitudes of the potential errors associated with temperature-dependent transducer
performance for these models.
Ultimately of consequence are the performances of the
echosounder-transducer pairs, which combine the characteristics
of the transceivers with changes of Z, fr, Q, M0, S0, and h with
T. Therefore, changes in g0(T) should be characterized for each
echosounder–transducer pair. To do so, the self-reciprocity
method could be used to ensure that these measurements are
not dependent on the temperature-dependent performances of
other hydrophones and/or projectors (Van Buren et al., 1999),
or the temperature-dependent longitudinal and transverse sound
speeds of materials comprising a standard sphere (Foote and
MacLennan, 1984). The resulting characterizations of g0(T)
could be coupled with continuous measurements of transducer
temperatures actively to maintain the correct echosounder-system
gains between pre- and post-survey calibrations using the standard
sphere technique (Foote et al., 1987). Therefore, this source of
uncertainty could be minimized in the processes of multifrequency target identification and biomass estimation.
Conclusions
To conclude and summarize, Z, fr, Q, M0, S0, and h were measured
against T for the Simrad ES18, ES38-B, ES38-12, ES70-7C,
ES120-7, ES120-7C, ES200-7C, ES200-28E, Combi D-50, and
Combi D-200 transducers, i.e. all the transducers tested. All parameters changed appreciably over the measured range of potential
operational temperatures (1–188C), but the directions of these
changes were not consistent or monotonic. In general, the performances of the newer composite transducers were least sensitive
to changes in T.
Changes in Z with T can result in significant changes in
SNR(T), potentially different for each transducer, which can
result in frequency-dependent measurement biases and changes
in maximum detection ranges. In fact, multifold changes in observation ranges can result, and differ with frequency (see Demer,
2004). The effectiveness of multifrequency algorithms for remotetarget classifications can therefore be compromised.
Changes in the transducer performances with T may also affect
calibrated echosounder gains with T. In fact, changes in M0(T ) and
S0(T ) (Figure 7) should correspond directly to changes in g0, considering changes in c(T ). Therefore, g0(T ) should be characterized
for each echosounder–transducer pair and used to adjust the
on-axis system gains during surveys using measurements of transducer or seawater temperature. Moreover, changes in c(T ) need
also be considered (see Foote, 1991, for details). By adopting
temperature-dependent calibration procedures, this contribution
to random and systematic survey error can be minimized.
Acknowledgements
We appreciate the help we received from Derek Needham, Mike
Paterson, and Hannes Smit, STS, in designing and constructing
the transducer-mounting plate, multiplexer, and junction box.
Steve Sessions and Douglas Krause, AST, are thanked for assembling, transporting, and setting-up the large transducer array,
1034
and Charles Coughran and David Anglietti, SIO, for accommodating the experiments at Deep Tank. We are also very appreciative of
the helpful discussions, guidance and review of this work by
Charles Greenlaw and the constructive reviews of an early
version of this paper that came from Håvard Nes, Lars Nonboe
Andersen, and Frank Tichy, of Simrad. Roger Hewitt, Mike
Soule, and Nicolas Colson are thanked for assisting with earlier
investigations into transducer performance with temperature,
and John Simmonds, Alex De Robertis, and three anonymous
reviewers for their constructive comments on various drafts.
Funding for the investigation was provided by the NMFS
Advanced Sampling Technology Working Group.
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Variations in echosounder–transducer performance with water temperature
1035
Continued
Appendix
Symbols and corresponding descriptions and units.
Symbol Definition
Unit
B. . . . . . . . . . . . . . . . ..Susceptance
S
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
c. . . . . . . . . . . . . . . . ..Speed
of sound
m s–1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
d
Transducer directivity
Dimensionless
. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Width
of
unloaded
admittance
circle
S
D
A
. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Width
of
loaded
admittance
circle
S
D
w
. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
EK500
operational
frequency
kHz
f. .EK500
. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
EK60 operational frequency
kHz
f. .EK60
. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
frequency
kHz
f. .r. . . . . . . . . . . . . . ..Resonance
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
G
Conductance
S
. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
g. . 0. . . . . . . . . . . . . . ..On-axis
system
gain
Dimensionless
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Maximum
conductance
(occurs
at
f
)
S
G
max
r
. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Minimum conductance
S
G
min
. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
current
A
I. .t. . . . . . . . . . . . . . ..Transmitter
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
J. . . . . . . . . . . . . . . . ..Reciprocity
at 1 m
W mPa22
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
p
j. . . . . . . . . . . . . . . . ..Imaginary
number ( 21)
Dimensionless
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Receiver
free-field
voltage
response
V mPa21
M
0
. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
p. . . . . . . . . . . . . . . . ..Pressure
dbar
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
power
W
P. . .n. . . . . . . . . . . . . ..Noise
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
electrical power
W
P. . .r. . . . . . . . . . . . . ..Received
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
electrical
power
W
P. . .t. . . . . . . . . . . . . ..Transmitted
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Q
Quality
factor
Dimensionless
. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
r
Range from transducer to air –water
M
interface
. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
R
Resistance
V
. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Symbol Definition
Unit
range
of
1
m
M
r. .0. . . . . . . . . . . . . . ..Reference
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
s. . . . . . . . . . . . . . . . ..Salinity
Dimensionless
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S. . . . . . . . . . . . . . . . ..Siemens
S
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
current
response
mPa
A21 at 1 m
S. . 0. . . . . . . . . . . . . . ..Transmitting
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
snr
Signal-to-noise ratio
Dimensionless
. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SNR
Signal-to-noise ratio
dB
(dimensionless)
. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
coefficient
m21
s. .v. . . . . . . . . . . . . . ..Volume-backscattering
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
T
Temperature
8C
. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
V
Peak-to-peak
voltage
V
p-p
. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Open-circuit
voltage
V
V
r
. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
X
Reactance
V
. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Y
Electrical
admittance
S
. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Z. . . . . . . . . . . . . . . . ..Electrical
impedence
V
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Z’
Total impedance
V
. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Reflectional impedance
V
Z. . .ref
. . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
a
Absorption
coefficient
dB m21
. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
h
Electro-acoustic transducer efficiency
% (dimensionless)
. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
u. . . . . . . . . . . . . . . . ..Phase
8
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
l
Wavelength of sound
m
. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
r. . .c. . . . . . . . . . . . . ..Characteristic
impedance
of
water
kg m22 s21
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
r. . . . . . . . . . . . . . . . ..Water
density
kg m23
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
s
Backscattering cross-sectional area
m2
. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
t. . . . . . . . . . . . . . . . ..Pulse
length
ms
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C
Equivalent two-way solid beam-angle
sr
Continued
doi:10.1093/icesjms/fsn066