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Proceedings of the 45th Scandinavian Symposium on Physical Acoustics, Online, 31 Jan – 1 Feb 2022
Open Access
1 ISBN 978-82-8123-022-4
Finite-amplitude sound propagation effects
in fish abundance estimation
Audun O. Pedersen1, Per Lunde1,
Rolf J. Korneliussen2, Frank E. Tichy3
1 University of Bergen, Department of Physics and Technology, P. O. Box 7803,
N-5020 Bergen, Norway
2 Institute of Marine Research, P. O. Box 1870, N-5817 Bergen, Norway
3 Kongsberg Maritime AS, P. O. Box 111, N-3191 Horten, Norway
Contact email: audun.pedersen@uib.no
Extended abstract
Quantitative echosounder measurements for fish abundance estimation relies on high
accuracy in measurements of backscattered acoustic power. As scientific echosounder
systems have evolved in terms of power and accuracy, finite-amplitude sound propaga-
tion effects have become a potentially significant error source. The waveform distortion
due to finite-amplitude propagation manifests itself as excess attenuation at the funda-
mental (operating) frequency and generation of harmonic overtones. The excess attenu-
ation in echosounder measurement results, also referred to as “nonlinear loss”, has been
studied since around year 2000 [1–3]. Advice has been given to limit the transmitted
acoustic power so that the nonlinear loss would be insignificant [4, 5]. The advice how-
ever fails to indicate the residual nonlinear loss when the recommended power limits
are used. Nonlinear loss in echosounder sound beams have been measured experimen-
tally [1, 6–8], in both fresh water and seawater, and simulated [2, 3, 6–8] using the “Ber-
gen Code” finite difference solution [9] of the KZK second-order, parabolic equation [10,
11]. Generation of harmonics has also been studied for its implications for simultaneous
measurement at multiple frequencies [6, 12]. Quantitative experimental and numerical
data have only been obtained for 120 kHz and 200 kHz operating frequencies, while
other frequencies and wide-band signals are also important for marine research applica-
tions.
A formal framework has been established so that nonlinear loss can be described
within the power budget terminology commonly used in fisheries research [6, 13, 14].
The power budget equation used, assuming linear sound propagation, is [15]
where is the volume backscattering coefficient of the target volume at range ,
and
are the transmitted and received electrical powers at the echosounder transducer ter-
minals, respectively, is the absorption coefficient, is the axial transducer gain, is
the equivalent two-way beam solid angle, is the acoustic wavelength, is the small-
signal sound speed, is the effective signal duration, and is an electrical termination
factor.
2
To account for nonlinear loss in the forward (incident) direction, both upon echo-
sounder calibration and field measurements, the power budget equation can be
amended to [8, 13]
is the axial finite-amplitude factor, equal to the ratio of the
axial sound pressure amplitude under finite-amplitude propagation conditions,
, to the theoretical axial sound pressure amplitude assuming no fi-
nite-amplitude effects but otherwise the same conditions.
is the axial finite-
amplitude factor for the case of echosounder calibration, where a reference target with
known target strength is positioned on the sound beam axis at range . The axial finite
amplitude factors are always on the interval (0, 1).
is the beam solid
angle finite-amplitude factor, defined as the ratio between the equivalent two-way beam
solid angles with and without nonlinear loss.
is greater than unity since the
sound pressure amplitude and thus the nonlinear loss are stronger on the sound beam
axis (accounted for by
) and weaker elsewhere. The applicability of this formal
framework has been tested on field survey measurements of volume backscatter from
fish schools [8]. Fair agreement is found between field measurement data and predic-
tions made with the Bergen Code. The agreement has been improved compared to ear-
lier work [6] by applying the Francois-Garrison [16] absorption formula to all frequency
components in the numerical calculations [8].
Figure 1. Calculated correction factor
for nonlinear loss, assuming the transmit
power setting 1000 W upon calibration and field measurements using an EK60 echosounder sys-
tem. The calibration target is positioned on the sound beam axis at the ranges . Left: 120 kHz
operating frequency. Right: 200 kHz operating frequency.
Example simulations are shown in Figure 1 for the Simrad EK60 system with ES120-7C
and ES200-7C transducers, operating at 120 kHz and 200 kHz frequencies, respectively.
The correction factor
is plotted against range for various calibration ranges when a 1000 W power setting
has been used for both calibration and subsequent measurements. Seawater parameters
3
from a survey cruise in the North Sea [6, 8] have been applied in the numerical calcula-
tions.
Measurement errors due to the nonlinear loss are largely systematic. Given a speci-
fied bound on the acceptable measurement uncertainty, illustrated as an example as
0.2 dB by coloured areas in Figure 1, one can balance the applied transmit signal ampli-
tude against the need to correct for nonlinear loss. Such considerations depend on quan-
titative knowledge of the parameters of the specific echosounders considered and of the
seawater as propagation medium.
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