ASSESSING THE VARIABILITY OF NEAR-BOUNDARY
SURFACE AND VOLUME REVERBERATION USING
PHYSICS-BASED SCATTERING MODELS
ROGER C. GAUSS, JOSEPH M. FIALKOWSKI AND DANIEL WURMSER
Naval Research Laboratory, Code 7144, Washington, DC 20375-5350, USA
E-mail: roger.gauss@nrl.navy.mil
The increased importance of responding to regional conflicts has focused Navy attention
on littoral waters, with active sonar expected to be a favored mode of operation. Major
performance drivers of such systems are the acoustic interactions with the ocean
boundaries and fish. The vicinity of the air-sea interface is in particular a complex mix
of scattering by surface roughness and scattering from bubble clouds and fish, coupled
with boundary-interference effects. The Naval Research Laboratory has recently
developed broadband, physics-based scattering strength models that both unify and
advance our understanding of boundary scattering at low frequencies (< 5 kHz) by
providing a physical basis for isolating scattering mechanisms. In this paper, these
models are used to assess both the sensitivity of scattering strength to environmental
variables and their utility as tools for estimating these variables. These efforts are
supported by a series of data-model comparisons that demonstrate both the
environmental variability of acoustic response with frequency and scattering angle, and
the importance of using physics-based tools to predict these responses.
1
Introduction
For a low- (50–1000 Hz) or mid-frequency (1–5 kHz) active sonar, scattering from the
ocean boundaries and biologics, coupled with propagation conditions, can severely limit
the detectability of returns from features of interest. Furthermore, reverberation levels
can vary dramatically, depending on the local geology, oceanography, and biology.
Hence, making accurate predictions of active sonar performance will in turn depend on
finding suitable models that accurately describe the scattering.
The Naval Research Laboratory (NRL) has been developing physics-based models of
scattering strength [1,2]. By having a physics basis, the models allow extrapolation in
frequency and to any 3-D scattering geometry. The models have proved essential for
isolating scattering mechanisms, and so further the understanding of the complex
acoustic interaction processes at the ocean boundaries.
This paper uses several of these physics-based models to explore the sensitivity in the
upper ocean of surface and volume (fish) scattering strength to the grazing angle, the
acoustic frequency, biological descriptors of the fish, and physical descriptors of the
environment. In this case, the total scattering strength (in dB) is
SS = 10 ⋅ log10 (σ int + σ bub + σ fish ) ,
345
N.G. Pace and F.B. Jensen (eds.), Impact of Littoral Environmental Variability on Acoustic Predictions and
Sonar Performance, 345-352.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
(1)
346
R.C. GAUSS ET AL.
where
σ
is the scattering cross section per unit area, and
σ int ,σ bub ,σ fish
represent the
contributions due to the rough air-sea interface, bubble clouds and fish, respectively.
(MKS units will be used throughout this paper.)
FISH
+SURFACE
(b)
INTERFACE
3.0 m/s
Figure 1. Measured backscattering strength vs. grazing angle and frequency: (a) surface scattering
at two wind speeds (February 1992) and (b) surface + salmon scattering (May 1984).
Figure 1 illustrates some of the variability of SS that can be expected due to
environmental and biological factors. Shown are at-sea data collected using SUS charges
in the Gulf of Alaska [1]. Figure 1a illustrates the dramatic differences in surface
scattering strength between low and high sea states. The narrow band of curves
corresponds to a wind speed of 4.5 m/s and exhibits almost no frequency dependence,
while the set of curves to the left corresponds to a wind speed of 17.9 m/s and exhibits a
strong, non-monotonic — peak at ~925 Hz — frequency dependence, with levels
elevated up to 30 dB over the lower wind speed data. Figure 1b shows the interesting
behavior when fish are added to the mix. In this low-wind speed case, scattering from
salmon exhibits a complex frequency behavior, with levels elevated up to 20 dB over
air-water-interface scattering at low grazing angles above 130 Hz.
This paper begins with a discussion of the scattering characteristics of the ocean
surface (air-sea interface and bubble clouds), followed by a discussion of the scattering
characteristics of dispersed bladdered fish near the ocean surface. For simplicity, in this
paper we restrict ourselves to monostatic backscattering geometries as they will still
illustrate the key relationships. We end with a few comments and recommendations.
2
Surface scattering
Surface scattering is caused by the interaction of acoustic energy with environmental
features at or near the ocean surface. The dynamic nature of the air-sea boundary
interaction zone complicates this process. As the winds and seas increase, air becomes
entrained by breaking waves in the form of subsurface bubbles. Under these conditions,
VARIABILITY OF SURFACE AND VOLUME REVERBERATION
347
both the rough air-sea interface and bubble clouds may contribute to the acoustic
scattering. (For surface scattering strength (SSS), we set σ fish ≡ 0 in Eq. (1).)
2.1
Scattering Model
Interface scattering strength σ int is well modeled by lowest-order small slope theory
[3,4], which requires as input the surface-wave roughness spectrum. The sea surface
contains many scales of roughness, from the long gravity waves to the short capillary
waves. Scattering from a rough interface is proportional to the spectral density at the
Bragg wavelength with modifications due to tilt and modulation by longer waves. While
a variety of directional surface-roughness spectral models are available, for this paper we
assume an isotropic, pure power-law spectral model:
S ( K ) = ASU / K γ 2
,
(2)
where K is the surface wavenumber and U is the wind speed (in m/s) at an elevation of
10 m. With this spectral model, σ int depends primarily on three environmental
parameters: U , AS , and γ 2 . Typical open-ocean values of the latter two parameters are:
3
γ 2 ∈ (3.4, 4) and AS ∈ (5 × 10−5 ,20 × 10−5 ) m -s. Best-fit values to low wind-speed
Critical Sea Test (CST)-7 data were: γ 2 = 3.8 and AS = 19 × 10−5 m3-s.
A semi-empirical approach is used to model σ bub . In the ocean, breaking waves
generate subsurface bubbles whose properties are governed by advective transport, gas
dissolution, and buoyancy. At low frequencies (~5 kHz or less), acoustic scattering from
bubbles depends primarily on the air-void fraction, and not on the details of the bubble
distribution. Our semi-empirical model derives from a stochastic model of Gilbert [5],
replacing some of its terms with ones whose parameters were empirically determined
from a variety of open-ocean data. The monostatic result is:
σ bub =
0.006d 5.15k03.4 sin 4 θ
(1 + d 2k02 sin 2 θ )(1 + 4d 2k02 sin 2 θ )
,
(3)
where k0 = 2π f / c0 (with f the acoustic frequency and c0 the sound speed in bubble-free
water), and d is the air-void fraction e-folding depth, quadratically related to the wind
speed U [5] via an empirical formula of Farmer and Vagle (derived from CST-7 data)
[6]. Thus, σ bub depends primarily on one environmental parameter: U .
2.2
Parameter Study
Figure 2 plots the dependence of SSS on grazing angle, frequency and wind speed. In
this study, we set: γ 2 = 3.9 and AS = 2 × 10−4 m3-s. This figure illustrates that bubble
clouds become an increasingly important driver of backscattering strength with both
increasing frequency and wind speed, and with decreasing grazing angle. Figures 2a-c
show the strong dependence of σ bub on wind speed and, below ~1 kHz, on frequency. It
348
R.C. GAUSS ET AL.
has a fairly flat dependence on grazing angle, especially during appreciable winds. In
contrast, Figs. 2d-f show that σ int has a very strong dependence on grazing angle, but a
relatively weak dependence on frequency and wind speed. As a result, when wave
breaking is significant, SSS can have a complex dependence on angle, frequency and
wind speed (Figs. 2g-i).
BUBBLE CLOUDS
(a)
(b)
(c)
AIR-SEA INTERFACE
(e)
(d)
(f)
TOTAL
(h)
(g)
(i)
Figure 2. Monostatic predictions of scattering strength versus grazing angle, frequency and wind
speed for: (a)-(c) bubble clouds only, (d)-(f) interface only, and (g)-(i) bubble clouds + interface.
The model for σ int is more complex than σ bub in that it also depends on the
roughness spectrum through AS and γ 2 as illustrated in Fig. 3. Figure 3c shows that as
γ 2 decreases from 4, σ int exhibits increasing frequency dependence. (With our choice of
S in Eq. (2), σ int depends on frequency only through its dependence on γ 2 and is
VARIABILITY OF SURFACE AND VOLUME REVERBERATION
349
frequency independent if γ 2 = 4 [4].) The other figures show generally monotonic
increases of σ int with decreasing γ 2 and increasing AS , but that this can depend on the
range of angles, wind speeds, and frequencies under consideration. In general, γ 2 drives
the frequency dependence, and both γ 2 and AS the level. The range of possibilities will
expand when more sophisticated spectral models are considered in the future.
(b)
(c)
o
1500 Hz
60
o
AS = 0.0002
30
o
10
θ
U = 20 m/s
U = 20 m/s
(e)
(d)
1500 Hz
γ 2 = 3.9
(f)
o
60
o
30
o
10
Figure 3. Monostatic predictions of interface scattering strength as a function of grazing angle,
wind speed and frequency, for two sets of surface-wave spectral variables: (a)-(c) and (d)-(f).
3
Volume scattering
Due to their variety and dynamic nature, estimating the scattering contributions of fish is
particularly challenging. When fish are well separated from the ocean surface or bottom,
recognizable broadband acoustic signatures identifying their presence and strength have
been observed [1]. However, when fish are in the vicinity of an ocean boundary, as is
common in the littoral, these characteristic fish signatures can undergo significant
modification due to boundary-interference effects.
3.1
Scattering Model
Below 10 kHz, the primary scattering mechanism of most fish is their air-filled
swimbladder [7], typically occupying just ~5% of a fish’s volume. The acoustic response
depends on the bladder size, which in turn primarily depends upon the fish’s size and
depth. (The frequency response changes with depth as its bladder compresses due to the
increased water pressure at the deeper depths—e.g., the single salmon of Fig. 4a.) For a
layer of dispersed fish, we take their total scattering to be the incoherent sum of
scattering from the individuals, and so depends on their depths, sizes and total number.
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R.C. GAUSS ET AL.
When a fish is near an ocean boundary, the scattering picture increases in complexity.
Besides backscattering from the rough air-sea interface, fish backscatter energy to a
receiver along multiple paths. The relative time delay of these various paths generates a
(Lloyd-mirror) pattern of constructive and destructive interference, the intensity of
which depends strongly on the surface grazing angle θ, the distance of the scatterer from
the boundary, and the acoustic frequency. This can significantly alter the free-field fish’s
backscattered intensity (by a factor between 0 and 16—Fig. 4b), leading to a rich variety
of frequency and grazing-angle behaviors, especially at low grazing angles:
z2
σ fish = 16 ∫ ρ ( z )σˆ bladder ( f , z )sin 4 ( k0 z sin θ )dz
(4)
z1
for bladdered fish of density ρ and mean target strength (TS) σˆ bladder (m2) in layer(s)
covering depths z1 to z 2 ( z2 > z1 ). Figure 4c shows an example of this modification
at θ = 10 degrees for the single salmon of Fig. 4a (assuming a swimbladder radius of r0
= 0.015 m). (Note the enhanced scale of Fig. 4c.)
For practical applications of this model as a kernel in a reverberation model, a
layer of fish is treated as locally spatially (and temporally) uniform, which in turn is
treated as an effective modifier of boundary conditions. Hence, it can be used like a
surface scattering strength, with no need to introduce a separate layer into the modeled
waveguide. (A corresponding formula for fish near the ocean bottom may be found in
Ref. 2.)
(a)
-45
(b)
-35
-25
-8
(c)
(dB)
+12 -33
-23
-13
Figure 4. Monostatic predictions of near-surface fish scattering. (a) Free-field salmon scattering;
and at θ = 10 o : (b) surface acoustic interference pattern and (c) near-surface salmon scattering.
Figure 1b showed a real-world example of backscattering from salmon in the
presence of the air-sea interface in the Gulf of Alaska. Figure 5a shows our model
prediction for these data. Using our model, salmon depths were inferred to be 2.5 to 7
meters. (The contribution of the rough interface is included in the modeling and is shown
as a dashed line in Fig. 1b.) This data-model comparison shows that even at relatively
low densities—a few hundred individuals per square kilometer during this measurement
[1], fish near resonance can dominate interface scattering at low grazing angles.
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VARIABILITY OF SURFACE AND VOLUME REVERBERATION
3.2
Parameter Study
Figures 5b-c show how this picture can change when the depth of the salmon layer
changes. These correspond to typical CST-7 nighttime and daytime depth ranges,
respectively. (Here, we now have U = 5 m/s for the SSS contribution.) This shows when
the fish are very shallow, the Lloyd-mirror pattern suppresses the resonance pattern (and
the data resemble interface scattering). In contrast, when the salmon are deeper and
spread over a greater depth range, their grazing-angle behavior becomes flat with a clear
resonance (in this case at ~500 Hz).
2.5-7 m
15-40 m
0.5-2 m
(a)
(b)
(c)
Figure 5. Monostatic predictions of near-surface salmon + interface scattering for 3 depth ranges.
Figure 6a-b illustrates the sensitivity of the TS of a particular fish, the salmon, to its
size (as parameterized by r0 ) and depth, respectively. Figure 6a shows that for a given
depth, there is a strong sensitivity to fish size. That said, often an ensemble of fish of a
given species in the ocean are of comparable size so that their depths become more of a
driving factor. Figures 5 and 6b explore this for the salmon, and Fig. 6c for another
species, the rockfish [2]. While size and depth are key parameters for a given species,
the general volume scattering picture is even more complicated, as TS depends on more
than just z and r0 [2]. Adding to the acoustical complexity are their species-dependent
diurnal and seasonal behaviors, as well as their temporal and spatial variability.
Salmon
Salmon
Rockfish
Depth 10 m
r0 = 0.01 m
r0 (m)
(a)
0.02
0.01
0.005
0.0025
0.00125
50
10
1
Depth
(m)
1000
(b)
1
250
10
50
250
(c)
1000
Figure 6. Modeled free-field fish TS vs. frequency for (a) 5 swimbladder radii at a depth of 10 m
and at (b)-(c) 5 depths for a swimbladder radius of 0.01 m.
352
4
R.C. GAUSS ET AL.
Discussion
In general, measures of sonar performance depend nonlinearly on the reverberation,
which in turn depends nonlinearly on environmental variables. A key benefit of the
models presented is that they allow a systematic determination of the relative influence
of these environmental inputs on the strength of the acoustic scattering. In turn, used as
scattering submodels in reverberation models, they allow a more accurate estimation of
the relative influence of the environment on sonar performance. Furthermore, by
independently varying the values of the environmental parameters, the resultant impact
on the scattering can be estimated in a statistical sense. Hence, the relative variability or
uncertainty in sonar performance can be assessed, and the expected variance modeled.
While these models promise improved predictions of mean scattering levels,
technical issues remain. A primary need is high-quality acoustic and
environmental/biological data to provide the ground truth necessary to rigorously
evaluate the models, and to assess the generality and limitations of their physical
assumptions. Additional needs include a deeper understanding of fish behavior and the
physical properties of bubbles, and robust methods to statistically measure/assess them
in situ.
We close with some recommendations for any scattering measurement:
• Maximize the frequency and grazing-angle coverage to sort out scattering
mechanisms and help invert for environmental parameters.
• Perform day/night measurements to help sort out the fish contributions.
Acknowledgements
This work was supported by the Office of Naval Research. The authors are grateful for
continuing technical discussions on fish acoustics with Dr. Redwood W. Nero (NRL).
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