VARIABILITY OF THE ACOUSTIC RESPONSE FROM
SPHERICAL SHELLS BURIED IN THE SEABED
BY MODEL-BASED ANALYSIS OF AT-SEA DATA
A. TESEI, A. MAGUER AND W.L.J. FOX
SACLANT Undersea Research Centre, Viale S. Bartolomeo 400, 19138 La Spezia, Italy
E-mail: tesei@saclantc.nato.int, maguer.alain@tms-pty.com, warren@apl.washington.edu
R. LIM
CSS/Dahlgren Naval Surface Warfare Centre, Panama City, Florida 32407-7001, USA
E-mail: LimRA@ncsc.navy.mil
H. SCHMIDT
Dept. of Ocean Engineering, MIT, Cambridge, MA 02139, USA
E-mail: henrik@keel.mit.edu
The acoustic response from elastic spherical shells buried in the seabed is studied in the
bandwidth 1–15 kHz as a function of changing environmental parameters. The targets
are either partially or completely buried in the seabed or in the free field. Particular
attention has been paid to the elastic surface-guided waves circulating around the target,
which are expected to provide significant features for target classification. The variations
of their dynamics with the environment were studied by comparing at-sea monostatic
data with appropriate models. Three identical spherical shells were measured under
different conditions during the GOATS experiment conducted jointly by SACLANTCEN
and MIT in 1998. This paper reports the data interpretation results compared with
theoretical expectations demonstrating the strong influence of the environment on target
response.
1 Introduction
Mines that are completely buried in sandy bottoms are generally considered to be undetectable and unclassifiable by conventional high frequency (k x( ,<9) minehunting
sonars due primarily to the low levels of energy that are transmitted into the sediment
at these frequencies at the low grazing angles used. As the attenuative effect of the
sediment is less at lower frequencies, the possibility of using much lower frequency
sonars, with higher fractional bandwidth (1–15 kHz), has been investigated for detection
and classification of proud and buried mines. At high frequency, the acoustic scattering
by mine-sized targets ( d 8) is well described by geometrical theory of diffraction,
but at lower frequencies (W c n( ,<9), man-made targets in particular may support the
excitation of strong structural waves or resonances that are consistent with their typical
structural symmetries and can represent potentially significant classification clues.
Past experimental and modelling work has provided evidence for the excitation of
structural waves in completely buried spherical shells, including investigations on the
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N.G. Pace and F.B. Jensen (eds.), Impact of Littoral Environmental Variability on Acoustic Predictions and
Sonar Performance, 497-504.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
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Figure 1. Experimental geometry.
sensitivity of the target response to burial depth, sediment type and grazing angle [1].
The excitation of target resonances for flush and partially buried targets has been investigated using new modelling capabilities [2]. This paper focuses on the dynamics of
the predicted structural waves of a thin-walled, steel spherical shell in the bandwidth
2–15 kHz. Appropriate models of elastic waves dynamics [3] are also used. The target
typology is ideal for the study as the free-field scattering physics is relatively simple
to model and well understood. Theoretical considerations will be validated with at-sea
measurements acquired during GOATS’98. This paper will be limited to the analysis
of backscattering with insonification above critical grazing for three identical spherical
shells: one half buried, one flush buried, and one completely buried.
2
Experimental setup
The GOATS’98 experiment [4] was carried out on a sandy bottom in 12–15 m water off
the island of Elba, Italy. The TOPAS source was used to insonify the targets with a highly
directional beam in the frequency range 2–16 kHz (secondary frequency) with a vertical
beamwidth of 3◦ –5◦ and horizontal beamwidth of about 8◦ . The far field is estimated to
start at about 35 m in front of the transducer while the volume of nonlinear interaction is
estimated to extend for the first 11 m. The experimental configuration is shown in Fig.1.
In order to acquire data from various source-receiver geometries, the transmitter was
mounted on a 10 m tower, which in turn was mounted on a 24 m linear rail on the bottom.
A linear receiving array of 16 hydrophones (94 mm-spaced) was mounted vertically in a
near-monostatic configuration. Three identical spherical shells were deployed in line with
the rail at different burial depths (about 35 cm into the sediment, flush and half-buried).
One of the shells was also measured suspended in the water column. The shells were
air-filled, thin-walled, steel, nominally of 53 cm radius and 3 cm wall thickness, and with
a steel lug for deployment. As the spheres were constructed by welding two hemispherical
shells together, there was the possibility of thickness nonuniformity.
The average density of the sediment was 1.91 g/cm3 . The sediment propagation loss
was estimated to be 0.5 dB/λ, the sound speed 1640 m/s [4] and the sand critical angle
22◦ .
ACOUSTIC RESPONSE OF BURIED SPHERES
3
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Theoretical concepts and models
Scattering models for a spherical shell either in the free field or buried in the seabed are
used for the study of acoustic variability with the environment. Models are developed
in the frequency domain and provide the scatterer transfer function. The modelled and
measured spherical shells have the same nominal elastic parameters (steel compressional
speed cp = 5950 m/s, shear speed cs = 3240 m/s, density ρ = 7.7 g/cm3 ), the density of
the sea water is set to 1 g/cm3 and its sound speed is set to the measured value 1520 m/s.
Under free field conditions the acoustic pressure scattered by an elastic fluid-filled
spherical shell insonified by an incident plane wave is represented by a partial wave series
(PWS) model. In the case of fully and partly buried spherical shells the scattering model
used is based on transition- (T-) matrix solutions for the scattered field [1, 2].
In the low-to-medium frequency range, for thin air-filled spherical shells, the elastic
contribution to scattering is due to the lowest-order flexural and compressional waves of
the shell [1]. Their resonance frequencies appear as sharp dips or peaks of the scattering
spectral response, and will be predicted through the models developed in [3] based on the
application of the shell theories with modified inertia to the scattering of a thin-walled
spherical shell. The symmetric (or compressional) S0 Lamb-type wave is supersonic,
almost non-dispersive, and travels in the shell with phase and group speeds asymptotically
tending to the shell material membrane speed, c∗shell . The antisymmetric (or flexural),
A0 Lamb-type wave of a spherical shell in vacuum bifurcates into two dispersive waves
upon fluid loading. Of the two, the wave that more strongly influences the acoustic
scattering amplitude, hence that is selected as a potentially robust classification clue, is
the subsonic A0− Lamb-type wave. At low frequencies (until its phase speed approaches
the outer-medium sound speed at the so-called coincidence frequency, fc ), it is flexural
in nature. Around the coincidence frequency the A0− wave starts to behave like a fluidborne wave, becoming difficult to detect with increasing frequency because of increased
radiation damping. Its group speed reaches its maximum at the coincidence frequency.
First we will study a sphere completely buried in different sediment types (Fig. 2).
Assuming that the water-sediment interface cannot significantly influence the target response for completely-buried cases at supercritical grazing, the sphere is simulated as
flush-buried in order to minimize signal loss due to burial. Theoretically [1, 2], the dynamics and energetic contribution to backscattering of the S0 wave should not be unduly
influenced by the external fluid, or by burial, except for a slight shift towards lower
frequencies of its first modes as the external density increases. The shift should decrease
as the modal order (and frequency) increases. Similarly, at low frequency the effect of
fluid loading on the dynamics of the A0− wave is essentially inertial: its first free-field
modes are predicted to shift to lower frequencies as the exterior density increases. As the
A0− wave becomes fluid-borne in nature, it is predicted to be much influenced by the
exterior, as its phase speed tends to the exterior sound speed.
The effect of burial depth will be considered in the following (Fig. 3). At low
frequencies, a shift of the first S0 and A0− wave modes to lower frequencies is expected
with burial, due to the significantly greater inertial loading of the shell in the sediment
possessing grater relative density than water. The shift should increase with the percentage
of target surface in contact with sediment. In the coincidence frequency region, the phase
speed of the A0− wave approaches the exterior sound speed, which is higher when the
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Figure 2. a) Amplitude of the form function of a buried spherical shell as the external fluid changes.
b) Model of the related dispersion curves of S0 and A0− waves.
Figure 3. a) Amplitude of the form function of a spherical shell as burial depth changes from
partially to deeply buried. b) Model of the related dispersion curves of S0 and A0− waves.
target is completely buried. This means the modes of the A0− wave that are excited
around fc are expected to experience an upward shift upon burial. For partial burial,
we hypothesize that these modes will again shift consistent with the percentage of target
surface in contact with sediment. Hence, the simple empirical formula cext ≈ fc 2πd
ACOUSTIC RESPONSE OF BURIED SPHERES
501
Figure 4. Ray diagram of the travel path of the Lamb-type S0 (left) and A0− (right) waves in
the case of partial burial. The travel path of the A0− wave is drawn outside the shell in order to
emphasize its fluid-borne nature around the coincidence frequency. The wall thickness is not in
scale.
(being cext the external medium loading the shell), which was shown to be valid for steel
and similar materials is extended to the case of partial burial. If the shell is loaded by
more than one fluid the target exterior will be treated as an effective medium characterized
by an effective sound speed ceff
ext such that:
ceff
ext ≈ fc 2πd.
(1)
This assumption should be reasonable for determining the dispersion characteristics of
the S0 and A0− waves if the dominant contributions to the backscatter from these waves
are from complete circumnavigations of the shell. Under these circumstances, one might
f
also expect cef
ext to be defined by a weighted harmonic average of the sound speeds of
the two exterior fluids in order to account for propagation of the exterior diffracted field
f
through both fluids. Similarly the effective external density ρef
ext will be defined as an
average of the water and sediment densities, ρw and ρs , respectively weighted by the
fractions Vw and Vs of the total volume V of the sphere loaded by water and sediment:
eff
ceff
ext = L/(Lw /Cw + Ls /Cs ), ρext = (Vw ρw + Vs ρs )/V,
(2)
where Lw and Ls are the wave pathlengths around the sphere in water and sediment
respectively, L = Lw + Ls , Cw the water sound speed and Cs the sediment sound speed.
On the basis of the above definitions, the models used for the dispersion curves of the S0
and A0− waves [3], originally developed in the free field, are applied also to the case of
a partly-buried sphere. A simplified scheme of the travel paths of the S0 and A0− elastic
waves around the coincidence frequency is shown in Fig. 4 in the case of partial burial.
The dynamics of these waves are not expected to be significantly influenced by the
grazing angle of sound on the seabed, as shown by the simulations in Fig. 5. Even in
the case of subcritical insonification, no significant change in the resonance locations is
detected. For this reason we will compare the dispersion curves of waves scattered by
spheres buried at various depths, even if measured at different grazing angles, which will
be maintained low in order to limit reverberation, but above the sediment critical angle
in order to increase penetration.
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Figure 5. Amplitude of the form function of a buried sphere as the grazing angle θg varies.
Figure 6. Model-data comparison of the spectral response by free-field, half-, flush- and deeplyburied spheres. The results of resonance mode extraction and identification are superimposed.
4
Experimental results
For model-data comparison the simulated transfer functions are convolved with the model
of the incident pulse and inverse transformed in time. A Ricker function centered at 8 kHz
is used for the incident pulse. The data selected are the aligned coherent average of 50
pings of the beamformed acquisitions by the vertical array. While the free-field target
could be measured in the far field of the source so that the far-field, free-field model
presented in Sect. 3 is applicable, the proud and buried targets were measured in the nearfield of the TOPAS and the T-matrix model was adapted to simulate directional sound
beams in the near-field of the source. The model-data comparison is shown in Fig. 6 for
the free-field, partially-, flush- and deeply-buried spheres in the frequency domain. The
ACOUSTIC RESPONSE OF BURIED SPHERES
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Figure 7. Experimental dispersion curves of S0 wave as the sphere burial depth varies.
Figure 8. Experimental dispersion curves of A0− wave as the sphere burial depth varies.
S0 and A0− wave modes are extracted by the approach described in [5], and identified
on the basis of model-data comparison.
The free-field (FF) spherical shell was measured at a range of 35 m. Model-data
agreement is generally good, except for mismatch in the mid-frequency region, presumably
due to the sphere nonuniform wall thickness, and evident also in the other data sets. For
the half-buried (HB) shell measurements, the grazing angle was about 26◦ and the range
22 m. The best fit is obtained for a burial depth of 10.6 cm below the sphere equator
and a sand sound speed set to 1647 m/s. The estimate of the effective external sound
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speed obtained from Eq. (1) is 1555 m/s. This result validates the hypothesis that even
when the A0− wave becomes fluid-borne in nature, it continues to revolve around the
whole spherical shell. For the flush-buried spherical shell, the measured grazing angle
was 35◦ and the range 18 m. Equation (1) provides the outer medium speed estimate of
1652 m/s. For the measurements of the deeply-buried spherical shell, the grazing angle is
about 42◦ and the range 16 m. The best fit with the model was found by setting the burial
depth to 35 cm from the top of the target and the sand sound speed to 1652 m/s. Due to
the attenuation caused by propagation through the sand, the A0− wave level decreases
significantly. In all buried cases, a significant mismatch can be noticed at low-frequency
(for f < 2.5 kHz) and beyond 13 kHz presumably due to a significant decrease of the
signal-to-reverberation ratio.
The wave analysis is performed in terms of wave speed dispersion curves (Figs. 7
and 8). The free-field, half-buried, and flush-buried cases are compared first in order to
analyze the wave characteristics as the percentage of shell surface loaded by the sediment
increases from 0 to 100. The trend of the S0 curves (Fig. 7) are in agreement with theory
and the models used in Sect. 3. Between the flush-buried and deeply-buried cases the
changes in wave dynamics are slight [1] as the corresponding dispersion curves almost
coincide. The nature of the A0− wave (Fig. 8) has been correctly predicted by theory
and models. As for the S0 wave, also for the A0− wave, the changes in dynamics
between the flush-buried and deeply-buried cases are slight. Only a slight shift towards
higher frequencies of the deeply-buried A0− highest-order modes is detectable, which is
in agreement with the slightly greater value of the sand sound speed estimated from the
deeply-buried target with respect to the flush-buried case.
In conclusion, the at-sea data analysis, successfully supported by theoretical expectations and models, has allowed the evaluation of the sensitivity of elastic target scattering
to burial at low-to-medium frequency.
Acknowledgements
The authors wish to thank E. Bovio, M. Mazzi and M. De Grandi, who contributed greatly
to the success of the experiment. Thanks also to the Engineering and Technology Dept.
of SACLANTCEN and the MANNING crew, for their professional support in the trial.
References
1. Lim, R., Lopes, J.L., Hackman, R.H. and Todoroff, D.G., Scattering by objects buried in
underwater sediments: Theory and experiment, J. Acoust. Soc. Am. 93(4),1762–1783
(1993).
2. Lim, R., Scattering by partially buried shells. In Proc. ICA/ASA Meeting (AIP, New York,
1998) pp. 501–502.
3. Kaplunov, J.D., Kossovich, L.Yu. and Nolde, E.V., Dynamics of Thin Walled Elastic Bodies
(Academic Press, San Diego, 1998).
4. Maguer, A., Fox, W.L.J., Schmidt, H., Pouliquen, E. and Bovio, E., Mechanisms for subcritical
penetration into a sandy bottom: Experimental and modeling results, J. Acoust. Soc. Am.
107(3), 1215–1226 (2000).
5. Tesei, A., Fox, W.L.J., Maguer, A. and Løvik, A., Target parameter estimation using resonance
scattering analysis applied to air-filled, cylindrical shells in water, J. Acoust. Soc. Am.
108(6), 2891–2900 (2000).