ESTIMATING SHALLOW WATER BOTTOM GEO-ACOUSTIC
PARAMETERS USING AMBIENT NOISE
DAJUN TANG
Applied Physics Laboratory, University of Washington, 1013 NE 40th St., Seattle WA 98105, USA
E-mail: [email protected]
Knowing bottom geo-acoustic parameters is of great importance for using sonar systems
effectively in shallow waters. In this paper, ambient noise data recorded on a vertical
hydrophone array taken in the frequency range of 1000 to 3000 Hz were used. Forward
modeling and model/data comparison show that the energy ratio of down-looking and
up-looking beams, after proper average over time and frequency, is the energy reflection
coefficient of the bottom. From the reflection coefficient, critical parameters of the
sediments, the sound speed, density and attenuation coefficient, are obtained. Core data
taken at the experimental site support the inversion results.
1 Introduction
This paper is motivated by the desire of devising a practical and reliable way to estimate
sediment geo-acoustic parameters in shallow water. In shallow water environments, sound
propagation is dominated by modes corresponding to small grazing angles, as such, the
sound field is greatly influenced by the presence of sediments, especially the surficial layer
of sediments. Therefore, knowing the geo-acoustic parameters of the surficial sediments is
of crucial importance for improving sonar performances in shallow water regions. Direct
measurements of reflection loss is difficult and impractical, since at least one pair of
well separated source and receiver are needed, and such scheme only provides reflection
coefficient at one particular grazing angle. In addition, at small grazing angles this
approach is prohibitively challenging because the presence of shallow water boundaries.
In this paper, we present a method of estimating key sediment parameters using
ambient noise recorded on a vertical line array. The parameters obtained this way are the
compressional sound speed, the density, and the attenuation coefficient. The approach
has the following advantages:
1. Needs only a single measuring station with a vertical array.
2. Is passive.
3. Provides data over wide frequency band.
4. With a moving vertical array, provides potential for large area survey.
5. Needs no knowledge of the noise sources.
6. Has potential to be applied to range-dependent environments since the array is sensitive only to local modes.
The idea of taking advantage of the presence of ambient noise to measure bottom
properties is not new. For examples, Deane and Buckingham >dH, Buckingham and
147
N.G. Pace and F.B. Jensen (eds.), Impact of Littoral Environmental Variability on Acoustic Predictions and
Sonar Performance, 147-154.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
148
D. TANG
Carbone [2], and Harrison [3] presented models and model/data comparisons of vertical coherence of noise and provided a basis for using coherence to invert for bottom
properties. Extensive numerical evaluations of such models are also available [5]. Carbone et al. [4] used that approach to estimate both the compressional and shear wave
speeds. While the vertical coherence is simple to measure, for this method to be applicable, certain conditions on the noise source have to be met, which in many environments
are not the case.
A team of Russian scientists led by Furduev has reported their work on using ambient
noise to estimate bottom relection coefficient in deep water [6–8]. Their approach is based
on ray theory and uses a vertical line array to measure up- and down-looking beams, and
from which estimates the bottom energy reflection coefficient as a function of angle and
frequency.
Our approach in the present paper is very similar to that used by the Russian scientists.
However, since we work in a shallow water area where modal interference is strong, no
simple analytical results can be obtained. For our experiment scenario, numerical analysis
shows that the energy ratio of the down- and up-looking beams of noise is indeed the
energy reflection coefficient of the bottom, provided that averaging over frequency as
well as time is performed. At small grazing angles, the noise comes from distant sources;
near normal incidence (large grazing angle), the noise in our case comes from the ship
from which the vertical array is deployed; there is no appreciable noise in the mid-grazing
angles. The energy reflection coefficient at small grazing angles provides information on
sediment sound speed, whereas that at large grazing angles gives information on sediment
density. Information concerning bottom attenuation coefficient are found in both grazing
angle regions.
We will in the following two sections present experimental data and modeling results,
respectively, and conclude by discussions.
2
Experiment
During May and June, 2001 in the East China Sea, as part of the Office of Naval Research
sponsored ASIAEX experiment, noise over the band of 500 to 5000 Hz was recorded on
a 31 element vertical array, which was deployed from the research ship the Melville.
The experiment was conducted in an area where many small fishing boats are within
visible range, and shipping and wind noise are also present. In addition, the Melville
was performing dynamic positioning, therefore engine noise from the Melville is a major
source to be considered. The water depth in the experiment site is 105 m. The sound
speed profile in the water column corresponding to the time of the noise measurements
was measured from CTD casts and is given in Fig. 1. It is a typical summer time profile
with a thermocline extending to a depth of 30 m. The sound speed below the thermocline
(deeper than 70 m) is essentially a constant, where the vertical line array is deployed.
The element spacing is 21.43 cm, the sampling rate is 12,000 Hz, and the noise band
recorded is 500 to 5000 Hz. Segments of noise data, each 0.5 s long, are taken every 5 s
on each of the 31 elements of the array. The data segments are bandpass filtered and
Fourier transformed. At each frequency bin from 1000 to 3000 Hz, beams are formed
using all elements and a Hanning window. The beam angle ranges from −90◦ (uplooking) to +90◦ (down-looking) with one degree increments. The square of the absolute
ESTIMATING GEO-ACOUSTIC PARAMETERS USING AMBIENT NOISE
149
0
20
Depth (m)
40
60
80
100
120
1518
1520
1522
1524
1526
1528
1530
1532
Sound Velocity (m/sec)
Figure 1. Sound speed profile obtained from CTD measurements.
1
0.9
Directionality (arbitrary units)
0.8
dotted:
fc = 1250 Hz
dashed:
f = 1750 Hz
c
solid:
f = 2250 Hz
c
dot−dashed: fc = 2750 Hz
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−100
−80
−60
−40
−20
0
20
40
60
80
100
Grazing Angle (degree)
Figure 2. Directionality from data.
value of the beams are termed Directionality. Figure 2 gives the directionality that was
first averaged over 50 data segments in the same frequency bins, and was then averaged
over neighboring frequencies of 500 Hz. In the figure, directionality is given for four
center frequencies. The values of the directionality from different frequencies show the
relative strength of the noise field over the frequency band, with decreasing strength versus
increasing frequency. The directionality of all four frequencies show similar features: (1)
A minimum at zero grazing angle, caused by the fact that the noise sources are all near
150
D. TANG
Ratio of down−looking to up−looking directionality
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
10
20
30
40
50
60
70
80
90
Grazing Angle (degree)
Figure 3. Ratio of down-looking directionality to the up-looking directionality from data. The 4
curves correspond to frequencies as given in Fig. 2. The crosses are the average of result from all
four frequency bins.
the sea surface and the thermocline minimizes the excitation of modes with very small
grazing angles. This will be further explained in the next section. (2) Within 20◦ there is
a peak on either side of the minimum, with the one corresponding to up-looking beams
larger than the one corresponding to the down-looking beams. These beams are associated
with noise trapped in the waveguide and propagated from long distance to the array. (3)
The large peak on the left of the figure is due to the self noise from the Melville, and
the small peak on the right is the reflected beam by the bottom of the self noise. The
ratio of the down-looking directionality to that of the corresponding up-looking one is
given in Fig. 3. We will show in the next section that this ratio corresponds to the energy
reflection coefficient of the bottom.
3
Modeling
We assume that the noise filed with frequency f on an array element at depth z can
be modeled as the summation of a large number of un-correlated points sources of the
following modal form:
!
√
pj (z) = aj
φn (z)φn (zj )eikn rj / rj
n
= aj
!
√
φn (zj )eikn rj / rj (e−ikzn z + Vn eiψn eikzn z ),
(1)
n
where aj is the source strength, zj and rj are the depth and range of the source, kn is the
complex eigenvalue of mode n of the waveguide, and kzn is the vertical wavenumber of
ESTIMATING GEO-ACOUSTIC PARAMETERS USING AMBIENT NOISE
151
0
10
20
30
Depth (m)
40
50
60
70
80
90
100
110
−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
Normalized mode function amplitude
Figure 4. Modes number 1 (dotted), 15 (dot-dashed) and 30 (solid) at 2000 Hz. Notice that modes
1 and 15 have low amplitudes near the surface
mode n. The quantity Vn is the bottom reflection coefficient at the particular frequency
associated with an angle related to the eigenvalue, and ψn is simply a phase factor
accumulated through one cycle in the water column for mode n. This expression is true
only when the receiver array is in a region where sound speed profile is a constant. In
the expression φn is the depth-dependent mode function. Figure 4 shows three mode
functions versus depth and demonstrates that lower order modes have little excitation if
the source is near the surface.
To form a beam at direction θ, we have
!
Bj (θ) = aj
φn (zj )eikn rj [b(k sin θ − kzn ) + Vn eiψn b(k sin θ + kzn )],
(2)
n
where k is the wavenumber at depth zj and b is the array response of a beam pointed
at angle θ. Sum over all sources, and average over realizations, we obtain the following
expression for the directionality:
!
!!
|aj |2
φn (zj )φ∗n! (zj )ei(kn −kn! )rj [b(k sin θ − kzn ) +
< |B(θ)|2 > ≈
j
iψn
Vn e
n!
n
b(k sin θ + kzn )][b(k sin θ − kzn! ) + Vn! eiψn b(k sin θ + kzn! )]∗ (3)
where the star represents complex conjugate and < ... > represents averaging over realizations. If the array has an ideal response: b(θ) = δ(θ), then
!
!
|aj |2
|φn (zj )|2 ,
< |B(θn )|2 > =
n
j
2
< |B(−θn )| > =
!
j
|aj |
2
!
n
|φn (zj )|2 |Vn |2 ,
(4)
and the energy reflection coefficient |Vn |2 can be obtained by the ratio of the two beams.
However, for a finite-length array such as the one used, we do not have a close form result
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D. TANG
1
0.35
f = 1250 Hz
Directionality
0.25
0.6
0.2
0.4
0.15
0.1
0.2
0
−100
0.05
−50
0
50
100
0.25
0
−100
−50
0
50
100
0.08
fc = 2250 Hz
0.2
Directionality
fc = 1750 Hz
0.3
c
0.8
fc = 2750 Hz
0.06
0.15
0.04
0.1
0.02
0.05
0
−100
−50
0
50
Grazing Angle (degree)
100
0
−100
−50
0
50
100
Grazing Angle (degree)
Figure 5. Model/data comparison of beam directionality. The dotted curves are data, solid curves
are model results.
showing that the ratio of the two terms in Eq. (4) is the energy reflection coefficient. Here
we used KrakenC [9], a normal mode code, to simulate the array response to the noise
field. For a given frequency, we assume that there are 200 independent point sources
randomly distributed near the sea surface. The ranges of the sources are 100 to 5000 m.
The depth of the sources is also random and ranges from 0.1 to 5.0 m. The contribution
of the 200 sources are summed on each element on the array and beamforming was
performed at all angles. This constitutes one realization. Repeating this for 100 time,
and an average is obtained. The same procedure was performed for many frequencies,
with 50 Hz increments. Further, the beam output from neighboring frequency bins (500
Hz total) was also averaged. By comparing the simulation results to those from data, and
changing bottom parameters in the normal mode code, we arrive at a set of ”optimal”
results (eyeball fit). The results are given in Fig. 5. Note that the model results are
scaled to fit the experiment result. The set of parameters used in the Kraken code for
this optimal case are: sound speed is 1600 m/s, density is 1.78 g/cm3 , and the attenuation
coefficient is 0.11 dB/m kHz. The energy reflection coefficient based on these parameters
is given in Fig. 6, along with simulation results and results from data.
Cores were taken [10] in the experiment site. Analysis of the core show that the
surficial sediment has a sound speed of 1600±10 m/s from 11 out 14 cores taken. This is
consistent with our result from noise analysis. So far density and attenuation coefficient
analysis from cores are not available.
153
ESTIMATING GEO-ACOUSTIC PARAMETERS USING AMBIENT NOISE
Energy Reflection Coefficient
1
0.8
0.6
0.4
0.2
0
0
10
20
30
40
50
60
70
80
90
Grazing Angle (degree)
Figure 6. Energy reflection coefficient from data and model. The solid curve is the theoretical
energy reflection coefficient. The circles are results from simulations averaged over realizations
and all frequency bins. Others are the same as those in Fig. 3.
4
Discussion
Summarizing the results from data analysis and simulations, we found that by averaging
over time segments (for data) and realizations (for simulations), we obtained approximate
energy reflection coefficient with considerable fluctuations. By further averaging over a
wide band of frequencies, the ratio of the down- and up-looking directionality converges
to the true energy reflection coefficient.
What needs to be done to further validate this approach is to conduct a detailed
statistical analysis through simulations. A set of criteria should be established to guide
field data processing.
Since the vertical array response is sensitive only to local geo-acoustic conditions,
this approach can potentially be used to conduct surveys in shallow water with changing
sediment composition.
Another intriguing possibility is to use the data in mid-angles, where there is no real
noise source, to estimate bi-static bottom and surface scattering coefficients.
Acknowledgements
This work was supported by the U.S. Office of Naval Research, Code 321OA.
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154
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