his paper presents an application of an acoustic signal characterization scheme for ocean acoustic tomography and geoacoustic inversions proposed by Taroudakis et al., using real data.  The work is the first attempt to validate the proposed scheme with data taken from sea experiments. The data have been collected during the SW06 experiment held in the New Jersey Continental Shelf and the inversion results (sea-bed geoacoustic  parameters and source range) are compared with those reported by Bonnel and Chapman. The comparison and the signal reconstruction using estimated values of the model parameters is satisfactory being an indication that the new signal characterization method can be used in practical applications of acoustical oceanography

Chapman, Ross

Smaragdakis, Costas

Taroudakis, Michael

English

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Inversion of acoustical data from the SW06 experiment, using a
statistical method for signal characterization
Michael Taroudakis and Costas Smaragdakis and Ross Chapman
Original Citation:
Taroudakis, Michael and Smaragdakis, Costas and Chapman, Ross
(2013)
Inversion of acoustical data from the SW06 experiment, using a statistical method for signal
characterization.
(Unpublished)
This version is available at: http://preprints.acmac.uoc.gr/278/
Available in ACMAC’s PrePrint Repository: February 2014
ACMAC’s PrePrint Repository aim is to enable open access to the scholarly output of ACMAC.
http://preprints.acmac.uoc.gr/Inversion of acoustical data from the SW06 experiment,
using a statistical method for signal characterization
Taroudakis Michael
Department of Mathematics and Applied Mathematics, University of Crete
University Campus, 70013, Heraklion, Crete, Greece
FORTH, Institute of Applied and Computational Mathematics
Smaragdakis Costas
Department of Mathematics and Applied Mathematics, University of Crete
University Campus, 70013, Heraklion, Crete, Greece
FORTH, Institute of Applied and Computational Mathematics
N. Ross Chapman
School of Earth and Ocean Sciences, University of Victoria,
P.O.Box 3055, Victoria, BC, V8W3P6 Canada
December 27, 2013
Abstract
This paper presents an application of an acoustic signal characterization scheme
for ocean acoustic tomography and geoacoustic inversions proposed by Taroudakis
et al. [1], using real data. The work is the ﬁrst attempt to validate the proposed
scheme with data taken from sea experiments. The data have been collected during
the SW06 experiment held in the New Jersey Continental Shelf and the inversion results
(sea-bed geoacoustic parameters and source range) are compared with those reported
by Bonnel and Chapman [2]. The comparison and the signal reconstruction using
estimated values of the model parameters is satisfactory being an indication that the
new signal characterization method can be used in practical applications of acoustical
oceanography.
1I Introduction
In 2006 a multipurpose experiment (SW06) was carried out oﬀ the coast of New Jersey.
For geoacoustic inversion purposes, light bulb were dropped in water and the sound of their
implosion, which occurred at a depth of approximately 22 m were recorded at a distance
about 7 km away from the source location. The geoacoustic model of the environment where
the experiment was held is illustrated in Fig. 1. It is a shallow water waveguide with range-
independent characteristics. The water depth (79.1 m)a n dt h es o u n ds p e e dp r o ﬁ l ei nt h e
water (Table 1) were known. The sea-bed is described as a two layer medium with a sand layer
of approximately 20 m thickness overlying a harder substrate. For the purposes of our study,
both layers will be considered as ﬂuid. The recordings were made at an array of hydrophones
but in the present work a single recording of a hydrophone placed at the depth of 67.1 m was
used. One of the tasks of the experiment was the validation of geoacoustic inversion schemes.
To this end, the sound speeds and densities of the sediment layer and the substrate as well
as the thickness of the layer and the actual range of the source were the unknowns to be
recovered. Bonnel and Chapman [2] presented inversion results based on dispersion curves
estimation using warping operators to improve mode separability. It was our purpose to
use same data from the experiment under consideration to test the applicability of the new
method of signal characterization based on the statistical distributions of the wavelet sub-
band coeﬃcients already presented in [1] and validated with simulated data as in [3, 4, 5], in
real world applications. The scheme will thereafter be cited as ”SCS”. An important issue in
this respect is the modeling of the source excitation function which will be brieﬂy presented
in the next section. Section III presents the inversion results to be discussed in Section IV.
II Simulation of the Source Excitation Function
For inversion purposes, the SCS is associated with an optimization process based on repeated
simulations of the received signal for a class of candidate environments. The simulations are
2Depth z (m) Sound Speed Proﬁle cw (m/s)
0.0 1525.0
10.0 1525.0
27.0 1483.0
79.1 1490.0
Table 1: The sound speed proﬁle in the water column.
made by calculating the system transfer function H(xs,xr;ω), where xs and xr are the source
and receiver position vector respectively, at a speciﬁc frequency ω multiplying it with the
source excitation function S(ω),
p(xs,xr;ω)=H(xs,xr;ω)S(ω), (1)
repeating this process for all frequencies in the eﬀective signal bandwidth and taking the
signal in the time domain by inverse Fourier transform. Here, the system transfer function
is calculated using a forward propagation model, which in our case is the MODE1 program
based on normal-mode representation of the acoustic ﬁeld). Therefore, the source excitation
function must be given or calculated prior to the application of the inversion algorithm. Raw
data of the light bulb implosions implied that the eﬀective bandwidth of the acoustic signals
was from 30 to 200 Hz ([2]). Thus, we passed the raw data from a band-pass ﬁlter allowing
frequencies in this spectrum. By further inspection of the signal spectrum we decided to
model the source signal using a Gaussian excitation function with central frequency f0 =
150 Hz and bandwidth ∆f = 100 Hz :
S(ω)=
1
2π · ∆f
√
2π
exp
￿
−
(ω − 2π · f0)2
2(2π · ∆f)2
￿
. (2)
At this point, we needed a validation test for the eligibility of the Gaussian as a model
of the light-bulb excitation function. This was in particular important as the Gaussian
function is not an obvious simulation of the light bulb signal function. To this end, we
used the estimated values of the bottom geoacoustic parameters by Bonnel and Chapman
3to simulate the received signal using the hypothesis of a Gaussian excitation function. The
values estimated by Bonnel and Chapman appear in Table 2.
For consistency reasons we have used in our study the same recording as in the case
of Bonnel and Chapman’s inversions. Figure 2 presents a comparison of the energy signiﬁ-
cant part of the actual signal (recording) after the band-pass ﬁlter has been applied (dashed
line) with respect to the simulated signal, using the inversion results of Bonnel and Chap-
man (continuous line), the Gaussian source excitation function as described above and the
Normal Mode program MODE1 for the calculation of the system transfer function. The
comparison can be considered satisfactory although not perfect. Changing the parameters
of the Gaussian function no improvement was observed. Eventually we decided to use this
speciﬁc excitation function for inversion purposes.
III The Inversion Procedure and Results
Following the work by Taroudakis et al. [1] an acoustic signal is characterized by the statis-
tical parameters of the wavelet sub-band coeﬃcients. In particular, for typical signals used
in applications of Acoustical Oceanography, it has been shown that the wavelet coeﬃcients
obey a symmetric alpha stable distribution (SaS) characterized by two parameters (α,γ).
For a L-level wavelet analysis, the signal can be characterized by L detailed and 1 approxi-
mation coeﬃcient vectors Φ, each one of which consisting of only two elements. Hence the
signal feature is represented by a vector d as following:
S ↔{ Φ
0,...,Φ
L}↔d =[ ( α
0,γ
0,α
1,γ
1,...,α
L,γ
L)]
T, (3)
where T denotes the transpose.
It has been shown in previous works [3, 4, 5] that L =3i sa na d e q u a t el i m i to ft h e
multilevel analysis of typical underwater acoustic signals. Therefore in our work we have
4used a feature vector in R8
d =[ α
0,γ
0,α
1,γ
1,α
2,γ
2,α
3,γ
3]
T (4)
for signal characterization.
For the geoacoustic inversion experiment under consideration, the six unknown parame-
ters can be described by a vector in R6 as
m =[ r,cp,ρ p,h,c b,ρ b]
T (5)
Using the concepts described above, the following non-linear inverse problem is formu-
lated :
• Given a single acoustic signal characterized by the vector d,e s t i m a t et h em o d e lp a -
rameters m given a certain propagation model and the speciﬁc signal characterization
scheme (SCS), jointly described by means of the vector function T through an equation
of the form :
T(d,m)=0 ( 6 )
The problem being non-linear and ill-posed is amenable to a solution based on an opti-
mization process, where the cost function is chosen so that the statistical character of the
feature vector is exploited. It has been shown that the Kullback-Leibler Divergence (KLD)
written analytically for the case of SaS distributions by the following closed form relation :
Ds(S1,S 2)=
L ￿
k=0
￿
ln
￿ck
2
ck
1
￿
−
1
αk
1
+
￿γk
2
γk
1
￿αk
2 Γ(
αk
2+1
αk
1 )
Γ( 1
αk
1)
￿
, (7)
5where Γ(x) is the Gamma function and
c
k
i =
2Γ( 1
αk
i
)
αk
iγk
i
,i=1 ,2 ,k=0 ,...,L. (8)
is an appropriate cost function [4] expressing the diﬀerence between signals S1 and S2.
The optimization process in our work is controlled by a Genetic Algorithm (GA) (see
[4, 5]). Here, the GA was applied for 50 generations of 80 individuals each, with probabilities
of crossover 0.8a n dm u t a t i o n0 .02. The search space was chosen to be exactly the same
as in the work by Bonnel and Chapman [2] . Figure 3 presents the a-posteriori probability
distribution of the individual members of the ﬁnal population indicating by cross symbol the
best individual of the GA algorithm and by ”x” the inversion results obtained by Bonnel
and Chapman.
Both inversion results are presented in Table 2. The results by Bonnel and Chapman are
denoted as ”B-C” and the results by the SCS are denoted as ”SCS”.
The comparison of the results obtained by the two totally diﬀerent inversion schemes can
be summarized as following :
The source range estimated by both methods is practically the same. The sound speed
in the sediment layer is estimated by the two methods with a diﬀerence of approximately
15 m/sec. The diﬀerence for most applications of acoustical oceanography is not considered
important. The sound speed in the substrate is estimated by the two methods with a diﬀer-
ence of 75 m/sec. Although this diﬀerence in absolute terms seems considerable, given the
fact that he substrate is very hard this diﬀerence again can be considered as non-important.
The densities of the sediment layer and the substrate are estimated by the two methods with
values exhibiting larger diﬀerences. It is however well known that the density is among the
parameters that are hardly estimated by acoustical means with high accuracy. Finally the
sediment thickness estimated by the two methods gave diﬀerent values. It is interesting to
note that the results by Bonnel and Chapman indicate value at the upper limit of the search
6space, whereas in the SCS results the best individual lies in the middle of the search space.
Moreover the inversion results by the SCS method indicate a thickness much closer to its
a-priori estimation being approximately 20 m.
By comparing the energy signiﬁcant part of the signal simulated using the inversion
results of the two methods and the MODE1 program for the calculation of the system
transfer function (Fig. 4), it can be seen that the diﬀerences are not important. The two
sets of model parameters lead to signals with very similar shape. This is an interesting
result, suggesting that the inversion scheme based on the statistical characterization of the
recorded signal can give estimations of the model parameters that reproduce the signal in
similar quality with respect to other inversion schemes.
Unknown Parameters B-C estimations SCS estimations
Range r(m) 6951.0 6958.8
Sediment sound speed cp(m/s) 1603.0 1586.1
Sediment density ρp(g/m3) 1890.0 2022.2
Sediment thickness h(m) 26.9 21.0
Basement sound speed cb(m/s) 2199.0 2121.3
Basement density ρb(g/m3) 2280.0 2657.1
Table 2: Inversion results
IV Conclusions
The paper presented a ﬁrst attempt to apply a new method of acoustic signal characterization
for geoacoustic inversions with real data. A Genetic Algorithm was used in the optimization
process associated with the characterization scheme and the source excitation function was
modelled by a Gaussian function. The inversion results were compared with those reported
by Bonnel and Chapman [2] and it was shown that, they lead to a similar reconstruction
of the acoustic signal. The obvious diﬀerences between the actually recorded signal and the
simulated ones can be attributed to the modeling of the source and the presence of noise
which was not taken into account in the simulated signals. The important conclusion from
7the work presented here, is that the acoustic signal characterization scheme based on the
statistics of the sub-band wavelet coeﬃcients validated so far by simulations only, can indeed
be used for geoacoustic inversions in real world experiments.
V Acknowledgments
The work was partially supported by the program ”ACMAC” of the Department of Ap-
plied Mathematics of the University of Crete funded by the European Commission and the
program ”Kripis” of FORTH/IACM funded by the General Secretariat of Research and
Technology of Greece.
References
[1] M. Taroudakis, G. Tzagkarakis, and P. Tsakalides, “Classiﬁcation of shallow water
acoustic signals via alpha stable modeling of the one dimensional wavelet coeﬃcients”,
J. Acoust. Soc. Am. 119,1 3 9 6 – 1 4 0 5( 2 0 0 6 ) .
[2] J. Bonnel and N.R. Chapman, “Geoacoustic inversion in a dispersive waveguide using
warping operators”, J. Acoust. Soc. Am. 130(2),E L 1 0 1 - E L 1 0 7( 2 0 1 1 ) .
[3] G. Tzagkarakis, M.I. Taroudakis, and P. Tsakalides, “A statistical geoacoustic inversion
scheme based on a modiﬁed radial basis functions neural network”, J. Acoust. Soc. Am.
122,1 9 5 9 - 1 9 6 8( 2 0 0 7 ) .
[4] M.I Taroudakis, C. Smaragdakis, “On the use of Genetic Algorithms and a statistical
characterization of the acoustic signal for tomographic and bottom geoacoustic inver-
sions”, Acta Acust. united with Acust. 95,8 1 4 - 8 2 2( 2 0 0 9 ) .
8[5] M. Taroudakis, C. Smaragdakis, “Inversions of statistical parameters of an acoustic sig-
nal in range-dependent environments with applications in ocean acoustic tomography”,
J. Acoust. Soc. Am. 134,2 8 1 4 – 2 8 2 3( 2 0 1 3 ) .
9Figure 1: A geoacoustic model of the environment.
104.7 4.72 4.74 4.76 4.78 4.8 4.82 4.84 4.86 4.88 4.9
 1
 0.8
 0.6
 0.4
 0.2
0
0.2
0.4
0.6
0.8
1
 
 
Time (s)
N
o
r
m
a
l
i
z
e
d
 
a
m
p
l
i
t
u
d
e
Actual and Simulated Signal
Actual Signal (filtered)
Bonnel Chapman Simulated Signal 
Figure 2: Actual and simulated signals. The simulated signal are based on the inversion
results by Bonnel and Chapman.
116500 6600 6700 6800 6900 7000 7100 7200 7300 7400 7500
0
0.5
1
r (m)       
 
 
1560 1570 1580 1590 1600 1610 1620 1630 1640 1650
0
0.5
1
C
p (m/s)  
1400 1500 1600 1700 1800 1900 2000 2100 2200
0
0.5
1
 
p (kg/m
3)
17 18 19 20 21 22 23 24 25 26 27
0
0.5
1
h (m)       
1700 1750 1800 1850 1900 1950 2000 2050 2100 2150 2200
0
0.5
1
C
b (m/s)   
1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800
0
0.5
1
 
b (kg/m
3)
 
 
Figure 3: A-posteriori statistical distributions of the ﬁnal population of the GA. A cross
denotes the value of the model parameter corresponding to the best individual of the ﬁnal
population according to SCS and X denotes the value of the parameter estimated by Bonnel
and Chapman
4.7 4.72 4.74 4.76 4.78 4.8 4.82 4.84 4.86 4.88 4.9
 1
 0.8
 0.6
 0.4
 0.2
0
0.2
0.4
0.6
0.8
1
 
 
Time (s)
N
o
r
m
a
l
i
z
e
d
 
a
m
p
l
i
t
u
d
e
Simulated signals
Taroudakis Simulated Signal
Bonnel Chapman Simulated Signal 
Figure 4: Simulated signals using model parameters estimated by the two inversion methods.
12

A statistical geoacoustic inversion scheme based on a modiﬁed radial basis functions neural network”,

Classiﬁcation of shallow water acoustic signals via alpha stable modeling of the one dimensional wavelet coeﬃcients”,

Geoacoustic inversion in a dispersive waveguide using warping operators”,

On the use of Genetic Algorithms and a statistical characterization of the acoustic signal for tomographic and bottom geoacoustic inversions”, Acta Acust. united with Acust.

Inversion of acoustical data from the SW06 experiment,

using a statistical method for signal characterization

Inversion of acoustical data from the SW06 experiment, using a statistical method for signal characterization

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