XI Session of the Russian Acoustical Society.
Moscow, November 19-23, 2001.
V.V. Bezotvetnykh, V.P. Dzyuba, P.V. Gladkov, S.I. Kamenev,
E.V. Kuz’min, Yu.N. Morgunov, A.V. Nuzhdenko
ACOUSTIC MONITORING OF THE JAPAN SEA SHELF:
EXPERIMENT AND MODELLING
Pacific Oceanological Institute, Far Eastern Branch, Russian Academy of Sciences
Russia, 690041 Vladivostok, 43 Baltiyskaya Street
Tel. (4232) 311-400; Fax (4232) 312-575
E-mail: pacific@online.marine.su
In the issue are presented acoustic tomography scheme for reconstruction of the sound speed profile. It
is based on comparison of the modeling and experimental cross-correlation functions between transmitted and
received broadband sounding signals. The procedure of reconstruction allows minimizing the residual function
between modeling and experimental cross-correlation functions. The results of the numerical and environmental
experiments on the Japan Sea shelf applying this tomography scheme are presented.
In September-October 1999 within the framework of the JASAEX project [1], on the acoustichydrophysical polygon near Gamov Peninsula in the Japan Sea, a series of experiments for water
medium acoustic monitoring with usage of complicated phase-manipulated signals were performed.
The broadband electromagnetic-type source was used. It projected multiplex phase manipulated
signals of M-code, with a symbol selection of 511 and carrier frequency of 250 Hz. Source was placed
at a distance of 200m from the shore and at a depth of 25m (the bottom depth was 27m). Autonomous
receiver was placed at a distance of 15km offshore and a depth of 75m (the bottom depth was 76m).
The hydrological conditions on the shelf, in the arrangement area of receiving/transmitting systems
were characterized by 24-hourly variations of temperature (fig. 1). During processing the experimental
cross-correlation functions K Ex s s0 between
transmitted and received signals were
evaluated.
The results showed what the crosscorrelation function is sensitive parameteres
of the medium sea. In the article the
possibility using of this function to obtain the
sound speed field directly are considered.
r
Let source is situated at point r0 and
radiates the acoustic signal S 0 ( t ) . This source
r
produce at a point r acoustic field
r
S (t , r ) =
1
2π
∞
r r
∫ S 0 (ω ) ⋅ G (ω , r , r0 ) ⋅ e
iω t
dω
,
−∞
where S 0 ( ω ) =
∞
∫S
0
( t ) ⋅ e −i ω t dt -Fourier trans-
−∞
r r
form, G ( ω,r , r0 ) - Green's function, which
Fig. 1. Dependence of water temperature in °C
from time of day at different depths in m
must satisfy corresponding condition on the
boundary of the waveguide and equation

ω2 
r r
r r
∆
+
⋅ G (ω , r , r 0 ) = − 4 π ⋅ δ( r − r 0 ) . The cross-correlation function between transmitted and

2 r 
(
)
c r 

received sounding signals
K ss
(rr, rr0 , t , t 0 ) =
0
1
∞
∫
(2π )2 − ∞
248
S 0 (ω )
2
[
]
r
N
r iω t − t j (r )− t 0
⋅ ∑ A j (r ) ⋅ e
,
j =1
(1)
XI Session of the Russian Acoustical Society.
rr
i.e. in the ray approach we have G ( ω , r , r0 ) =
N
∑A
j =1
Moscow, November 19-23, 2001.
( rr ) ⋅ e − i ω t ( r ) , where j
r
j
r
t j ( r ) and A
j
( rr ) are
amplitude and travel time of the signal along the j-th ray, N is number the rays.
r
Assuming the spectral density of S 0 (t , r0 ) to have following form
S 0 (ω )
2
 B , for ω + ∆ω ≥ω ≥ω − ∆ω
=
.
0 , for other ω
We find real part
K ss
0
(2)
(rr, rr0 , t , t 0 ) in the form
r r
r sin ∆ω (t − t j − t 0 )
2 B∆ω N
A
(
r
)
cosω 0 (t − t j − t 0 ) ,
Re K s s0 (r , r0 , t , t 0 ) =
∑
j
∆ω (t − t j − t 0 )
(2π )2 j =1
(3)
and it is function what we measure. For the monochromatic signal of frequence ϖ 0 we have
(
rr
N
B
) ( ) ∑ A (rr ) cos ω
2π
Re K s s 0 r , r0 , t , t 0 =
2
j =1
j
0
(t − t
j
− t0
)
.
(4)
In the mode approach the Green's function form determinates by propertys of the waveguide
r r
directly. However, can be shown that K s s 0 (r , r0 , t , t 0 ) have same structure as for the ray approach.
The Green's function can be written
∞
r r
r
r r r
r
1
T Ô (ω ,γ , z , z 0 )exp (− i γ ( ρ − ρ 0 )) d γ
G (r , r0 , t , t 0 ) =
∫
∫
(2π )2 − ∞
r
{
where - γ = γ x ( ω ); γ y ( ω )
,
(5)
} is a horisontal component the wave vector of the signal propagating in
the waveguide.
The function (mode)
r
Ô (ω , γ , z , z 0 )
must satisfy following the equation
 d2

ω2
r
+
− γ 2  Ô ( ω , γ , z , z 0 ) = − 4 π δ( z − z 0 )
 2
2
c (z)
 dz

r
r
r
r
The vector ρ and ρ0 are both horisontal component of the vectors r and r0 . The operate T is
(
)
N
r
r
r r
defined as T = ∑ δ γ − γ j for discrete portion of the spectrum γ and T = 1 for continues values γ .
j =1
r
The vector γ can be written a Teylor's series
(ω − ω 0 ) υr +K , where - υr = d ωr is horisontal component of the group
r r
γ =  γ (ω 0 ) +
υ2
d γ ω =ω


r
velosity of the mode Ô (ω , γ , z , z 0 ) . Using two first members the series and assuming what modes
don't dependence from ω near ω 0 we have
∞
r r
r r
r
1
− i (ω −ω 0 ) t (ω 0 )+ i γ (ω 0 )( ρ − ρ 0 )d γr
G (r , r0 , t , t 0 ) =
T
Ô
(
ω
,
γ
,
z
,
z
)
e
, (6)
0
0
∫∫
(2π )2 − ∞
r r
ρ − ρ0 ) r
(
where - t (ω 0 ) =
υ.
υ2
r
Using (1) ,(2) and (6) we obtain for discrete spectrum γ that
0
249
XI Session of the Russian Acoustical Society.
Re K s s
Moscow, November 19-23, 2001.
(
N sin ∆ω t − t − t
j
0
r r
2 B ∆ω
(
r , r0 , t , t 0 ) =
∑
0
(2π )2 j =1
1
r
where - A j ( r ) =
(2 π) 2
(
r
(
∆ω t − t j − t 0
)
( )
Ô ω 0 , γ j ω 0 , z, z 0 e
r
r r
− i γ j ( ω 0 )( ρ − ρ0 )
)
) Re  A
r −iω 0 (t −t 0 ) 
 ,
(r )e
 j
.
Making limits of (7) for ∆ω → 0 we obtain
2B N
r r
r i ω ( t −τ −t )
Re K s s 0 r , r0 , t , t 0 =
Re A j ( r ) e 0 j 0  .
2

(2 π ) j=1 
where - τ j is the travel time j-th mode is measured by the phase velosity of the mode.
(
)
(7)
∑
(8)
Examination the expression (3), (4), (7) and (8) we can see that being discussed correlation
function is determined only by spectral density of the signal and properties of waveguide. The travel
times both of the rays and the modes can be determined under following condition
∆ t = t j +1 − t j >
π
1
=
.
∆ω 2 ∆f
r r
This type of dependence
K s s (r , r0 , t , t 0 )
of both the signal spectrum and waveguide properties
permit to use the cross correlation function directly to solve of the problem inverse in acoustic
tomography of the ocean.
As minimum, we see two ways to decision this problem. First, we can obtain the travel time
and/or parameters of the channel sound. Second, we may solve the problem inverse directly defining
r
of the sound speed c ( r ) as function of coordinates.
Take in to account written up we can permit following main stages of the scheme to decide the
problem inverse:
r
1. Choice a modeling sound speed field c ( r ) and calculate the modeling cross-correlation
r r
function K M s s 0 (r , r0 , t , t 0 ) .
2. Construct a mistake function and formulate task mathematical.
2.1.It is the task of mathematical programming to determine of the travel times or/and
waveguide parameters.
2.2.It is the task of variational calculus to determine of the sound speed field as function of
position.
3. Solve of the formulated problem for necessary us values.
r
The varying of the signal spectrum we can obtain equation systems for parameters of c ( r ) if
need.
The figure 2a shows the modulus of the experimental cross-correlation function
Ex
K s s0 between transmitted and received signals and times that are corresponding to fig. 1. The
procedure of reconstruction of the sound speed profile consists of selection such profile that allows us
t2
minimizing
the
residual
function
r r 2
Ex r r
M
η(β,c 0 ) = ∫ K SS
r
,
r
,
t
−
K
r
, r0 , t ) dt
(
)
(
0
SS 0
0
between
t1
M
Ex
modeling K s s0 and experimental K s s0 function. The results of the reconstruction are shown in fig.
2b and corresponding profiles in fig. 2c.
The obtained sound speed profiles (fig. 2c) correspond to real ones in the area of the
experiment. These profiles are conditioned by temperature field of the sea water showed in the fig. 1.
The theoretical predictions are being based on the fact that cross-correlation function contains
the information about medium ocean in both propagation times of the ray or modes and their
amplitudes. Important, what Green’s function is single for many cases of boundary conditions and
speed sound profiles.
250
XI Session of the Russian Acoustical Society.
Moscow, November 19-23, 2001.
Fig. 2. Modulus of the experimental (a) and the modeling (b) cross-correlation
functions and corresponding to them sound speed profiles (c).
In summary,
It is possible to using cross-correlation function between transmitted and received sounding
signals to obtain the sound speed field directly;
The travel times both of the rays and the modes and their numbers can be determined reliably
under following condition ∆ω ⋅ ∆t ≥ π ;
The task to determine both of the travel times rays and modes and their numbers, or
waveguide parameters may be formulated as the task of mathematical programming;
The task to determine of the sound speed field as function from position may be formulated as
the task of variational calculus.
REFERENCES
1. V.A. Akulichev, V.V. Bezotvetnykh, S.I. Kamenev, E.V. Kuz’min, Yu.N. Morgunov, A.V.
Nuzhdenko, “The Japan/East Sea Acoustic Experiment (JESAEX) Project: Acoustic tomography for coastal
areas,” Proc. Institute of Acoustics, Southampton, UK, 2001, 23, Part 2, pp. 315-320.
251