In this paper the Passive Ocean Acoustic Tomography (P-OAT) methodology is presented. This technique, avoiding the use of a dedicated active sound source, estimates
the sea water temperature spatial distribution from the received noise emitted from ships of opportunity. The feasibility of the proposed methodology has been confirmed both by test-runs on semi-synthetic data and by the use of real acoustic and environmental data collected during INTIMATE00 experiment performed on October 2000 in the Atlantic Ocean off the Portuguese coasts

Crise, A.

Gasparini, O.

Jesus, S. M.

Marinis, E. de

Picco, P.

Salon, S.

Sapientia

Passive Ocean Acoustic Tomography: Theory and Experiment   E. de Marinisa, O. Gasparinia, P. Piccob, S. Jesusc, A. Crised, S. Salond  aDUNE via Tracia 4, Roma (I), demarinis@dune-sistemi.com bENEA Marine Environment Research Centre Po.Box 224   19100 La Spezia (I) cSiPlab, University of Algarve, Faro (P) dOGS DOGA Borgo Grotta Gigante, Trieste (I)  Abstract   In this paper the Passive Ocean Acoustic Tomography (P-OAT) methodology is presented. This technique, avoiding the use of a dedicated active sound source, estimates the sea water temperature spatial distribution from the received noise emitted from ships of opportunity. The feasibility of the proposed methodology has been confirmed both by test-runs on semi-synthetic data and by the use of real acoustic and environmental data collected during INTIMATE00 experiment performed on October 2000 in the Atlantic Ocean off the Portuguese coasts.   1. Introduction  The objective of the Ocean Acoustic Tomography (OAT) [1] is to estimate ocean physical parameters (temperature distribution, currents variability, sediment structure) on wide areas using acoustic data analysis ([2], [3]). OAT basic principle relies on dependence of the acoustic propagation on the spatial distribution of the ocean parameters, in particular temperature.  Classical OAT uses a known sound source and in fixed location and, from the inversion of the acoustical pressure or of the travel time of the acoustic pulse received on an hydrophone array, estimates the sound speed field in the area between the source and the receivers; temperature and current field can be then deduced. Even though OAT cannot be regarded as a routine monitoring technique, tomography experiments conducted so far have demonstrated that  OAT can be successfully applied for long-term remote marine environment monitoring. Important oceanographic processes such as the evolution of seasonal thermocline [4], deep water formation [5], El Niño [6] and internal tides can be observed by means of acoustic methods. To face most of the typical problems of active tomography, in this work an innovative approach – passive OAT (P-OAT) – developed in the frame of the TOMPACO project (TOmografia PAsssiva COstiera) is presented. In the passive tomography, differently from classical OAT, the unknown acoustic emission from ships of opportunity passing within the detection/classification range of the receiving array is the sound source [7]. This approach exhibits two main advantages: avoids the need of both economically and operationally expensive signal sources and allows the investigation of areas as wide as those swept by the moving ships.  After preliminary tests on semi-synthetic data, this methodology has been tested with real acoustic and environmental data collected in the framework of INTIMATE00 experiment; this paper reports the results  achieved so far.   2. Passive OAT In Fig. 1 a schematic representation of the link between a (point) source and the generic kth hydrophone (k =1, …, N) of the receiving array is reported. The nth received snapshot segment yk(t,tn) of duration T is the convolution between the signal s(t) emitted by the source (modelled as a member function of a random process in P-OAT), and the (supposed) deterministic channel impulse response gk(t; a), where a=[a1; … , aN]T is the ocean parameters vector (e.g. sound speed profile, bottom properties, absorption) on which the propagation depends.           Fig. 1 – Representation of the acoustic link. For a time-invariant channel and a stationary emitted signal, the link  between the source and the kth receiver is thus formally given by the relation: );();();( nknk tfSfGtfY a=  (1) where the uppercase symbols are the finite time Fourier transforms (i.e. FFT) of the corresponding lowercase symbols and where the dependence from the environmental parameters set a has been explicitly indicated only in Gk(ƒ; a) for sake of simplicity. In vector notation we have );(),(),( agy ftfStf nn =  (2)  where y(ƒ,tn) = [Y1(ƒ,tn), ... ,YN(ƒ,tn)]T and g(ƒ;a) = [G1(ƒ; a), ... , GN(ƒ; a)]T The (incoherent) P-OAT approach can be formally faced using the NxN cross spectral matrix C(ƒ; a) = E[y(ƒ, tn) yH(ƒ, tn)] of the received signal (superscript H is the transpose conjugate) which, from (2), can be expressed as  ),()()],(),([);(2 aWyyaCfftftfEfSnHnσ== (3)  where the NxN matrix W(ƒ; a) = g(ƒ; a) gH(ƒ; a) can be viewed as the cross spectral matrix of a unitary impulsive source and )(2 fSσ = E[|S(ƒ,tn)|2] is the unknown source power spectral density. Nearly all the OAT processors rely on (3), as the estimation of the unknown environmental parameters a can be performed in the usual following steps:  • compute a finite-time estimate  (ƒ; a) of the unknown received cross spectral matrix C(ƒ, a) from the received signals;  • guess an arbitrary environmental parameter vector b and compute the estimate of the propagation matrix  (ƒ; b) =  (ƒ; b)  H(ƒ; b) using  an acoustic propagation model well suited to the measurement area;  • introduce a metric for the distance between (ƒ;a) and  (ƒ;b) and let the guessed environ-mental parameter set b span its physically meaningful ensemble. A possible simple metric D(a,b) of the “distance” between real (unknown) and estimated environmental parameter sets a and b may be  );(ˆ);(ˆ);(ˆ);(ˆ);(ˆ),(bgbgbgaCbgba fffffD HH=  (4) If the propagation model used to estimate the transfer functions vector exactly reproduces the true propagation in the medium, then D(a,b) defined by (4), known as Ambiguity Function, attains one maximum value when the b=a, i.e. when the estimated parameters match with the real ones.   Of course, the basic relation used in the present paper is particularly focussed toward the P-OAT, where the source signal is unknown and no absolute signal phase is available; in different contexts (i.e. active OAT) other approaches may be better suited.  2.1 The passive pre-processing block As the source power spectral density is unknown, before the Ambiguity Function evaluation, the passive OAT has first to select the frequency bins belonging to the propagating signal, rejecting from the subsequent processing the noise bins. In this work, the extraction of the source main sound components relies on the decomposition properties of the received signal cross spectral matrix, whose structure is closely related to the useful signal spectral distribution. Sea surface Receiving array Oceanic Transfer function From the source to the kth receiving hydrophone at frequency ƒ hk(ƒ) Bottom From (3), introducing noise, the (j, k) element of the cross-spectral matrix C(ƒ;a) can be expressed as kjNkjXkj ffWffC ,2,2, )();()();( δσσ += aa  (5) where )(2 fNσ  is the noise power spectral density at frequency ƒ, supposed independent on  hydrophone index. Performing now the singular value decomposition (SVD) of the received cross-spectral matrix C(ƒ; a) we have the relation: );();();();( aUa aVa ffffC H=  (6) where V(ƒ;a), U(ƒ;a) and Λ (ƒ;a) respectively are the left and right eigenvectors matrices and the singular values diagonal matrix of rank R. From (5) and (6), only when the frequency ƒ really belongs to a signal component propagating trough the medium, there is one dominant eigenvalue and V(ƒ;a) and U(ƒ;a) are ill conditioned (rank~1). Thus, whether the source signal or the noise component dominates at given frequency might be assessed by analysing the dominant eigenvalues distribution of the SVD decomposition of the cross spectral matrix C(ƒ;a).   This eigen-decompostion approach reveals more powerful then classical FFT analysis to select the frequencies where the signal can be extracted from noise. FFT approach only analyses the power spectral levels, discarding the spatial coherence information. However, care must be taken in the lower frequency band, if the wavelength appreciably exceeds the hydrophone spacing. In such a case a suitable normalization factor has been inserted in Λ (ƒ;a) analysis to account for the spatially correlated noise effect. The proposed method has been also applied to the experimental passive data collected during the INTIMATE00 sea trial. In Fig. 2 the estimated cross spectral matrix magnitude has been reported for signal and noise frequency bins (vessel moving at 2 Km from the array); in the two cases, the diagonal and off diagonal structure of C(ƒ;a) allows an unambiguous classification and selection of the frequency bins to be subsequently processed by the P-OAT.  A further analysis has been carried out on the experimental data to confirm that the amplitude and relative phase time variability of the C(ƒ;a) is practically negligible during the time window (i.e. 2 sec.) chosen for P-OAT, thus allowing reliable estimates.               Fig. 2 – Cross spectral matrix magnitude on signal and noise bins.  3. INTIMATE00 sea trial campaign The data used to test the tomographic processor were collected in the framework of INTIMATE00 (INternal TIdes Measurements with Acoustic Tomography) experiment, carried out from 15 to 22 October 2000 in the Atlantic Ocean, in front of the Portugal coasts off Setubal.  Acoustic data were collected by a 16 hydrophones Ultra Light Vertical Array (ULVA) also equipped with thermistors, pressure and tilt gauges. The array, floating around a fix position located at 8° 56' W - 38° 18' N at a sea depth of ~110 m, ensured an acoustic aperture between 30 and 90 m.  Environmental condition in the area of the experiment (from 8° 50’W to 9°03’ W and from 38°13’ N to 38° 22’ N) were monitored during the whole period by means of three fixed mooring with currentmeters, temperature and salinity sensors, two thermistor chains, which operated for shorter periods and by XBT profiles taken from the oceanographic vessel. A short description of the main oceanographic characteristics during the experiment can be found in [8] and some preliminary results in [9].  Both acoustic and non-acoustic data collected by the ULVA were transmitted onboard through a radio link, thus allowing a constant quality control, although limiting the distance between the vessel and the ULVA position up to few kilometres.  For the passive OAT test, the oceanographic vessel steamed at a speed of 10 kn following a radial trajectory between the NW and the NE transects, respectively at 1, 2 and 3 km from ULVA position (Fig. 3). The selected ship track insured a quite uniform flat and a mid-range variant bottom. The vessel (acoustic source) position and its relative sea bottom depth were directly recorded onboard. The test lasted about 1 hour and was performed with a good whether condition. The experimental area was free from other vessels.            Fig. 3 – Ship (acoustic source) track for P-OAT experiment from GPS data.  4. Passive OAT results To reduce the parameter space to be inverted, a routine technique in OAT is the SSP decomposition with the Empirical Orthogonal Functions (EOF) [10] which relies on the availability of an SSP historical database in the investigated area. Unfortunately, apart few tens of XBT deployed during the sea trial, the absence of an historical database in the Setubal area led us either to use the limited XBT samples to estimate an EOF base or to steer toward an alternative approach, based on the Hydrostatic Normal Modes (HNM) for which a single mean SSP profile is needed [11]. In the processing carried out so far we addressed to the latter technique: using either the thermistors chains or XBT data a single mean temperature profile s0(z) has been estimated; solving the Navier-Stokes equation in the hydrostatic approximation, the HNMs to be used in the P-OAT inversion have been estimated [12]. In Fig. 4 a thermistors chain temperature has been reported vs. Julian day. In Fig. 5 the first four HNF estimated from thermistors data have been reported. Relying on the HNFs expansion functions Hk(z), z being the depth, we explicitly assume that each unknown SSP s(z) (to be estimated by the P-OAT) may be approximated by the expansion  )()()(10 zHzszs kMkk∑=+= α  (7)           Fig. 4 – A thermistors chain measured temperature vs. time.           Fig. 5 – First 4 HNMs estimated for the experimen-tal area up to 120 m depth. From experimental XBT data, it has been confirmed that, using (7), every experimental SSP collected during the campaign is actually well approximated with only the first 2 or 3 HNM The processed time segment for P-OAT corresponds to 2 sec. data window (start of the 100 sec. track segment indicated in Fig. 3) with a 10 kn ship track at 2000 m nearly constant distance from the ULVA and a nearly flat sea bottom (~103 m) from the ship to the ULVA.  Although the singular value analysis used for the signal bins selection indicated a very high signal component at 366 Hz; a mid-energy signal bin at 100 sec of Vessel track 665 Hz has been selected for the P-OAT subsequent processing. The choice of selecting a less favourable frequency component comes from the need to test the P-OAT feasibility on the more dense spectral components rather then on a unique best-case bin, which is not necessary present in every ship sound spectra.  For the P-OAT processing the assumed environmental model is reported in Fig. 6, with sound source (vessel) distance and depth, array geometry and bottom physical properties (density ρ, absorption α and sound speed c). The SSP reported in Fig. 6 is the one measured by the closest, both in time and space, XBT deployment and it will be used to benchmark the SSP estimated after the P-OAT inversion. For the estimation of   (ƒ; b) in (4) the PROSIM broadband adiabatic normal mode propagation model [13] has been adopted.             Fig. 6 – Environmental model used for the inversion processing with experimental SSP.  P-OAT inversion has been used to jointly estimate, in an unique process, four environmental parameters: the cooperative ship depth, range and the HNM α1,2 expansion coefficients (assuming M=2). The resulting four-dimensional Ambiguity Function has been separately projected for ship sound source location in Fig. 7 and for the two HNM coefficients in Fig. 8. The estimated source location complies with what expected from the vessel used as sound source (~2020 m distance and 0-3 m depth). The presence of an unique maximum in Fig. 8 leads to an unambiguous estimate of the Sound Speed Profile, which has been reported in Fig. 9, together with an SSP actually measured in a nearby position. The agreement between the SSP estimated by P-OAT and the experimental one is satisfactory, also taking into consideration that the measured SSP location doesn’t match with the ship-ULVA propagation line. 5. Conclusions  The first results achieved for passive acoustic tomography performed in the framework of TOMPACO and INTIMATE00 projects have been described. The Sound Speed Profile estimation has been satisfactory achieved by processing the acoustic data of a unknown passive source (vessel) with no a priori information about its distance and depth.            Fig. 7 – P-OAT Ambiguity Function for source range and depth estimation.            Fig. 8 – P-OAT Ambiguity Function for HNM expansion coefficients. c=1750 m/s c=1800 m/s ρ=1.9g/cm3 ρ=1.9g/cm3 α=-0.8 dB/λ α=-0.8 dB/λ 110 m 32 m (1) 92 m (16) 2 m 2000 ±30 m  103 m 0-6 m (source depth)  Acknowledgments TOMPACO project, is carried out in the framework of the program "Mediterranean Environment: analysis and assessment of observation methodologies" partially supported by MURST (Italian Ministry of  University and Scientific and Technological Research.                Fig. 9 – P-OAT estimated SSP and measured SSP in a nearby position.  References  [1] Baggeroer A.B., W.A.Kuperman, and P.N. Mikhalevsky: An overview of match field methods in ocean acoustics. IEEE Journ. Ocean. Engin. 18 (1993) pp. 401-424. [2] Munk W. H. and C. Wunsch. 1979. Ocean acoustic tomography: a scheme for large scale monitoring, Deep Sea Res. 26, 123-161. [3] Munk W., P. Worcester, and C. Wunsch, 1995: Ocean Acoustic Tomography. Cambridge University Press. 433 pp. [4] Skarsoulis E.K., U. Send, 2000: one-step Analysis of nonlinear Traveltime Data in Ocean Acoustic Tomography. Jou. Atmos. Oceanic Tech., 17,  240-254 [5] Send, U., F. Schott, F. Gaillard, and Y. Desaubies, Observation of a deep convection regime with acoustic tomography. J. Geophys. Res., 100,  6927-6941, 1995  [6] Shang, E.C., Y.Y.Wang. 1994. Tomographic Inversion of the El Niño Profile by Using a Matched-Mode Processing (MMP) Method, IEEE Jou. of Oc. Eng., vol. 19(2), pp. 208-213. [7] Gasparini O., C.Camporeale, A.Crise, Intro-ducing Passive Matched Field Acoustic Tomography, Il Nuovo Cimento C, vol. 20(4), Lug.-Ago. 1997, pp. 497-520. [8] Jesus S.M., Tomografia Passiva Costiera Data Report – Phase 1, Rep 01/01 – SiPLAB, CINTAL, Universitade of Algarve, 2001. [9] Demoulin, X., Y. Stephan, S. Jesus, E. Coelho, M.B. Porter: INTIMATE96: a shallow water tomography experiment devoted to the study of internal tides, Proc. of SWAC'97, Beijing. 1997 [10] Le Blanc L.R, F.H. Middleton, An Underwater Acoustic Sound Velocity Data Model, J. Acoust. Soc. Am., 67 (6) (1980) p. 2055. [11] Rodriguez O.C., S. Jesus, Y. Stephan, X. Demoulin, M. Porter, E. Coelho, Internal tide acoustic tomography: reliability of the normal modes expansion as a possible basis for solving the inverse problem, Proceedings of the Fourth European Conference on Underwater Acoustics, Edited by A. Alippi and G.B. Cannelli, Rome (1998). [12] L.A Ostrovsky, Nonlinear Internal Waves in a Rotating Ocean, Oceanology, 2, Vol.18 (1978) pp. 119-125.  [13] Bini-Verona, F., P.L. Nielsen and F.B. Jensen, PROSIM Broadband Normal-Mode Model. A user's guide, (SACLANTCEN SM-358).   

Passive ocean acoustic tomography: theory and experiment

Universidade do Algarve

Passive Ocean Acoustic Tomography: Theory and Experiment  
 
E. de Marinisa, O. Gasparinia, P. Piccob, S. Jesusc, A. Crised, S. Salond 
 
aDUNE via Tracia 4, Roma (I), demarinis@dune-sistemi.com 
bENEA Marine Environment Research Centre Po.Box 224   19100 La Spezia (I) 
cSiPlab, University of Algarve, Faro (P) 
dOGS DOGA Borgo Grotta Gigante, Trieste (I) 
 
Abstract  
 
In this paper the Passive Ocean Acoustic Tomography (P-OAT) methodology is 
presented. This technique, avoiding the use of a dedicated active sound source, estimates 
the sea water temperature spatial distribution from the received noise emitted from ships 
of opportunity. The feasibility of the proposed methodology has been confirmed both by 
test-runs on semi-synthetic data and by the use of real acoustic and environmental data 
collected during INTIMATE00 experiment performed on October 2000 in the Atlantic 
Ocean off the Portuguese coasts.  
 
1. Introduction  
The objective of the Ocean Acoustic 
Tomography (OAT) [1] is to estimate ocean 
physical parameters (temperature distribution, 
currents variability, sediment structure) on wide 
areas using acoustic data analysis ([2], [3]). OAT 
basic principle relies on dependence of the acoustic 
propagation on the spatial distribution of the ocean 
parameters, in particular temperature.  
Classical OAT uses a known sound source and 
in fixed location and, from the inversion of the 
acoustical pressure or of the travel time of the 
acoustic pulse received on an hydrophone array, 
estimates the sound speed field in the area between 
the source and the receivers; temperature and 
current field can be then deduced. 
Even though OAT cannot be regarded as a 
routine monitoring technique, tomography 
experiments conducted so far have demonstrated 
that  OAT can be successfully applied for long-term 
remote marine environment monitoring. Important 
oceanographic processes such as the evolution of 
seasonal thermocline [4], deep water formation [5], 
El Niño [6] and internal tides can be observed by 
means of acoustic methods. 
To face most of the typical problems of active 
tomography, in this work an innovative approach – 
passive OAT (P-OAT) – developed in the frame of 
the TOMPACO project (TOmografia PAsssiva 
COstiera) is presented. In the passive tomography, 
differently from classical OAT, the unknown 
acoustic emission from ships of opportunity passing 
within the detection/classification range of the 
receiving array is the sound source [7]. This 
approach exhibits two main advantages: avoids the 
need of both economically and operationally 
expensive signal sources and allows the 
investigation of areas as wide as those swept by the 
moving ships.  
After preliminary tests on semi-synthetic data, 
this methodology has been tested with real acoustic 
and environmental data collected in the framework 
of INTIMATE00 experiment; this paper reports the 
results  achieved so far. 
 
 
2. Passive OAT 
In Fig. 1 a schematic representation of the link 
between a (point) source and the generic kth 
hydrophone (k =1, …, N) of the receiving array is 
reported. The nth received snapshot segment yk(t,tn) 
of duration T is the convolution between the signal 
s(t) emitted by the source (modelled as a member 
function of a random process in P-OAT), and the 
(supposed) deterministic channel impulse response 
gk(t; a), where a=[a1; … , aN]T is the ocean 
parameters vector (e.g. sound speed profile, bottom 
properties, absorption) on which the propagation 
depends.  
 
 
 
 
 
 
 
 
 
Fig. 1 – Representation of the acoustic link. 
For a time-invariant channel and a stationary 
emitted signal, the link  between the source and the 
kth receiver is thus formally given by the relation: 
);();();( nknk tfSfGtfY a=  (1) 
where the uppercase symbols are the finite time 
Fourier transforms (i.e. FFT) of the corresponding 
lowercase symbols and where the dependence from 
the environmental parameters set a has been 
explicitly indicated only in Gk(ƒ; a) for sake of 
simplicity. In vector notation we have 
);(),(),( agy ftfStf nn =  (2)  
where y(ƒ,tn) = [Y1(ƒ,tn), ... ,YN(ƒ,tn)]T and 
g(ƒ;a) = [G1(ƒ; a), ... , GN(ƒ; a)]T 
The (incoherent) P-OAT approach can be 
formally faced using the NxN cross spectral matrix 
C(ƒ; a) = E[y(ƒ, tn) yH(ƒ, tn)] of the received signal 
(superscript H is the transpose conjugate) which, 
from (2), can be expressed as  
),()(
)],(),([);(
2 aW
yyaC
ff
tftfEf
S
n
H
n
σ=
=
 (3)  
where the NxN matrix W(ƒ; a) = g(ƒ; a) gH(ƒ; a) 
can be viewed as the cross spectral matrix of a 
unitary impulsive source and )(2 fSσ = E[|S(ƒ,tn)|2] 
is the unknown source power spectral density. 
Nearly all the OAT processors rely on (3), as the 
estimation of the unknown environmental 
parameters a can be performed in the usual 
following steps:  
• compute a finite-time estimate 
 
(ƒ; a) of the 
unknown received cross spectral matrix C(ƒ, a) 
from the received signals;  
• guess an arbitrary environmental parameter 
vector b and compute the estimate of the 
propagation matrix  (ƒ; b) =  (ƒ; b)  H(ƒ; b) 
using  an acoustic propagation model well suited 
to the measurement area;  
• introduce a metric for the distance between 

(ƒ;a) and  (ƒ;b) and let the guessed environ-
mental parameter set b span its physically 
meaningful ensemble. 
A possible simple metric D(a,b) of the 
“distance” between real (unknown) and estimated 
environmental parameter sets a and b may be  
);(ˆ);(ˆ
);(ˆ);(ˆ);(ˆ),(
bgbg
bgaCbgba ff
fffD H
H
=  (4) 
If the propagation model used to estimate the 
transfer functions vector exactly reproduces the true 
propagation in the medium, then D(a,b) defined by 
(4), known as Ambiguity Function, attains one 
maximum value when the b=a, i.e. when the 
estimated parameters match with the real ones.   
Of course, the basic relation used in the present 
paper is particularly focussed toward the P-OAT, 
where the source signal is unknown and no absolute 
signal phase is available; in different contexts (i.e. 
active OAT) other approaches may be better suited. 
 
2.1 The passive pre-processing block 
As the source power spectral density is 
unknown, before the Ambiguity Function 
evaluation, the passive OAT has first to select the 
frequency bins belonging to the propagating signal, 
rejecting from the subsequent processing the noise 
bins. In this work, the extraction of the source main 
sound components relies on the decomposition 
properties of the received signal cross spectral 
matrix, whose structure is closely related to the 
useful signal spectral distribution. 
Sea surface 
Receiving 
array 
Oceanic Transfer function 
From the source to the kth receiving 
hydrophone at frequency ƒ 
hk(ƒ) 
Bottom 
From (3), introducing noise, the (j, k) element of 
the cross-spectral matrix C(ƒ;a) can be expressed as 
kjNkjXkj ffWffC ,2,2, )();()();( δσσ += aa  (5) 
where )(2 fNσ  is the noise power spectral 
density at frequency ƒ, supposed independent on  
hydrophone index. Performing now the singular 
value decomposition (SVD) of the received cross-
spectral matrix C(ƒ; a) we have the relation: 
);();();();( aUa aVa ffffC H=  (6) 
where V(ƒ;a), U(ƒ;a) and Λ (ƒ;a) respectively 
are the left and right eigenvectors matrices and the 
singular values diagonal matrix of rank R. From (5) 
and (6), only when the frequency ƒ really belongs 
to a signal component propagating trough the 
medium, there is one dominant eigenvalue and 
V(ƒ;a) and U(ƒ;a) are ill conditioned (rank~1). 
Thus, whether the source signal or the noise 
component dominates at given frequency might be 
assessed by analysing the dominant eigenvalues 
distribution of the SVD decomposition of the cross 
spectral matrix C(ƒ;a).   
This eigen-decompostion approach reveals more 
powerful then classical FFT analysis to select the 
frequencies where the signal can be extracted from 
noise. FFT approach only analyses the power 
spectral levels, discarding the spatial coherence 
information. However, care must be taken in the 
lower frequency band, if the wavelength 
appreciably exceeds the hydrophone spacing. In 
such a case a suitable normalization factor has been 
inserted in Λ
 (ƒ;a) analysis to account for the 
spatially correlated noise effect. 
The proposed method has been also applied to 
the experimental passive data collected during the 
INTIMATE00 sea trial. In Fig. 2 the estimated 
cross spectral matrix magnitude has been reported 
for signal and noise frequency bins (vessel moving 
at 2 Km from the array); in the two cases, the 
diagonal and off diagonal structure of C(ƒ;a) allows 
an unambiguous classification and selection of the 
frequency bins to be subsequently processed by the 
P-OAT.  
A further analysis has been carried out on the 
experimental data to confirm that the amplitude and 
relative phase time variability of the C(ƒ;a) is 
practically negligible during the time window (i.e. 2 
sec.) chosen for P-OAT, thus allowing reliable 
estimates.   
 
 
 
 
 
 
 
 
 
 
 
 
Fig. 2 – Cross spectral matrix magnitude on signal 
and noise bins. 
 
3. INTIMATE00 sea trial campaign 
The data used to test the tomographic processor 
were collected in the framework of INTIMATE00 
(INternal TIdes Measurements with Acoustic 
Tomography) experiment, carried out from 15 to 22 
October 2000 in the Atlantic Ocean, in front of the 
Portugal coasts off Setubal.  
Acoustic data were collected by a 16 
hydrophones Ultra Light Vertical Array (ULVA) 
also equipped with thermistors, pressure and tilt 
gauges. The array, floating around a fix position 
located at 8° 56' W - 38° 18' N at a sea depth of 
~110 m, ensured an acoustic aperture between 30 
and 90 m.  Environmental condition in the area of 
the experiment (from 8° 50’W to 9°03’ W and from 
38°13’ N to 38° 22’ N) were monitored during the 
whole period by means of three fixed mooring with 
currentmeters, temperature and salinity sensors, two 
thermistor chains, which operated for shorter 
periods and by XBT profiles taken from the 
oceanographic vessel. A short description of the 
main oceanographic characteristics during the 
experiment can be found in [8] and some 
preliminary results in [9].  
Both acoustic and non-acoustic data collected by 
the ULVA were transmitted onboard through a 
radio link, thus allowing a constant quality control, 
although limiting the distance between the vessel 
and the ULVA position up to few kilometres.  
For the passive OAT test, the oceanographic 
vessel steamed at a speed of 10 kn following a 
radial trajectory between the NW and the NE 
transects, respectively at 1, 2 and 3 km from ULVA 
position (Fig. 3). The selected ship track insured a 
quite uniform flat and a mid-range variant bottom. 
The vessel (acoustic source) position and its 
relative sea bottom depth were directly recorded 
onboard. The test lasted about 1 hour and was 
performed with a good whether condition. The 
experimental area was free from other vessels.  
 
 
 
 
 
 
 
 
 
 
Fig. 3 – Ship (acoustic source) track for P-OAT 
experiment from GPS data. 
 
4. Passive OAT results 
To reduce the parameter space to be inverted, a 
routine technique in OAT is the SSP decomposition 
with the Empirical Orthogonal Functions (EOF) 
[10] which relies on the availability of an SSP 
historical database in the investigated area. 
Unfortunately, apart few tens of XBT deployed 
during the sea trial, the absence of an historical 
database in the Setubal area led us either to use the 
limited XBT samples to estimate an EOF base or to 
steer toward an alternative approach, based on the 
Hydrostatic Normal Modes (HNM) for which a 
single mean SSP profile is needed [11]. In the 
processing carried out so far we addressed to the 
latter technique: using either the thermistors chains 
or XBT data a single mean temperature profile s0(z) 
has been estimated; solving the Navier-Stokes 
equation in the hydrostatic approximation, the 
HNMs to be used in the P-OAT inversion have 
been estimated [12]. In Fig. 4 a thermistors chain 
temperature has been reported vs. Julian day. In 
Fig. 5 the first four HNF estimated from thermistors 
data have been reported. 
Relying on the HNFs expansion functions Hk(z), 
z being the depth, we explicitly assume that each 
unknown SSP s(z) (to be estimated by the P-OAT) 
may be approximated by the expansion  
)()()(
1
0 zHzszs k
M
k
k∑
=
+= α  (7) 
 
 
 
 
 
 
 
 
 
 
Fig. 4 – A thermistors chain measured temperature 
vs. time. 
 
 
 
 
 
 
 
 
 
 
Fig. 5 – First 4 HNMs estimated for the experimen-
tal area up to 120 m depth. 
From experimental XBT data, it has been 
confirmed that, using (7), every experimental SSP 
collected during the campaign is actually well 
approximated with only the first 2 or 3 HNM 
The processed time segment for P-OAT 
corresponds to 2 sec. data window (start of the 100 
sec. track segment indicated in Fig. 3) with a 10 kn 
ship track at 2000 m nearly constant distance from 
the ULVA and a nearly flat sea bottom (~103 m) 
from the ship to the ULVA.  
Although the singular value analysis used for the 
signal bins selection indicated a very high signal 
component at 366 Hz; a mid-energy signal bin at 
100 sec of Vessel track 
665 Hz has been selected for the P-OAT 
subsequent processing. The choice of selecting a 
less favourable frequency component comes from 
the need to test the P-OAT feasibility on the more 
dense spectral components rather then on a unique 
best-case bin, which is not necessary present in 
every ship sound spectra.  
For the P-OAT processing the assumed 
environmental model is reported in Fig. 6, with 
sound source (vessel) distance and depth, array 
geometry and bottom physical properties (density 
ρ, absorption α and sound speed c). The SSP 
reported in Fig. 6 is the one measured by the 
closest, both in time and space, XBT deployment 
and it will be used to benchmark the SSP estimated 
after the P-OAT inversion. For the estimation of 
  (ƒ; b) in (4) the PROSIM broadband adiabatic 
normal mode propagation model [13] has been 
adopted. 
 
  
 
 
 
 
 
 
 
 
 
Fig. 6 – Environmental model used for the 
inversion processing with experimental SSP. 
 
P-OAT inversion has been used to jointly 
estimate, in an unique process, four environmental 
parameters: the cooperative ship depth, range and 
the HNM α1,2 expansion coefficients (assuming 
M=2). The resulting four-dimensional Ambiguity 
Function has been separately projected for ship 
sound source location in Fig. 7 and for the two 
HNM coefficients in Fig. 8. The estimated source 
location complies with what expected from the 
vessel used as sound source (~2020 m distance and 
0-3 m depth). The presence of an unique maximum 
in Fig. 8 leads to an unambiguous estimate of the 
Sound Speed Profile, which has been reported in 
Fig. 9, together with an SSP actually measured in a 
nearby position. The agreement between the SSP 
estimated by P-OAT and the experimental one is 
satisfactory, also taking into consideration that the 
measured SSP location doesn’t match with the ship-
ULVA propagation line. 
5. Conclusions  
The first results achieved for passive acoustic 
tomography performed in the framework of 
TOMPACO and INTIMATE00 projects have been 
described. The Sound Speed Profile estimation has 
been satisfactory achieved by processing the 
acoustic data of a unknown passive source (vessel) 
with no a priori information about its distance and 
depth. 
 
 
 
 
 
 
 
 
 
 
 
Fig. 7 – P-OAT Ambiguity Function for source 
range and depth estimation. 
 
 
 
 
 
 
 
 
 
 
 
Fig. 8 – P-OAT Ambiguity Function for HNM 
expansion coefficients. 
c=1750 m/s 
c=1800 m/s ρ=1.9g/cm3 
ρ=1.9g/cm3 
α=-0.8 dB/λ 
α=-0.8 dB/λ 
110 m 
32 m (1) 
92 m (16) 
2 m 
2000 ±30 m  
103 m 
0-6 m 
(source 
depth) 
 Acknowledgments 
TOMPACO project, is carried out in the 
framework of the program "Mediterranean 
Environment: analysis and assessment of 
observation methodologies" partially supported by 
MURST (Italian Ministry of  University and 
Scientific and Technological Research.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. 9 – P-OAT estimated SSP and measured SSP 
in a nearby position. 
 
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Passive ocean acoustic tomography: theory and experiment

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