A simple and fast approach to retrieve equivalent geoacoustic parameters is presented in
this paper. The method is based upon the processing of 300-800 Hz broadband signals on a
single hydrophone.Two stable characteristics of the impulse response of the shallow water
waveguide are estimated: the time dispersion and the bottom reflection amplitudes. This two
features are analytically linked to the compressional speed and to the attenuation coefficient
of the medium. The inversion of the two latter geoacoustic parameters is straightforward
since it relies on an analytical expression. The method is tested on INTIMATE96 data. The
results show an excellent agreement between the reflection of the true medium and the
reflection coefficient of the equivalent medium.The partners of the INTIMATE project wish to thank the staff of NRP ANDROMEDA,
the staff of BO D’ENTRECASTEAUX and people of Mission Océanographique de
l’Atlantique (aboard D’ENTRECASTEAUX). We also wish to thank the SACLANT
Undersea Research Center for lending the Portable Array System and Roberto Chiarabini
(SACLANTCEN) for his participation in the array preparation, deployment and use. Thanks
to T. Folegot and G. Bonnaillie (CMO) for their active contribution in this work. The study
was jointly sponsored by SHOM (exploratory program 95901), the Portuguese Ministery of
Research (PRAXIS XXI) and ONR (contract N00014-95-1-0558)

Coelho, E.

Demoulin, X.

Jesus, S. M.

Pelissero, L.

Porter, M. B.

Stephan, Y.

Sapientia

Proceedings of the Fifth European Conference on Underwater Acoustics, ECUA 2000Edited by P. Chevret and M.E. ZakhariaLyon, France, 2000ESTIMATING EQUIVALENT BOTTOM GEOACOUSTICALPARAMETERS FROM BROADBAND INVERSIONX. Demoulin*, L. Pelissero*, §, Y. Stéphan*, S. Jesus+, M. Porter$, E. Coelho#*Centre Militaire d’Océanographie, EPSHOM, BP 426, 29275 Brest Cedex, France.§ PROG/SM, 83100 Toulon Naval, France+UCEH, Universidade do Algarve, Campus de Gambelas, 8000 Faro, Portugal.$Science Applications International Corporation, Prospect Ave, La Jolla, CA92037, USA.#Instituto Hidrografico, Rua das Trinas, 1296 Lisboa, Portugal.A simple and fast approach to retrieve equivalent geoacoustic parameters is presented inthis paper. The method is based upon the processing of 300-800 Hz broadband signals on asingle hydrophone.Two stable characteristics of the impulse response of the shallow waterwaveguide are estimated: the time dispersion and the bottom reflection amplitudes. This twofeatures are analytically linked to the compressional speed and to the attenuation coefficientof the medium. The inversion of the two latter geoacoustic parameters is straightforwardsince it relies on an analytical expression. The method is tested on INTIMATE96 data. Theresults show an excellent agreement between the reflection of the true medium and thereflection coefficient of the equivalent medium.1. INTRODUCTIONAcoustic inversion can lead to good estimates of the bottom geoacoustic parameters,especially when very low frequencies are used. Bottom models can also be built asequivalent media, which means that the estimated medium behaves as the true medium inthe limit of the acoustic application (frequency, aperture). Of course, such an approachmay be totally unadapted for geophysical characterization since the equivalent mediummay not be physically relevant. However, the major advantage of the equivalent mediumapproach is that it allows the assessment of most important parameters consistently withthe sonar systems. On the other hand, a new trend in geoacoustic inversion lies in the useof broadband acoustic signals received on sparse arrays, possibly reduced to a singlehydrophone [1]. The bottom properties can be robustly and efficiently retrieved from thetime dispersion and the attenuation of the amplitudes of bottom-reflected rays [2].However, the inversion process still relies on a few hundred runs of the forward model.In this paper, we combine the broadband inversion concept with the equivalent mediumconcept. This approach is based upon analytical developments of the reflection coefficientto retrieve the equivalent medium properties. Such a method avoids intensivecomputations. This approach is tested on the INTIMATE96 data set, which consists inbroadband signals between 300 and 800 Hz.2.   THE INTIMATE'96 EXPERIMENTThe main objective of the INTIMATE project is to monitor internal tides by use of acoustictomography [3]. However, data exploitation, based upon broadband signal processing on asingle hydrophone, turned out to show that several other issues could be efficiently adressedincluding source tracking [4] and geoacoustic inversion, which is treated in this paper. Thefirst exploratory experiment of the project, called INTIMATE96, was carried out in June 1996on the continental shelf off the coast of Portugal. A broadband acoustic source, towed fromthe oceanographic vessel D’ENTRECASTEAUX, and a 4-hydrophone vertical array wereused. Acoustic data were collected for 5 days, including legs where the source ship wasmoving and legs with the ship on station. The signals received on the phones were transmittedand processed aboard the Portuguese hydrographic vessel NRP ANDROMEDA for real timeanalysis. Intensive environmental surveys (including corings and seismic survey) were alsoconducted to evaluate the sedimentogical bottom structure. The emitted signal is a LinearFrequency Modulation (LFM) chirp from 300 to 800 Hz. The chirps lasted for 2 seconds andwere repeated every 8 seconds. The acoustic signal are pulse-compressed by cross-correlatingeach received sequence with the emitted signal replica. All sequences are lined up on theleading edge to filter out instrument position fluctuations. A typical sequence of data isrepresented in Figure 1. The environment of the experiment along a range independent track isgiven in Figure 2. The received sequence is divided in two parts. The first spike consists indirect paths refracted in the thermocline with a few number of bottom reflection, highlysensitive to the sound speed profile. The second part, quite stable, exhibits a textbookmultipath structure, composed with surface and bottom reflected rays.Fig. 1: Typical INTIMATE’96 sequence of data (averaged on 10’ min).3. GEOACOUSTICAL FORWARD PROBLEMThe three-layers geoacoustical model described in Fig. 2 is not adapted to geoacousticalinversion due to the large number of parameters which have different impact on the measuredacoustic field. It is interesting to note that for most of sonar applications, predicting detectionranges mainly relies on the ability to estimate transmission loss for small grazing angles. In thatsense, the Rayleigh reflection coefficient R(q) is an efficient bottom describer for acousticpropagation purposes: R(q) has two parts bounded by the critical angle. Rays whose grazingangles are smaller that the critical angle are propagated in the water column with a lossproportional to the pre-critical part of R. At a given frequency, for most of cases (even forcomplicated seabed), the typical shape of the pre-critical part of R can be parametrized by asemi infinite fluid layer, i.e. the equivalent bottom.Fig. 2: Experimental set up and environment parameters in the range independant leg.Considering a semi-infinite fluid medium, the last arrival is related to the critical anglei.e. to the compressional sound speed of the equivalent medium. The amplitude of a single raydecreases with its time of arrival (or equivalently the grazing angle) giving a sample of thereflection coefficient value (related to attenuation) at power n, n being the number of bottombounces. If it is possible to obtain experimentally the time dispersion and the attenuation law(filtered from the surface reflection losses), a rather straigtforward inversion will be possible todetermine the compressional speed of the bottom and the attenuation coefficient of theequivalent medium. The previous analysis is valid at a single frequency. One can argue that theuse of broadband signal is not consistent with the fact that the reflection coefficient dependson frequency. In fact, the analysis can be carried out for several frequency ranges, in which itis considered that the equivalent medium is valid.The objective is to formalize the relation between the reflection coefficient and the impulseresponse. The Rayleigh reflection coefficient of a fluid-fluid interface is:( )R Z ZZ Zb wb wq = -+(1)with Zi = pi.ci/sinq , where i stands for b and w, respectively for the bottom and the sea water.The term cb, complex formulation of the bottom velocity, is a function of the compressionnalspeed Cb (m/s) and the attenuation ab (dB/l) expressed as cb=Cb/(1+iab/2p8,686). The bottomdensity is a second order parameter for propagation signals since it mainly affects the lowvalue of R. An approximated value of rb will be deduced from Cb using the Hamilton relation,valid for continental terrasse sediments [5], Cb=2330,4-(1257.rb)+487,7.rb2.R(q) finally depends on 2 parameters, ab (in dB/l) and Cb(in m/s). The next step is tocharacterize the impulse response with two parameters: the last arrival time Tla and a spikeamplitude yobs(qi). If the source level and the hydrophone sensitivity are unknown, it ispreferable to define the ratio :R y iy jspi j,( )( )= obsobsqq(2)We therefore make the assumption of a linear trajectory for the surface-bottom reflectedrays, easily justified by calculation. Using Dla = Tla .Cmoy and writing the critical angle as qc =acos(D/Dla), the last arrival time is simply related to the geoacoustic parameters Cb by Tla =D.Cb/Cmoy2, Cmoy being the water column averaged sound speed value, D the range betweenthe transmitter and the receiver, Dla the linear trajectory of the ray reflected at the criticalangle. To relate Rsp and ab, we need to recall the amplitude of a given ray reflected on thebottom. It is theoretically expressed as :y iiDe R RiDis bp i q i( )cos( ) ( ) ( )q q a q q= × - × × (3)The first term is the geometrical dispersion (under a linear trajectory hypothesis), thesecond term is the volumic attenuation (a dB/km/Hz is the Thorp coefficient, and Di the lineartrajectory of the ray), Rs and Rb are repectively the surface and bottom reflection coefficientmodulus (p and q being the number of reflection on surface and bottom).Fitting the impulse response with a single basic eigenray calculation, we easily relate eachspike with the arrival time of the corresponding eigenray. For a given spike, we therefore useeigenray parameters : qi, p, q, Di . |Rs| is estimated from the wind measurement using standardlaws. We then obtain for Rsp:( )( )( )( )RDDRRCtespssRbRbRbRbppqqqq= × × × = ×12212211222121222121cos( )cos( )qq(4)An analytical expression linking ab and Rb is then necessary to calculate ab from Rsp.We have developed an asymptotical expression of Rb valid below the critical angle. Thecoefficient Rb can be written as:R vvbbb2 11» - ×+ ×aa   with (5)( )vAbb= ×+æèçöø÷× - ×21 1 2 8 6862rr p'' . . ,, ACCibw= ×cos( )q 222, rqrbibwbCCA'sin( )=×-×1(6)This asymptotic expression gives remarquably good results (except for very smoothbottom) from qi = 0 until qi < qc . This system basically express the forward geoacousticproblem for the equivalent medium.4. GEOACOUSTICAL INVERSIONUnder weak constraints, it is possible to have a simple formulation of the forward model. Ityields an analytical formulation of the inverse problem which can be stated as follows:C  =  f (T ) =C TDb-1lamoy la2 ´ (7)from which we deduce rb . Knowing Cb and r, we calculate( ) ( )ab-1spsp1 1 2 2 sp =  g (R ) =R - Cteq v - q v R + Cte×(8)qi being half the number of bottom bounce and vi calculated by eq. 5 for the ray defined by qi.Cte is calculated from eq. 4. INTIMATE'96 acoustical data set is split in three differentphases. The first phase consists in a 25h station with a flat bottom, following a North-Southdirection which is perpendicular to the presumed direction of propagation of the internal tide.This allows to assume a range independant environment. We extracted a 30-minutes data setfrom this station to test the inversion procedure. An incoherent treatment is done over 75pings corresponding to a 10-minutes average. The inversion being based on Tla and Rspmeasurement, we have as much inversion result (for ab) as multipath spike couples (definingRsp). We consider every couple. Consequently, we used 3 data set of spike couple to get Rsp,leading to 3 inversion sets. The first step of the inversion is then processed and gives anestimate of the compressional speed Cb using eq. 7. The density rb is then deduced from Cb.Each spike of the impulse response is then parametrized by it corresponding eigenraycharacteristic (fig. 3). Applying eq. 8, we deduce ab. Full results are presented in fig 4.Fig. 3: Superposed plot of eigenray calculation and data impulse response.Fig. 4: Plot of calculated attenuation versus the 3 data set used fo the inversion. For eachdata set, solid line gives the mean value of ab.Within a data set, the dispersion of the attenuation estimate is mainly due to fluctuations inthe spike amplitude, probably due to a noise effect or to bathymetric feature. Averaged valuesare more consistent even if a decrease is observed over the higher grazing angle range. Thispossibly be due to an experimental mismatch with the Rayleigh reflection model. The effect ofshear waves, for example, would increase the attenuation for lower grazing angle and woulddecrease it for higher grazing angles. Then, it is preferiable to retain the averaged valuecalculated from the whole data set, i.e ab=0.81 dB/l. Inverted equivalent medium is finallydefined by: rb=1.87 Kg/dm3, Cb=1685 m/s, ab=0.81 dB/l. As shown in Fig. 5, the comparisonbetween inverted equivalent medium and the true medium reflection coefficient shows anexcellent agreement within the precritical grazing angle range.Fig.5:Reconstruction of the reflection coefficient in the equivalent medium andcomparison with the true medium for sub-critical angles .5. CONCLUSIONA simple and fast approach to retrieve geoacoustic parameters has been presented in thispaper. The principle of the method is to invert for an equivalent medium which gives the samepropagation features than the true medium. The application on INTIMATE96 data shows verygood results. The same kind of work is in progress on different type of bottoms (data werecollecteted duting the INTIMATE98 experiment). Possible applications of the method couldlie in operationnal acoustic REA as well as in Environment Adaptive Sonar technology.6. ACKNOWLEDGEMENTSThe partners of the INTIMATE project wish to thank the staff of NRP ANDROMEDA,the staff of BO D’ENTRECASTEAUX and people of Mission Océanographique del’Atlantique (aboard D’ENTRECASTEAUX). We also wish to thank the SACLANTUndersea Research Center for lending the Portable Array System and Roberto Chiarabini(SACLANTCEN) for his participation in the array preparation, deployment and use. Thanksto T. Folegot and G. Bonnaillie (CMO) for their active contribution in this work. The studywas jointly sponsored by SHOM (exploratory program 95901), the Portuguese Ministery ofResearch (PRAXIS XXI) and ONR (contract N00014-95-1-0558).REFERENCES[1] J.-P. Hermand, E. Michelosi, P. Gurerrini and A. Barbagelata, «Advanced driftingacoustic buoy field for rapid assessment of bottom properties in shallow water: EnVerse97experiments», Proceedings of the 4th European conference on Underwater Acoustics, A.Phillipi & G.B Canneli Eds., Roma, 319-326.[2] J.-P. Hermand, «Broadband geoacoustic inversion in shallow water from waveguideimpulse response measurements on a single hydrophone: Theory and experimental results»,IEEE Journal of Ocean Engineering, 24, no 1, 41-66, 1999. [3] X. Démoulin, Y. Stéphan, S. Jesus, E. Coelho and M. Porter, «INTIMATE96: Ashallow water experiment devoted to the study of internal tides», Shallow Water Acoustics,Zhang & Zhou eds., China Ocean Press, 485-490, 1997.[4] M.B. Porter, S.M. Jesus, Y.A. Stéphan, E. Coelho and X. Démoulin, «Single phonesource tracking in a variable environment», Proceedings of the 4th European conference onUnderwater Acoustics, A. Phillipi & G.B Canneli Eds., Roma, 575-580, 1998.[5] E.L.Hamilton and R.T.Bachman, «Sound velocity and related properties of marinesediments», Journal of the Acoustical Society of America, 72, 1891-1904, 1982.[6] Y. Stéphan, X. Démoulin, T. Folégot, J.M. Léculier and J. Small, «TheINTIMATE98 experiment», in these proceedings.

Estimating equivalent bottom geoacoustial parameters from broadband inversion

Universidade do Algarve

Proceedings of the Fifth European Conference on Underwater Acoustics, ECUA 2000
Edited by P. Chevret and M.E. Zakharia
Lyon, France, 2000
ESTIMATING EQUIVALENT BOTTOM GEOACOUSTICAL
PARAMETERS FROM BROADBAND INVERSION
X. Demoulin*, L. Pelissero*, §, Y. Stéphan*, S. Jesus+, M. Porter$, E. Coelho#
*Centre Militaire d’Océanographie, EPSHOM, BP 426, 29275 Brest Cedex, France.
§ PROG/SM, 83100 Toulon Naval, France
+UCEH, Universidade do Algarve, Campus de Gambelas, 8000 Faro, Portugal.
$Science Applications International Corporation, Prospect Ave, La Jolla, CA92037, USA.
#Instituto Hidrografico, Rua das Trinas, 1296 Lisboa, Portugal.
A simple and fast approach to retrieve equivalent geoacoustic parameters is presented in
this paper. The method is based upon the processing of 300-800 Hz broadband signals on a
single hydrophone.Two stable characteristics of the impulse response of the shallow water
waveguide are estimated: the time dispersion and the bottom reflection amplitudes. This two
features are analytically linked to the compressional speed and to the attenuation coefficient
of the medium. The inversion of the two latter geoacoustic parameters is straightforward
since it relies on an analytical expression. The method is tested on INTIMATE96 data. The
results show an excellent agreement between the reflection of the true medium and the
reflection coefficient of the equivalent medium.
1. INTRODUCTION
Acoustic inversion can lead to good estimates of the bottom geoacoustic parameters,
especially when very low frequencies are used. Bottom models can also be built as
equivalent media, which means that the estimated medium behaves as the true medium in
the limit of the acoustic application (frequency, aperture). Of course, such an approach
may be totally unadapted for geophysical characterization since the equivalent medium
may not be physically relevant. However, the major advantage of the equivalent medium
approach is that it allows the assessment of most important parameters consistently with
the sonar systems. On the other hand, a new trend in geoacoustic inversion lies in the use
of broadband acoustic signals received on sparse arrays, possibly reduced to a single
hydrophone [1]. The bottom properties can be robustly and efficiently retrieved from the
time dispersion and the attenuation of the amplitudes of bottom-reflected rays [2].
However, the inversion process still relies on a few hundred runs of the forward model.
In this paper, we combine the broadband inversion concept with the equivalent medium
concept. This approach is based upon analytical developments of the reflection coefficient
to retrieve the equivalent medium properties. Such a method avoids intensive
computations. This approach is tested on the INTIMATE96 data set, which consists in
broadband signals between 300 and 800 Hz.
2.   THE INTIMATE'96 EXPERIMENT
The main objective of the INTIMATE project is to monitor internal tides by use of acoustic
tomography [3]. However, data exploitation, based upon broadband signal processing on a
single hydrophone, turned out to show that several other issues could be efficiently adressed
including source tracking [4] and geoacoustic inversion, which is treated in this paper. The
first exploratory experiment of the project, called INTIMATE96, was carried out in June 1996
on the continental shelf off the coast of Portugal. A broadband acoustic source, towed from
the oceanographic vessel D’ENTRECASTEAUX, and a 4-hydrophone vertical array were
used. Acoustic data were collected for 5 days, including legs where the source ship was
moving and legs with the ship on station. The signals received on the phones were transmitted
and processed aboard the Portuguese hydrographic vessel NRP ANDROMEDA for real time
analysis. Intensive environmental surveys (including corings and seismic survey) were also
conducted to evaluate the sedimentogical bottom structure. The emitted signal is a Linear
Frequency Modulation (LFM) chirp from 300 to 800 Hz. The chirps lasted for 2 seconds and
were repeated every 8 seconds. The acoustic signal are pulse-compressed by cross-correlating
each received sequence with the emitted signal replica. All sequences are lined up on the
leading edge to filter out instrument position fluctuations. A typical sequence of data is
represented in Figure 1. The environment of the experiment along a range independent track is
given in Figure 2. The received sequence is divided in two parts. The first spike consists in
direct paths refracted in the thermocline with a few number of bottom reflection, highly
sensitive to the sound speed profile. The second part, quite stable, exhibits a textbook
multipath structure, composed with surface and bottom reflected rays.
Fig. 1: Typical INTIMATE’96 sequence of data (averaged on 10’ min).
3. GEOACOUSTICAL FORWARD PROBLEM
The three-layers geoacoustical model described in Fig. 2 is not adapted to geoacoustical
inversion due to the large number of parameters which have different impact on the measured
acoustic field. It is interesting to note that for most of sonar applications, predicting detection
ranges mainly relies on the ability to estimate transmission loss for small grazing angles. In that
sense, the Rayleigh reflection coefficient R(q) is an efficient bottom describer for acoustic
propagation purposes: R(q) has two parts bounded by the critical angle. Rays whose grazing
angles are smaller that the critical angle are propagated in the water column with a loss
proportional to the pre-critical part of R. At a given frequency, for most of cases (even for
complicated seabed), the typical shape of the pre-critical part of R can be parametrized by a
semi infinite fluid layer, i.e. the equivalent bottom.
Fig. 2: Experimental set up and environment parameters in the range independant leg.
Considering a semi-infinite fluid medium, the last arrival is related to the critical angle
i.e. to the compressional sound speed of the equivalent medium. The amplitude of a single ray
decreases with its time of arrival (or equivalently the grazing angle) giving a sample of the
reflection coefficient value (related to attenuation) at power n, n being the number of bottom
bounces. If it is possible to obtain experimentally the time dispersion and the attenuation law
(filtered from the surface reflection losses), a rather straigtforward inversion will be possible to
determine the compressional speed of the bottom and the attenuation coefficient of the
equivalent medium. The previous analysis is valid at a single frequency. One can argue that the
use of broadband signal is not consistent with the fact that the reflection coefficient depends
on frequency. In fact, the analysis can be carried out for several frequency ranges, in which it
is considered that the equivalent medium is valid.
The objective is to formalize the relation between the reflection coefficient and the impulse
response. The Rayleigh reflection coefficient of a fluid-fluid interface is:
( )R Z Z
Z Z
b w
b w
q = -
+
(1)
with Zi = pi.ci/sinq , where i stands for b and w, respectively for the bottom and the sea water.
The term cb, complex formulation of the bottom velocity, is a function of the compressionnal
speed Cb (m/s) and the attenuation ab (dB/l) expressed as cb=Cb/(1+iab/2p8,686). The bottom
density is a second order parameter for propagation signals since it mainly affects the low
value of R. An approximated value of rb will be deduced from Cb using the Hamilton relation,
valid for continental terrasse sediments [5], Cb=2330,4-(1257.rb)+487,7.rb2.
R(q) finally depends on 2 parameters, ab (in dB/l) and Cb(in m/s). The next step is to
characterize the impulse response with two parameters: the last arrival time Tla and a spike
amplitude yobs(qi). If the source level and the hydrophone sensitivity are unknown, it is
preferable to define the ratio :
R y i
y j
sp
i j,
( )
( )
= obs
obs
q
q
(2)
We therefore make the assumption of a linear trajectory for the surface-bottom reflected
rays, easily justified by calculation. Using Dla = Tla .Cmoy and writing the critical angle as qc =
acos(D/Dla), the last arrival time is simply related to the geoacoustic parameters Cb by Tla =
D.Cb/Cmoy2, Cmoy being the water column averaged sound speed value, D the range between
the transmitter and the receiver, Dla the linear trajectory of the ray reflected at the critical
angle. To relate Rsp and ab, we need to recall the amplitude of a given ray reflected on the
bottom. It is theoretically expressed as :
y i
i
D
e R R
i
Di
s b
p i q i( )
cos( ) ( ) ( )q q a q q= × - × × (3)
The first term is the geometrical dispersion (under a linear trajectory hypothesis), the
second term is the volumic attenuation (a dB/km/Hz is the Thorp coefficient, and Di the linear
trajectory of the ray), Rs and Rb are repectively the surface and bottom reflection coefficient
modulus (p and q being the number of reflection on surface and bottom).
Fitting the impulse response with a single basic eigenray calculation, we easily relate each
spike with the arrival time of the corresponding eigenray. For a given spike, we therefore use
eigenray parameters : qi, p, q, Di . |Rs| is estimated from the wind measurement using standard
laws. We then obtain for Rsp:
( )
( )
( )
( )R
D
D
R
R
Ctesp
s
s
Rb
Rb
Rb
Rb
p
p
q
q
q
q= × × × = ×1
2
2
1
2
2
1
1
2
2
2
1
2
1
2
2
2
1
2
1
cos( )
cos( )
q
q
(4)
An analytical expression linking ab and Rb is then necessary to calculate ab from Rsp.
We have developed an asymptotical expression of Rb valid below the critical angle. The
coefficient Rb can be written as:
R v
v
b
b
b
2 1
1
» - ×
+ ×
a
a
   with (5)
( )
v
A
b
b
= ×
+æèç
ö
ø÷× - ×
2
1 1 2 8 686
2
r
r p
'
' . . ,
, A
C
C
i
b
w
= ×cos( )q 2
2
2
, r
q
rb
i
b
w
b
C
C
A
'
sin( )
=
×
-
×
1
(6)
This asymptotic expression gives remarquably good results (except for very smooth
bottom) from qi = 0 until qi < qc . This system basically express the forward geoacoustic
problem for the equivalent medium.
4. GEOACOUSTICAL INVERSION
Under weak constraints, it is possible to have a simple formulation of the forward model. It
yields an analytical formulation of the inverse problem which can be stated as follows:
C  =  f (T ) =
C T
D
b
-1
la
moy la
2 ´ (7)
from which we deduce rb . Knowing Cb and r, we calculate
( ) ( )ab
-1
sp
sp
1 1 2 2 sp
 =  g (R ) =
R - Cte
q v - q v R + Cte×
(8)
qi being half the number of bottom bounce and vi calculated by eq. 5 for the ray defined by qi.
Cte is calculated from eq. 4. INTIMATE'96 acoustical data set is split in three different
phases. The first phase consists in a 25h station with a flat bottom, following a North-South
direction which is perpendicular to the presumed direction of propagation of the internal tide.
This allows to assume a range independant environment. We extracted a 30-minutes data set
from this station to test the inversion procedure. An incoherent treatment is done over 75
pings corresponding to a 10-minutes average. The inversion being based on Tla and Rsp
measurement, we have as much inversion result (for ab) as multipath spike couples (defining
Rsp). We consider every couple. Consequently, we used 3 data set of spike couple to get Rsp,
leading to 3 inversion sets. The first step of the inversion is then processed and gives an
estimate of the compressional speed Cb using eq. 7. The density rb is then deduced from Cb.
Each spike of the impulse response is then parametrized by it corresponding eigenray
characteristic (fig. 3). Applying eq. 8, we deduce ab. Full results are presented in fig 4.
Fig. 3: Superposed plot of eigenray calculation and data impulse response.
Fig. 4: Plot of calculated attenuation versus the 3 data set used fo the inversion. For each
data set, solid line gives the mean value of ab.
Within a data set, the dispersion of the attenuation estimate is mainly due to fluctuations in
the spike amplitude, probably due to a noise effect or to bathymetric feature. Averaged values
are more consistent even if a decrease is observed over the higher grazing angle range. This
possibly be due to an experimental mismatch with the Rayleigh reflection model. The effect of
shear waves, for example, would increase the attenuation for lower grazing angle and would
decrease it for higher grazing angles. Then, it is preferiable to retain the averaged value
calculated from the whole data set, i.e ab=0.81 dB/l. Inverted equivalent medium is finally
defined by: rb=1.87 Kg/dm3, Cb=1685 m/s, ab=0.81 dB/l. As shown in Fig. 5, the comparison
between inverted equivalent medium and the true medium reflection coefficient shows an
excellent agreement within the precritical grazing angle range.
Fig.5:Reconstruction of the reflection coefficient in the equivalent medium and
comparison with the true medium for sub-critical angles .
5. CONCLUSION
A simple and fast approach to retrieve geoacoustic parameters has been presented in this
paper. The principle of the method is to invert for an equivalent medium which gives the same
propagation features than the true medium. The application on INTIMATE96 data shows very
good results. The same kind of work is in progress on different type of bottoms (data were
collecteted duting the INTIMATE98 experiment). Possible applications of the method could
lie in operationnal acoustic REA as well as in Environment Adaptive Sonar technology.
6. ACKNOWLEDGEMENTS
The partners of the INTIMATE project wish to thank the staff of NRP ANDROMEDA,
the staff of BO D’ENTRECASTEAUX and people of Mission Océanographique de
l’Atlantique (aboard D’ENTRECASTEAUX). We also wish to thank the SACLANT
Undersea Research Center for lending the Portable Array System and Roberto Chiarabini
(SACLANTCEN) for his participation in the array preparation, deployment and use. Thanks
to T. Folegot and G. Bonnaillie (CMO) for their active contribution in this work. The study
was jointly sponsored by SHOM (exploratory program 95901), the Portuguese Ministery of
Research (PRAXIS XXI) and ONR (contract N00014-95-1-0558).
REFERENCES
[1] J.-P. Hermand, E. Michelosi, P. Gurerrini and A. Barbagelata, «Advanced drifting
acoustic buoy field for rapid assessment of bottom properties in shallow water: EnVerse97
experiments», Proceedings of the 4th European conference on Underwater Acoustics, A.
Phillipi & G.B Canneli Eds., Roma, 319-326.
[2] J.-P. Hermand, «Broadband geoacoustic inversion in shallow water from waveguide
impulse response measurements on a single hydrophone: Theory and experimental results»,
IEEE Journal of Ocean Engineering, 24, no 1, 41-66, 1999.
 [3] X. Démoulin, Y. Stéphan, S. Jesus, E. Coelho and M. Porter, «INTIMATE96: A
shallow water experiment devoted to the study of internal tides», Shallow Water Acoustics,
Zhang & Zhou eds., China Ocean Press, 485-490, 1997.
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Estimating equivalent bottom geoacoustial parameters from broadband inversion

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