Inverse Problems in Underwater Acoustics

221 Pages·2001·5.41 MB·English

by  David M. F. Chapman (auth.)

Inverse Problems in
Underwater Acoustics
Springer Science+Business Media, LLC
Michael 1. Taroudakis
George Makrakis
Editors
Inverse Problems in
Underwater Acoustics
With 76 Figures
Springer
MichaelI. Taroudakis George N.Makrakis
DepartmentofMathematics Applied and Computational Mathematics
University of Crete Foundation
71409 Heraklion- Crete,Greece Foundation for Research andTechnology
711 10Herkalion,Greece
LibraryofCongressCataloging-in-PublicationData
Inverseproblemsinunderwateracoustics /editors Michael I.Taroudakis,George N.Makrakis.
p. cm.
Includesbibliographicalreferences and index.
1. Underwateracoustics-Mathematics. 2. Inverse problems(Differentialequations) I.
Taroudakis,MichaelI. II. Makrakis,G.
QC242.2.158 2001
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ISBN978-1-4419-2920-4 ISBN978-1-4757-3520-8(eBook)
DOI10.1007/978-1-4757-3520-8
Preface
This volume summarizes some recent developments in selected applications of
inverse problems in underwateracoustics.The chapters of the volume are based
on presentations made during a research workshop which was held at the Insti
tuteofAppliedand ComputationalMathematics,FORTH, inHeraklion,Crete on
May, 1999, and itwas also sponsored bythe University of Crete.The objectives
of this research workshop were tobring togetherscientists interestedinthe theo
retical issues ofinverse problemsarising inscienceandengineering, with people
working with specific applications in underwater acoustics, such as sea-bottom
characterization, ocean acoustic tomography, and target recognition.
Nowadays, an impressively large number of researchers are looking at these
inverse problemsfrom differentperspectives.Theoreticians usually deal with the
development of notions of solutions, which are both rigorous and appropriate
to apply in the inversions of measured data, mainly studying the conditions of
existence,uniqueness, and stabilityofthese solutions.Ontheotherhand, applied
scientists involved in real world applications, study the conditions under which
existing models can be incorporated in inversion schemes under the restrictions
posed bythe technological tools.
Duringseveralrecentconferencesandworkshops [Cl], [C2],[C3], [C4],[C5],
[C6],[C7],itbecameapparentthat there isadifficulty inapplyingrigorousinver
sionschemesinrealisticproblemsasthelatterrequire muchmoreinformationthan
is available in the experiments. Moreover, new aspects appearing in the applied
fieldcannotbeworked out withoutthe useofadvanced mathematicaltechniques.
Therefore theoreticians and applied scientists should work togetherin orderthat
the inverse problems are treated inthe most efficient way.The time für the orga
nizationofthe workshopandthe publicationofthis volume isappropriateforthe
following reasons:
• A great amount of experimental data, related to underwateracoustic applica
tions, havebeen gatheredand processedover thelast 15years.
• Theprocessingofthesedatahasdemonstratedthenecessityforusingadvanced
inversion schemes; as the traditional methods cannot cope with the complex
nature oftheexistingdata.
vi Preface
• As new algorithms (such as those related to matched-field processing) are
now successfully used for inverting experimental data, there is need for their
evaluationinrelationtotheir mathematicaljustification.
Webelievethatthisvolume containssome ofthemoreinterestingrecentresults
concerningocean acoustic tomography,bottomrecognition,andinversescattering
for acoustic waveguides, related totheabove-mentionedissues.Both newcomers
and researchers in underwater acoustics will find clear presentations of the ba
sie ideas, and useful updated references for some of the most important inverse
problemsin underwateracoustics.
Thestructureofthevolume isasfollowing.Chapters1-4dealwith theproblem
ofgeoacousticinversions.Chapter1commentsonthequestionofwhatitispossible
torecoverfromaspecificexperimentforbottomreconstruction.Chapter2presents
a method for range-dependent recovery of the bottom properties. Chapter 3 is
referred to the application ofthe concept ofocean acoustic tomography for the
same problem, while Chapter4 presents an alternative optimizationmethod also
basedontomographicconcepts.
Chapter5aims at defining whethercorrelationof deconvolutionis superiorin
estimatingtheimpulseresponseofanoceanicacoustic waveguide.Chapter6refers
to the problem of inverting data recorded at an array of hydrophones, when the
array shape is an additional unknown of the inverse problem.Chapter7 presents
aspectsofamodal inversionschemeappliedinocean acoustic tomography.
The last three chapters emphasize some mathematical aspects of inverse scat
tering related to the acoustic waveguide which is the underlying model for the
problemstreatedinthepreviouschapters. InChapter8aninverse scatteringtech
nique with incomplete data is applied for the reconstruction ofthe shape ofan
embeddedobject. Chapter9dealswiththetheoreticalaspects ofaninversebound
aryproblemforembeddedinhomogeneities.Chapter10isacomprehensivesurvey
ofmathematicalresultsconcerningtheinverseproblemfortheacousticwaveequa
tioninseveraldimensions.Therelationofthetomographicdatawiththeunderlying
oceanographicmodels isthoroughlyinvestigatedintheAppendix,which contains
an article publishedin Ocean Modeling (Paola Malanotte-Rizzoli, Ed.),Elsevier
ScienceBV,Amsterdam,pp.97-115(1996).Thisarticleprovidesthekernel ofthe
ocean acoustictomographyproblemasitistraditionallyusedindata assimilation
applications.
References
[C1] O.Diachock,A.Caiti,P.Gerstoft, andH.Schmidt(eds.).FullFieldInversion
Methods in Ocean and Seismo-Acoustics.Kluwer Academic, Amsterdam,
1995.
[C2] J.S. Papadakis (ed.). Proceedings ofthe Third European Conference on
UnderwaterAcoustics.FORTH-IACM,Hemeklion, 1996.
Preface vii
[C3] R.ZhangandJ.Zhou(eds.).Shallow-WaterAcoustics. China OceanPress,
Beijing, 1997.
[C4] R. Chapman and A. Tolstoy (Guest eds.). Special Issue: Benchmarking
geoacoustic inversionmethods.J. Comput.Acoust., 6(1&2), 1998.
[CS] A. Alippi and G.B. Cannelli (eds.). Proceedings 0/the Fourth European
Conference on UnderwaterAcoustics.CNR-IDAC,Rome, 1998.
[C6] vc.Teng,E.-c.Shang,Y.-H.Pao,M.Schultz,andA.Pierce.Theoretical
and ComputationalAcoustics '97.WorldScientific,Singapore, 1999.
[C7] M. Zakharia, P. Chevret, and P. Dubail (eds.). Proceedings 0/the Fifth
European Conference on Underwater Acoustics. European Communities,
Luxembourg, 2000.
Contents
Prefaee v
1 WhatAreWeInvertingFor?
DavidM.F. Chapman . . 1
1.1 Introduction . . . . . . 1
1.2 RangeandAngle . . . . 3
1.3 ReflectionCoefficientandSurfaceImpedance 4
1.4 ReflectionandImpedance ofaSimpleSeabedModel 5
1.5 EquivalentSeabedModels . . . . . . . . . . . . . . . 8
1.6 ReflectionandImpedance ofaRealisticSeabedModel 9
1.7 Conclusion . 12
1.8 References . .. . ....... . . ........... 12
2 FreezeBathInversionforEstimationofGeoaeousticParameters
N.Ross ChapmanandLotharJaschke 15
2.1 Introduction . . . . . . . . . . . . 15
2.2 Geoacoustic Inversion . . . . . . . 17
2.3 Parameter UncertaintyEstimation . 19
2.4 FreezeBathInversion 21
2.5 Simulation 25
2.6 Summary . 33
2.7 References 34
3 TomographieInversionon MultipleReeeiverslArraysfrom
Multiple Sources for the Estimation of Shallow Water
BottomProperties
AlexTolstoy . . . . 37
3.1 Introduction 37
3.2 Approach. . 40
3.3 Results . .. 42
3.4 Conclusions 44
3.5 References . 45
x Contents
4 NonlinearOptimizationTechniquesfor GeoacoosticTomography
Gopu R. Potty andJames H.Miller . 47
4.1 Introduction · ........... 47
4.2 Hybrid Schemes . . . . . . . . . . 48
4.3 ShelfBreak PRIMERExperiment. 51
4.4 Inversion Using SUS Signals 52
4.5 Results andDiscussion 55
4.6 Conclusions 61
4.7 References . . . . . . . 62
5 EstimatingtheImpulseResponseoftheOcean:
CorrelationVersosDeconvolution
Zoi-HeleniMichalopoulou 65
5.1 Introduction · . . . . 65
5.2 Source Signals . . . . 66
5.3 Signal Deconvolution 67
5.4 CrosscorrelationinDeconvolution 69
5.5 ComparisonofDeconvolutionand Crosscorre1ation 72
5.6 SWellEX-96 Results . 74
5.7 Conclusions 74
5.8 References . . . . . . 76
6 RegularizedInversionfor Towed-ArrayShapeEstimation
Stan E.DossoandNicole E. Collison 77
6.1 Introduction 77
6.2 Theory .. 80
6.3 Examples . 93
6.4 Summary . 101
6.5 References 101
7 Mode-CouplingEffectsin AcousticThermometry
oftheArcticOcean
AlexanderN. GavrilovandPeterN.Mikhalevsky .. . . . . . 105
· ......... . ... . . .. . . . . .
7.1 Introduction 105
7.2 The Response of Acoustic Signal Parameters to Mode
Coupling ... . . ... . . . . . . . . . . . . . . . 107
7.3 Numerica1Modeling for thePathFVS-LincolnSea 112
7.4 The ExperimentalResults 122
7.5 Conclusions 123
7.6 References . . . . . . . . 125
8 On the Characterization of Objects in Shallow Water Using
RigoroosInversionMethods
BernardDuchene, Mare Lambert, andDominiqueLesselier . 127
8.1 Introduction · . . . . . . . .. . ... ........ 127