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The Inverse Problem

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Fundamentals of Shallow Water Acoustics

Part of the book series: The Underwater Acoustics Series ((UA))

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Abstract

In considering the propagation of sound through fluid or elastic media (or light through optical media, or heat through materials, etc.), it is usual to first address the so-called “forward problem.” Specifically, one calculates the sound (light, heat) field assuming knowledge of both the medium properties and of the physics governing the radiation, propagation, diffusion, attenuation, etc. of the corresponding waves.

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References

  • Aikal T. (1972) The relationship between the physical properties of underwater sediments that affect bottom reflection. Marine Geology, 13, 251–266.

    Google Scholar 

  • R.C. Aster, B. Borchers, and C. Thurber, (2005) “Parameter estimation and inverse problems”, Elsevier, New York, 301 pages.

    Google Scholar 

  • Bachman, R.T. (1989), “Parameterization of geoacoustic properties” San Diego, CA: Scripps Institution of Oceanography.

    Google Scholar 

  • Battle, D.J., Gerstoft, P., Kuperman, W.A., Hodgkiss, W.S., and Siderius, M., (2003) “Geoacoustic inversion of tow-ship noise via near field matched field processing”, IEEE J. Oceanic Eng’g, 28(3), pp. 454–467.

    Google Scholar 

  • Biot M., (1956) Theory of propagation of elastic waves in a fluid saturated porous solid. I. low frequency range.,” [The Journal of the Acoustical Society of America 28(2),168–178.]

    Google Scholar 

  • Biot M. (1956) Theory of propagation of elastic waves in a fluid-saturated porous solid II. High frequency range [J. Acoust. Soc. Am., Vol. 28(2), pp. 179–191]

    Google Scholar 

  • Brekhovskikh L.M. and Lysanov Yu.P. (1991) Fundamentals of Ocean Acoustics [Springer-Verlag, 270 p.]

    Google Scholar 

  • Bunkin F.V., Katsnel’son B.G., Kravtsov Yu.A., Kulapin L.G., Petnikov V.G., Rivelis E.A., Reznikov V.M, Sabirov O.I. and Sidenko A.V. (1989) Average estimates of sound absorption in shallow ocean waveguides [Sov. Phys.-Acoust., Vol. 35(1), pp. 1–4]

    Google Scholar 

  • Bunkin F.V., Gindler I.V., Kozel’skii A.R., Kravtsov Yu.A. and Petnikov V.G. (1989) Dispersion distortion of complex acoustic signals in shallow water ocean waveguides [Sov. Phys. Acoust., Vol. 35(5), pp. 461–464]

    Google Scholar 

  • Chapman, N.R., Dizaji, R.M., and Kirlin, L. (2006) “Inversion of geoacoustic model parameters using ship radiated noise.” In “Acoustic sensing techniques for the shallow water environment,” A. Caiti, N.R. Chapman, J.P. Hermand, and S. Jesus (eds), pp. 289–302.

    Google Scholar 

  • S. D. Chuprov and R. F. Shvachko, (1974) in Acoustics of the Ocean, Ed. by L. M. Brekhovskikh, Nauka, Moscow, pp. 559–614.

    Google Scholar 

  • Collins M., Kuperman W., and Schmidt H., “Nonlinear inversion for ocean bottom properties”, J. Acoust. Soc. Am., 92(5), pp. 2770–2783 (1992).

    Google Scholar 

  • Frisk G.V., (1994) “Ocean and Seabed Acoustics”, Prentice Hall, Saddle River, N.J., 299 pp

    Google Scholar 

  • Frisk, G.V., Talk at ASA meeting (2005)

    Google Scholar 

  • Frisk G. and Lynch J., “Shallow Water Waveguide Characterization using the Hankel Transform,” J. Acoust. Soc. Am., 76(1), 205–216, July (1984).

    Google Scholar 

  • Grigor’ev V.A., Katsnelson B.G., Petnikov V.G. (1996) Frequency dependence of the effective bottom sound absorption in the Barents Sea [Acoust. Phys., Vol. 42(5), pp. 627– 629]

    Google Scholar 

  • Grigor’ev V A., Katsnel’son B. G., and. Petnikov V. G (1996) Frequency dependence of the effective bottom sound absorption in the Barents sea. Acoust. Phys. 42(5), 627–629

    Google Scholar 

  • Grigor’ev V. A, Katsnel’son B. G., and Petnikov V. G. (2001) Determination of the absorbing and scattering properties of the sea floor in a shallow water environment by the spectra of wide-band signals. Acoust. Phys. 47(3), 277–281.

    Google Scholar 

  • Hamilton E. L., (1976) Sound attenuation as a function of depth in the sea floor. J. Acoust. Soc. Am. 59(3), 528–535.

    Google Scholar 

  • Harrison, C.H. and Simons, D.G. (2002) “Geoacoustic inversion of ambient noise: a simple method.” J. Acoust. Soc. Am. 112(4), pp. 1377–1389.

    Google Scholar 

  • Heaney, K.D. and Cox, H., (2002) “Rapid geoacoustic characterization for limiting environmental uncertainty for sonar system performance prediction.” In “Impact of littoral environmental variability on acoustic predictions and sonar performance,” N. Pace and F. Jensen (eds.), pp. 163–170, Kluwer

    Google Scholar 

  • Heaney, K.D., (2004) Rapid geoacoustic characterization: applied to range dependent environments.” IEEE J. Oceanic Eng’g. 29(1), pp. 43–50

    Google Scholar 

  • Ivakin A.N. and Lysanov Yu. P., (1985) Backscattering of sound from inhomogeneous bottom at small grazing angles. Sov. Phys. Acoust. 31(3), 236–237.

    Google Scholar 

  • Katsnelson B.G., Petnikov V.G. (2002) Shallow water acoustics. Springer-Verlag.

    Google Scholar 

  • Koch, R.A. and Knobles, D.P. (2004) “Geoacoustic inversion with ships as sources”. J. Acoust. Soc. Am. 117(2), pp. 626–637.

    Google Scholar 

  • Kuperman W.A., Ingenito F. (1980) Spatial correlation of surface generated noise in a stratified ocean [J. Acoust. Soc. Am., Vol. 67(6), pp. 1988–1996]

    Google Scholar 

  • Lin Y.T.,. Chen C.F, and. Lynch J.F, (2006). “An Equivalent Transform Method for Evaluating the Effect of Water Column Mismatch on Geoacoustic Inversion”, in press IEEE J. Oceanic Eng’g. Special Issue on Effects of Environmental Uncertainty

    Google Scholar 

  • Lynch J.F, Rajan S.D., and. Frisk G.V, (1991). “A Comparison of Broadband and Narrowband Modal Inversions for Bottom Geoacoustic Properties at a Site near Corpus Christi, Texas,” [J. Acoust. Soc. Am., 89(2), 648–665]

    Google Scholar 

  • Lysanov Yu. P. (1980) Geoacoustic model of the upper sedimentary layer in a shallow sea. Dokl. Akad. Nauk. SSSR. 251(3), 714–716.

    Google Scholar 

  • Matthews J., Bucca P., and Geddes W., (1985) “Preliminary environmental assessment of the Project GEMINI site – Corpus Christi, Texas,” Naval Ocean Research and Development Activity, Rep. No. 120 (June).

    Google Scholar 

  • Menke W., (1989). “Geophysical data analysis: discrete inverse theory (revised edition)”, Academic Press, London, 289 pages

    Google Scholar 

  • Parker R.L., (1994). “Geophysical inverse theory,” Princeton University Press, Princeton, N.J., 386 pages

    Google Scholar 

  • Rajan S. D, (1992) “Waveform Inversion to Obtain the Geoacoustic Properties of Sediments in Deep Water”, Journal of the Acoustical Society of America, 91(6), 3228–3241

    Google Scholar 

  • Rubano.L. A., (1980) “Acoustic propagation in shallow water over a low-velocity bottom,” The Journal of the Acoustical Society of America 67(5), 1608–1613

    Google Scholar 

  • Siderius, M., Harrison, C.H., and Porter, M. (2006) “A passive fathometer technique for imaging seabed layering using ambient noise.” J. Acoust. Soc. Am. 120(3), pp 1315–1323.

    Google Scholar 

  • D. T. Smith, (1974) In Physics of Sound in Marine Sediments, Ed. by L. Hampton Plenum, New York.

    Google Scholar 

  • Tarantola A., (2005). “Inverse problem theory and methods for model parameter estimation, SIAM, Philadelphia, PA, 342 pages

    Google Scholar 

  • Thode A. (2004)., “The derivative of a waveguide acoustic field with respect to an arbitrary sound speed perturbation”, J. Acous. Soc. Am. 115(6), 2824–2833

    Google Scholar 

  • Turgut, A., Orr, M, and Rouseff, D.(2010) “Broadband source localization using horizontal beam acoustic intensity striations.” J. Acoust. Soc. Am. 127(1), pp. 73–84 (2010).

    Google Scholar 

  • Wunsch C., “The ocean circulation inverse problem”, Cambridge University Press, Cambridge, U.K., 442 pages (1996).

    Google Scholar 

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Correspondence to Boris Katsnelson .

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Katsnelson, B., Petnikov, V., Lynch, J. (2012). The Inverse Problem. In: Fundamentals of Shallow Water Acoustics. The Underwater Acoustics Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-9777-7_7

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  • DOI: https://doi.org/10.1007/978-1-4419-9777-7_7

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  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-9776-0

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