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Profile reconstruction of a continuously-stratified layer from reflection data on acoustic waves

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EN
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EN
The paper investigates the reflection-transmission process of acoustic waves, generated by an inhomogeneous fluid layer of finite thickness, which is sandwiched between two semi-infinite homogeneous half-spaces. First a direct problem is solved by determining the reflection and transmission coefficients along with the wave solution in the layer, produced by a known incident wave. Owing to the planar stratification of the layer, the unknown acoustic pressure is looked at as a generalized plane wave. Upon the Fourier transformation, the second-order wave equation is written as a firstorder system of equations for the dependence on the depth of the pressure and the partial derivative. The corresponding Volterra integral equation gives the pressure in the layer as a series of repeated integrals of powers of the pertinent depth-dependent matrix of the system. The reflection and transmission coefficients of the layer are then determined for any incidence angle. Next an inverse problem is investigated. The derivatives of the reflection coefficient, with respect to the frequency, are shown to provide the thickness of the layer, the speed beyond the layer and the moments, of any order, of the refractive index.
Rocznik
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73--98
Opis fizyczny
Bibliogr. 16 poz.
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Bibliografia
  • 1. A.B. WEGLEIN, F.V. ARAUJO, P.M. CARVALIIO, R.H. STOLT, K.H. MATSON, R.T. COATES, D. CORRIGAN, D.J. FOSTER, S.A. SHAW, II. ZHANG, Inverse scattering series and seismic exploration, Inverse Problems, 19, R27--R83, 2003.
  • 2. B.S. WHITE, M. ZHOU, Electroseismic prospecting in layered media, SIAM J. App. Math., 67, 69-98, 2006.
  • 3. L.M. BREKHOVSKIKH, Waves in Layered Media, Academic Press, New York 1980.
  • 4. A.J. ROBINS, Reflection of a plane wave from a fluid layer with continuously varying density and sound speed, J. Acoust. Soc. Am., 89, 1686-1696, 1991.
  • 5. L.-W. CAI, J. SANCHEZ-DEHESA, Acoustical scattering by radially stratified seatterers, .]. Acoust, Soc. Am., 124, 2715-2726, 2008.
  • 6. W.C. CHEW, Waves and Fields in Inhomogeneous Media, IEEE Press, New York 1995.
  • 7. G. CAVIGLIA, A. MORRO, Reflection and transmission of transient waves in anisotropic elastic multilayers, Q. J. Mech. Appl. Math., 56, 571--587, 2003.
  • 8. P. MARTIN, Acoustic scattering by inhomogeneous obstacles, SIAM J. Appl. Math., 64, 297-308, 2003.
  • 9. B. ZHANG, S.N. CHANDLER-WILDE, Acoustic scattering by an inhomogeneous layer on a rigid plate, SIAM J. Appl. Math., 58, 1931-1950, 1998.
  • 10. L. AMUNDSEN, A. REITAN, H.K. HELGESEN, B. ARNTSEN, Data-driven inversion/depth imaging derived from approximations to one-dimensional inverse acoustic scattering, Inverse Problems, 21, 1823-1850, 2005.
  • 11. G. CAVIGLIA, A. MORRO, Acoustic and elastic scattering by stratified media, Acta Me-chanica, 206, 173-191, 2009.
  • 12. D.S. AHLUWALIA, J.B. KELLER, Exact and asymptotic representations of the sound field in a stratified ocean, [in:] Wave Propagation and Underwater Acoustics, J.B. KELLER and J.S. PAPADAKIS [Eds.], Springer, Berlin 1977.
  • 13. P. MARTIN, Acoustic scattering by inhomogeneous spheres, J. Acoust. Soc. Am., Ill, 2013 2018, 2002.
  • 14. G. CAVIGLIA, A. MORRO, Reflection and transmission of transient acoustic waves with oblique incidence, Arch. Mech., 60, 243-262, 2008.
  • 15. A.D. PIERCE, Acoustics, p. 134, Acoustical Society of America, New York, 1994.
  • 16. M. ABRAMOWITZ, LA. STEGUN, Handbook of Mathematical Functions, Dover, New York 1965.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BATB-0001-0048
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