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One-Dimensional Inverse Scattering Problem in Acoustics

  • General and Applied Physics
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Abstract

We are concerned with the inverse scattering problem (ISP) in acoustics within the Marchenko inversion scheme. The quantum ISP is first discussed and applied in order to exhibit certain characteristics and application prospects of the method which could be useful in extending it to classical systems. We then consider the ISP in acoustics by assuming plane waves propagating in an elastic, isotropic, and linear medium. The wave equation is first transformed into a Schrödinger-like equation which can be brought into the Marchenko integral equation for the associated nonlocal kernel the solution of which provides us the full information of the underlying reflective profile. We apply the method in several model problems where the reflection coefficient of the multi-layer reflective medium is used as input to the ISP and in all cases we obtain excellent reproduction of the original structure of the scatterer. We then applied the inverse scattering scheme to construct profiles with certain predetermined reflection and transmission characteristics.

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Acknowledgement

This work was supported by the Greek General Secretariat for Research and Technology, innovation voucher 67107608–01–000171.

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Authors and Affiliations

  1. Department of Computer Science, University of Ioannina, 451 10, Ioannina, Greece

    Demetrios Gerogiannis & Isaac Elias Lagaris

  2. Physics Department, University of South Africa, Pretoria, 0003, South Africa

    Sofianos Antoniou Sofianos & Isaac Elias Lagaris

  3. Department of Physics, University of Ioannina, 451 10, Ioannina, Greece

    Georgios Antomiou Evangelakis

Authors
  1. Demetrios Gerogiannis
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  2. Sofianos Antoniou Sofianos
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  3. Isaac Elias Lagaris
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  4. Georgios Antomiou Evangelakis
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Correspondence to Sofianos Antoniou Sofianos.

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Gerogiannis, D., Sofianos, S.A., Lagaris, I.E. et al. One-Dimensional Inverse Scattering Problem in Acoustics. Braz J Phys 41, 248–257 (2011). https://doi.org/10.1007/s13538-011-0039-9

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  • DOI: https://doi.org/10.1007/s13538-011-0039-9

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