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An inverse problem for the two-dimensional wave equation in a stratified medium

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Book cover Inverse Problems of Wave Propagation and Diffraction

Part of the book series: Lecture Notes in Physics ((LNP,volume 486))

Abstract

Let D={(x, y) ∈ ℝ2 | x>0, y ∈ ℝ} and u(x, y, t) be the solution of an initial-boundary value problem for the two-dimensional wave equation in the half plane D. The half plane D carries a velocity stratification given by flat layers parallel to the boundary of the half plane characterized by a thickness and a constant velocity. We consider the following inverse problem: given the initial data, from the knowledge of u(0, 0, t), t>0, reconstruct the stratification. We give an algorithm to solve this problem based on an explicit formula for u(0, 0, t) and we report some numerical experience.

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References

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Authors and Affiliations

  1. Dipartimento di Matematica e Fisica, Università di Camerino, 62032, Camerino (MC), Italy

    Lorella Fatone, Pierluigi Maponi & Cristina Pignotti

  2. Dipartimento di Matematica “G.Castelnuovo”, Università di Roma “La Sapienza”, 00185, Roma, Italy

    Francesco Zirilli

Authors
  1. Lorella Fatone
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  2. Pierluigi Maponi
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  3. Cristina Pignotti
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  4. Francesco Zirilli
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Editor information

Guy Chavent Pierre C. Sabatier

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© 1997 Springer-Verlag

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Fatone, L., Maponi, P., Pignotti, C., Zirilli, F. (1997). An inverse problem for the two-dimensional wave equation in a stratified medium. In: Chavent, G., Sabatier, P.C. (eds) Inverse Problems of Wave Propagation and Diffraction. Lecture Notes in Physics, vol 486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105776

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  • DOI: https://doi.org/10.1007/BFb0105776

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62865-1

  • Online ISBN: 978-3-540-68713-9

  • eBook Packages: Springer Book Archive

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