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Determining the parameters of a stratified piecewise constant medium for the unknown shape of an impulse source

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Abstract

For a hyperbolic wave equation with some parameter λ, we consider the problem of finding the piecewise constant wave propagation speed and a series of parameters in the conjugation condition. Moreover, the shape is assumed unknown of the impulse point source that excites the oscillation process. We prove that, under certain assumptions on the structure of the medium, its sought parameters are determined uniquely from the displacements of points of the boundary given for two different values of λ. We give an algorithm for solving the problem.

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Author information

Correspondence to V. G. Romanov.

Additional information

Original Russian Text Copyright © 2007 Romanov V. G.

The author was supported by the Russian Foundation for Basic Research (Grant 05–01–00171) and the Siberian Division of the Russian Academy of Sciences, 2006 (No. 26).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 6, pp. 1338–1350, November–December, 2007.

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Romanov, V.G. Determining the parameters of a stratified piecewise constant medium for the unknown shape of an impulse source. Sib Math J 48, 1074–1084 (2007). https://doi.org/10.1007/s11202-007-0109-y

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Keywords

  • wave equation
  • inverse problem
  • solution algorithm