This article is cited in 2 papers

Direct and inverse problems of acoustic sounding in a layered medium with discontinuous parameters

A. A. Sedipkov<sup>ab

a</sup> Novosibirsk State University, 2 Pirogova st., 630090 Novosibirsk
^b Sobolev Institute of Mathematics, 4 Koptyug av., 630090 Novosibirsk

Abstract: We consider the direct problem of finding a solution to a one-dimensional acoustic equation with discontinuous coefficients on the whole line $y\in\mathbb R$ with boundary conditions of special kind at the interior point $y=0$. We prove that the direct problem is uniquely solvable in the corresponding function space and obtain a special presentation for its solution. Along with the direct problem, we study the inverse problem of recovering the acoustic impedance of the medium from known one-sided limits of the solution to the direct problem and its derivative at the point $y=0$. It is shown that, with the use of the obtained special representation of the direct problem, the inverse problem can be reduced to a inverse spectral problem for a Sturm–Liouville operator with discontinuous coefficients.

Keywords: direct and inverse problems, Sturm–Liouville operator, inverse spectral problem, acoustic impedance.

UDC: 517.984

Received: 03.08.2013

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