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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 5, Pages 1157–1183 (Mi smj1910)  

This article is cited in 6 scientific papers (total in 6 papers)

On the problem of determining the parameters of a layered elastic medium and an impulse source

V. G. Romanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (456 kB) Citations (6)
References:
Abstract: Considering the linear system of elasticity equations describing the wave propagation in the half-space $\mathbb R^3_+=\{x\in\mathbb R^3\mid x_3>0\}$ we address the problem of determining the density and elastic parameters which are piecewise constant functions of $x_3$. The shape is unknown of a point-like impulse source that excites elastic oscillations in the half-space. We show that under certain assumptions on the source shape and the parameters of the elastic medium the displacements of the boundary points of the half-space for some finite time interval $(0,T)$ uniquely determine the normalized density (with respect to the first layer) and the elastic Lamé parameters for $x_3\in[0,H]$, where $H=H(T)$. We give an algorithmic procedure for constructing the required parameters.
Keywords: elasticity system, layered medium, inverse problem, algorithm for solution.
Received: 17.08.2007
English version:
Siberian Mathematical Journal, 2008, Volume 49, Issue 5, Pages 919–943
DOI: https://doi.org/10.1007/s11202-008-0090-0
Bibliographic databases:
UDC: 517.958
Language: Russian
Citation: V. G. Romanov, “On the problem of determining the parameters of a layered elastic medium and an impulse source”, Sibirsk. Mat. Zh., 49:5 (2008), 1157–1183; Siberian Math. J., 49:5 (2008), 919–943
Citation in format AMSBIB
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\paper On the problem of determining the parameters of a~layered elastic medium and an impulse source
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\vol 49
\issue 5
\pages 1157--1183
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\transl
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\crossref{https://doi.org/10.1007/s11202-008-0090-0}
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  • https://www.mathnet.ru/eng/smj/v49/i5/p1157
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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    Abstract page:361
    Full-text PDF :124
    References:52
    First page:7
     
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