|
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
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
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
Linking options:
https://www.mathnet.ru/eng/smj1910 https://www.mathnet.ru/eng/smj/v49/i5/p1157
|
Statistics & downloads: |
Abstract page: | 361 | Full-text PDF : | 124 | References: | 52 | First page: | 7 |
|