Determining of isotropic medium parameters in a~sphere

T. V. Bugueva

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 524-530.

Résumé

We consider an inverse problem for a system of isotropic elasticity equations in a sphere domain. The linearized problem of identification of three characteristics of elastic isotropic medium is investigated. It is supposed that the medium density $\rho(r)$ depends on the radial variable only and the propagation velocity of longitudinal $c(r,\theta,\varphi)$ and transverse $a(r,\theta,\varphi)$ waves can be represented in the form $a^2(r,\theta,\varphi)=a_0^2+a_1(r,\theta,\varphi)$, $c^2(r,\theta,\varphi)=c_0^2+c_1(r,\theta,\varphi)$, where $a_0^2$, $c_0^2$ are some known constants, and unknown functions $a_1(r,\theta,\varphi)$, $c_1(r,\theta,\varphi)$ are small in comparison with the constants $a_0^2$ и $c_0^2$, correspondingly. The uniqueness theorem is proved and estimates of conditional stability of the inverse problem solution are obtained.

Détail

Keywords: inverse problems, isotropic elasticity, conditional stability estimate.

Bibliographie

[1] T. V. Bugueva, “Multidimensional inverse problem for isotropic elasticity system in a sphere”, J. Inv. Ill-Posed Problems, 15:9 (2007), 893–934 | DOI | MR