Определение параметров изотропной среды в шаре [Итоговый научный отчет по междисциплинарному интеграционному проекту СО РАН: “Разработка теории и вычислительной технологии решения обратных и экстремальных задач с приложением в математической физике и гравимагниторазведке”]

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.