Multidimensional inverse problem for isotropic elasticity system in a sphere

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 ρ(r) depends on the radial variable only and the propagation velocity of longitudinal c(r, θ ϕ) and transverse a(r, θ, ϕ) waves can be represented as a²(r; θ, ϕ) = a²₀ + a₁(r, θ, ϕ), c²(r, θ, ϕ) = c²₀ + c₁(r, θ, ϕ), where a²₀, c²₀ are some known constants, and unknown functions a₁(r, θ, ϕ), c₁(r, θ, ϕ) are small in comparison with the constants a²₀ and c²₀ correspondingly. The uniqueness theorem is proved and estimates of conditional stability of the inverse problem solution are obtained.