A conditional stability estimate for solution of an inverse problem for the acoustic equation

We consider the multidimensional inverse problem for the acoustic equation $u_{tt}=c^{2}\Bigl(\Delta u-\nabla\ln\rho\cdot\nabla u\Bigr)$ in a medium filling interior of a cylinder infinite with respect to the variable $z$. We assume that the velocity function $c(r)$ is known. The problem of unique determination of the density function $\rho (r, \varphi, z)$ is considered in the linear approximation. The conditional stability estimation is obtained.