Let a domain \(\Omega \subset {\mathbb{R}}^ 3\) with boundary \(\Gamma \subset C^ 2\) of bounded curvature be filled with a medium where the propagation speed of waves is variable. We consider inverse problems of recovering \(\rho\) (x)\(| \Omega\) from characteristic of wave processes in \(\Omega\) that are registered on \(\Gamma\). Two inverse problems, spectral and local (time-dependent) ones, are under consideration within the framework of a general scheme.