How correct is a velocity model?

We discuss fundamental properties of the kinematic inversion problem. We argue that the inverse problem is ill-posed and generally does not have solution in a strictly defined sense. The solution of the inverse problem based on the best fit of observed and calculated reflection travel times may result in several subsurface models with significantly different geological meaning, but which all fit the observed data equally well. Does the seismic method have the potential to resolve such problems? We present and discuss one of the possibilities related to the use of a simple locally homogeneous model.