Basin simulators have been used previously for deriving subsalt velocity models with the use of a correlation to relate effective stress to velocity. We build on this, and the work of others, to use physical models to relate porosity to velocity for migrating seismic data. This process yields a physically realizable isotropic velocity model that is consistent with the geologic model and matches the tomographic velocity model above salt and in regions where the tomographic velocity estimate is accurate. We then use a geomechanical simulator to model the stress distribution in and around allochthonous salt where material properties between salt and sediment change. Our stress model is the basis for an anisotropic velocity model using Murnaghan's theory for finite elastic deformation. This formulation, with bounds placed on the elastic coefficients, leads to significant imaging improvements adjacent to salt.