Directional dependence of the phase velocity to P, SV and SH waves in a transversely isotropic media (TI) with vertical (VTI) or tilted (TTI) symmetry axis are studied. A comparison of the velocities obtained through the exact formula, the weak anisotropy and the acoustic approximation are presented. The 2D impulse responses (P and SV waves) are obtained solving the elastic and acoustic wave equation using the finite difference approximation. The variation of the numerical results to different measured anisotropy in sedimentary rocks are presented.