We numerically study the Z2 phase diagram of a 3d topological insulator in the mass-disorder plane using the scattering matrix approach. We confirm the topological phase boundaries as calculated analytically from a self consistent Born approximation and previous transfer matrix studies. By computing the Z2 invariant directly for the disordered topological Anderson insulator, we unambiguously identify the topological nature of this phase without resorting to its connection with the clean case or being limited to small system sizes as in exact diagonalization. We further find evidence of a disorder induced 'weak' topological Anderson insulator transition and a transition to a trivial Anderson insulator in the strong disorder limit. |