Linearized scattering theory is used to describe three-dimensional surface wave scattering by topography on a layered medium. A short derivation for the scattered surface wave is presented. The implications and limitations of the scattering theory are discussed qualitatively. Furthermore, an expression is presented for the partial derivatives of the surface wave phase velocities with respect to topography. It is shown that for periods between 15 and 30 sec, the fundamental mode phase velocity perturbation due to topography is of the order of 1 per cent for a mountain of 1 km height. For the higher mode phase velocities, the effects of topography are negligible.