A method to study the response of surface topographies submitted to incident<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi mathvariant="normal">S</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:math>waves is presented. The method is based on the superposition of diffracted sources described in Jaramillo et al. (2013). Since the technique proceeds in the frequency domain in terms of the superposition of incident, reflected, and diffracted waves, it has been termed like a superposition based diffraction approach. The final solution resulting from the superposition approach takes the form of a series of infinite terms, where each term corresponds to diffractions of increasing order and of decreasing amplitude generated by the interactions between the geometric singularities of the scatterer. A detailed, step-by-step algorithm to apply the method is presented with regard to the simple problem of scattering by a V-shaped canyon. In order to show the accuracy of the method we compare our time and frequency domain results with those obtained from a direct Green’s function approach. We show that fast solutions with an error of the order of 6.0% are obtained.