We present the application of the theory of Padé approximants to extending the perturbative solutions of acoustic wave equation for a three dimensional vertically varying medium with one interface. These type of solutions have limited convergence properties depending on either the degree of contrast between the actual and the reference medium or the angle of incidence of a plane wave component. We show that the sequence of Padé approximants to the partial sums in the forward scattering series for the 3D wave equation is convergent for any contrast and any incidence angle. This allows the construction of any reflected waves including phase-shifted post-critical plane waves and, for a point-source problem, refracted events or headwaves, and it also provides interesting interpretations of these solutions in the scattering theory formalism.