We have developed a modified prestack time migration (PSTM) approach that can directly image nonplanar data by using two effective velocity parameters above and below a datum. The proposed extension improves the so-called topography PSTM by introducing a dip-angle domain stationary-phase migration (or filtering) and combining effective velocity inversion with the residual static corrections. The stationary-phase migration to constrain the imaging aperture within Fresnel zones significantly improves the signal-to-noise ratio (S/N) of the image gathers, especially in the presence of steeply dipping structures. This helps to extract an accurate residual moveout from the common shot and receiver image gathers, and the surface-consistent residual statics hidden in these image gathers can be simultaneously obtained from an inversion process. As a result, the final migrated images show higher S/N and are better focused than the conventional topography PSTM. The proposed technique can handle rugged topography, especially in the presence of high near-surface velocities, without the need for prior elevation static corrections. The SEG foothills overthrust model and a real data set acquired on a piedmont zone are used to validate the modified topography PSTM. Synthetic and field data examples are obtained with good results.