In seismic reflection surveying, by recording both pressure and shear-wave reflections, one can increase the amount of information obtained about the subsurface rather than by recording pressure waves alone. Geologic structures that are not visible by using conventional pressure-data may possibly be imaged using shear waves, thus mitigating the risk in oil and gas exploration and production. Horizontally layered sedimentary rocks exhibit anisotropy that can be approximated by an effective transverse isotropic medium with a vertical axis of symmetry. Taking into account a vertically transverse isotropic earth, we derive phase-slowness expressions for quasi-P and quasi-SV waves that are used in a one-way wave-equation migration scheme. We derive simplified slowness-expressions that are useful for processing of conventional pressure data. Numerical examples demonstrate that the slowness approximations are valid for wide-angle propagation, and the resulting one-way propagators are validated on a series of synthetic tests and applied on a field ocean-bottom seismic data set. The results show that the method accurately images both compressional and converted waves in OBS data over a vertically transverse isotropic medium.