We investigate in more detail the origin of chromospheric Alfvén waves that give rise to the separation of ions and neutrals, the First Ionization Potential Effect (FIP), through the action of the ponderomotive force. In open field regions, we model the dependence of fractionation on the plasma upflow velocity through the chromosphere for both shear (or planar) and torsional Alfvén waves of photospheric origin. These differ mainly through their parametric coupling to slow mode waves. Shear Alfvén waves appear to reproduce observed fractionations for a wider range of model parameters, and present less of a "fine-tuning" problem than do torsional waves. In closed field regions, we study the fractionations produced by Alfvén waves with photospheric and coronal origins. Waves with a coronal origin, at or close to resonance with the coronal loop, offer a significantly better match to observed abundances than do photospheric waves, with shear and torsional waves in such a case giving essentially indistinguishable fractionations. Such coronal waves are likely the result of a nanoflare coronal heating mechanism, that as well as heating coronal plasmas releases Alfvén waves that can travel down to loop footpoints and cause FIP fractionation through the ponderomotive force as they reflect from the chromosphere back into the corona.