The response of magnetic vortex cores to subnanosecond in-plane magnetic field pulses was studied by time-resolved x-ray microscopy. Vortex core reversal was observed and the switching events were located in space and time. This revealed a mechanism of coherent excitation by the leading and trailing edges of the pulse, lowering the field amplitude required for switching. The mechanism was confirmed by micromagnetic simulations and can be understood in terms of gyration around the vortex equilibrium positions, displaced by the applied field.