Surface-wave phase velocity dispersion measurements provide valuable information on the structure of the Earth's upper mantle, but direct measurements are limited by the distribution of seismic stations, leaving large part of the globe uncovered. Here we present a global dataset of 98 fundamental mode, Rayleigh and Love phase velocity maps in the 20-460s period range computed using the Automated Multimode Inversion (AMI) of millions of seismic waveforms. Thanks to the dense global coverage we can parameterise our model with a dense triangular grid with an average 225 km inter-knot spacing. The laterally continuous distribution of phase velocities and the smooth variations across separately inverted periods allow extraction of Love- and Rayleigh dispersion curves at any point on the Earth's Surface. This allows us to produce robust dispersion measurements in areas that are otherwise poorly sampled by seismic stations.