Love and Rayleigh waves generated by earthquakes on and near the Gibbs Fracture Zone travel along paths nearly parallel to the Reykjanes Ridge. Observations of the dispersion of such wave trains are used to determine models of shear velocity against depth for crustal ages of 0, 20, and 40 m.y. We find that the lithosphere increases in thickness from about 35 km near the ridge axis to about 65 km at crustal age 40 m.y. The increase in thickness is accompanied by an increase in shear wave velocity in the lithospheric lid and probably also in the underlying low-velocity channel.