A new way of reconstructing wave fronts is developed for testing the validity of the great circle approximation in dispersion analysis of surface waves. Phase and time delays between pairs of stations of an array are used to reconstruct the wave fronts or surfaces of equal phase. This technique is applied to fundamental mode Rayleigh waves recorded at the NARS stations during the ILIHA (Iberian Lithosphere Heterogeneity and Anisotropy) project. The resulting wave fronts are compared with the theoretical ones, i.e. calculated assuming that the waves have traveled along the great circle path with a constant phase velocity, and the angle between both fronts is calculated. Waves traveling mostly through a laterally homogeneous oceanic path before arriving to the Iberian Peninsula are analyzed for the frequency range of 10 to 60 mHz. These show angles up to 8 degrees between the theoretical wave fronts and the wave fronts reconstructed using the delay data. This implies that we make a relative error less than 1% when calculating path-averaged phase velocities ignoring the deviation of the arrival of the wave from the great circle direction. ¿ American Geophysical Union 1993