The ray theoretical great circle approximation in global surface wave tomography is found to be limited to Earth models with a maximum degree l≤30 for surface waves at 40 s and l≤20 for surface waves at 150 s. This result holds for both phase velocity and group velocity maps. The highest resolution in present-day global surface wave tomography is close to these limits of ray theory. In order to obtain higher degree resolution models of the Earth in future surface wave tomography, it is necessary to take the scattering of surface waves into account. Increasing the data coverage in seismological networks will not improve the details of tomographic images if ray theory is still applied. It is essential to include the finite-frequency effects as well. ¿ 2001 American Geophysical Union