We investigate anomalies of both the phase velocity and the amplitude of surface wave that depend on the direction traversed along the great circle. Pairs of observed Rayleigh wave packets are convolved to show that the great circle phase velocity may depend on the propagation direction. We calculate synthetic seismograms using the eigensolutions obtained by the variational method to see if these anomalies are reproduced by present laterally heterogeneous earth models. The results show that present models can reproduce these anomalies qualitatively. ¿ American Geophysical Union 1990