We have implemented surface wave full ray theory to investigate the influence of source, path and receiver effects on observed minor- and major-arc, long period (T~ 150 s), three-component surface waves. Calculations are carried out using a variety of global tomographic earth models. We conduct a synthetic numerical study of phase and amplitude anomalies due to source, path and receiver effects. We estimate that the influence of the local structure at the receiver is generally negligible compared with the other terms. Phase anomalies are mostly controlled by path effects. However, amplitude variations due to the source, particularly due to the local structure at the source, are also important. We show that, for the tomographic models we use, in theory this type of anomaly is as important as that produced by focusing and defocusing effects along the propagation path. We present results of a statistical experiment to assess the impact of these effects on the fit to observed waveforms. As expected, waveforms calculated using laterally varying models match the data better than spherical earth calculations. The improved waveform fit is mainly caused by more accurate phase predictions due to path corrections. On average, calculations using the laterally varying models do not improve the amplitude fit compared with that for a spherically symmetric earth. We assess the impact of uncertainties in the source mechanism and location on the anomalies, by updating the seismic source parameters using an inversion scheme similar to the Harvard CMT method. Even after correcting for the earthquake source location and mechanism, on average, the laterally varying tomographic models used in this study do not explain observed surface wave amplitudes better than spherical earth calculations. This probably reflects unmodelled effects, such as lateral variations in attenuation, azimuthal anisotropy and finite frequency effects. However, it also suggests that new earth models need to be built fully exploiting all the information in the data, particularly amplitudes.