How Well Do Tomographic Images Explain Surface Waveforms?

Surface wave tomography based on phase measurements has achieved great successes in the last decades. However, in order to interpret the fine details of tomographic models, it is necessary to go beyond classical resolution checks, using tests with data not employed in the construction of the images. Moreover, it is desirable to apply different forward modelling techniques to assess inaccuracies due to simplified theoretical formalisms. Seismic wave amplitudes potentially provide complementary constraints on the Earth's structure and should be used to check the accuracy of existing models. We have implemented surface wave full ray theory (FRT) to investigate observed minor and major arc three-component surface waveforms, giving special emphasis to amplitudes. Calculations are performed upon mantle model S20RTS and for three sets of published phase velocity maps, combined with global crust model CRUST2.0. The synthetic waveforms calculated fit the data better than the great circle approximation (GCA). To understand the reasons for this improvement we study amplitude and phase anomalies and how they are controlled by the source, path and receiver terms. We have conducted a synthetic numerical study of phase and amplitude anomalies due to each of the terms, as predicted by the different phase velocity maps. The resulting phase perturbation is mostly controlled by path effects. The influence of the local structure at the receiver is generally negligible compared with the other terms, except for the amplitudes of the horizontal components of Rayleigh waves. However, for Rayleigh waves, theoretical amplitude anomalies due to the local structure at the source and the deviation in takeoff azimuth of the ray leaving the source are more important than previously thought. The resulting perturbation is as important as that produced by focusing and defocusing effects along the propagation path. We subsequently present results of a statistical experiment to assess the impact of these effects on observed waveforms. The improved waveform fit of full ray theory synthetics is mainly caused by more accurate phase predictions due to path corrections. The predicted amplitude anomalies correlate with observations. Nevertheless, the observed amplitude signal is not fully explained, so that on average, full ray theory does not improve the amplitude fit compared with that for a spherical Earth model. Finally, we investigate the influence of uncertainties in the source mechanism and location on the waves, by implementing an iterative inversion procedure similar to the Harvard-CMT method to determine earthquake source parameters. We use the forward modelling techniques FRT and GCA upon the laterally varying models. In all cases using the new source locations reduce the misfit, but the considered laterally varying models still do not improve the average amplitude match compared with a spherical Earth calculation. The phase velocity maps considered in this study cannot explain observed surface wave amplitudes alone, even after correcting for the earthquakes source location and mechanism. This probably reflects unmodelled effects, such as lateral variations in attenuation, azimuthal anisotropy or, possibly, stations miscalibrations.