| Summary: | This thesis focuses on the global seismic forward modelling of body and surface waveforms in realistic 3-D Earth models using approximate and purely numerical methods. Firstly, we investigate two techniques: (i) the Born approximation, which should be valid for media with weak heterogeneity; and, (ii) the full ray theory approach, which should be valid for smooth media. We find that the Born approximation has a very limited domain of validity. It only models accurately surface waveforms with wave periods longer than T~80 s–90 s in existing earth models, and for T > 120 s–130 s when models with stronger heterogeneity are considered. On the other hand, the full ray theory is valid for almost all the earth models considered, failing only for unrealistically rough models. Hence, there is scope to build future improved global tomographic models using this technique, which is computationally very efficient. We then use a purely numerical technique, the spectral element method, to assess the quality of a recently built global radially anisotropic mantle model (SGLOBErani). We find that it explains independent seismic data slightly better than a previous widely used model (S40RTS). Moreover, our tests find small data misfit differences between isotropic and anisotropic versions of the models considered, which highlight the difficulties in constraining 3-D radially anisotropic structure. Finally, we carry out forward modelling experiments of short-period (T > 5 s) body waves travelling through the Earth’s lowermost mantle and investigate the effects of isotropic (1-D and 3-D), anisotropic and attenuation structure on wave propagation. We find that phase interference can change the shape and apparent arrival-time of wave pulses. This can give rise to apparent SH-SV wave splitting, even when isotropic earth models are used. This suggests that caution should be taken when interpreting SH-SV splitting of deep mantle body waves exclusively in terms of anisotropy in the lowermost mantle.
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