We have reached a stage in seismic tomography where further refinements with classical techniques become very difficult. Advances in numerical methods and computational facilities are providing new opportunities in seismic tomography to enhance the resolution of tomographic mantle images. 3-D numerical simulations of seismic wavefields also allow us to check the reliability of the current mantle images and the classical techniques. In this thesis, using 3-D wave simulations by a spectral element method, we present three specific studies which underline some shortcomings in global mantle tomography. We first investigated crustal corrections for fundamental mode surface waves. We compared the crustal corrections estimated by first order approximations such as great circle approximation, exact ray theory and finite-frequency theory, to those obtained from 3-D wave simulations. We observed that crustal corrections can produce errors larger than those in phase measurements at periods longer than 60 and 80 s for Rayleigh and Love waves, respectively. Rayleigh and Love waves are differently influenced by the crust. Therefore imperfect crustal corrections have potential to produce radial anisotropy which may bias our interpretation of anisotropy in the upper-mantle. Extensions to the great circle approximation do not improve the results because of the highly non-linear behaviour of the crust. Thus either the mantle has to be inverted together with the crust or 3-D background models have to be used for the measurements. We then compared real data with synthetic seismograms computed in various 3-D mantle models. We particularly investigated the effect of damping on global mantle models. In addition, we tried to examine the elastic and anelastic contribution of the models by comparing seismograms computed in 1-D and 3-D crustal and mantle models. Our results show that different 3-D mantle models give statistically similar results although they are different from each other. We observed that a large part of the seismograms remained unexplained, particularly the amplitudes. 3-D velocity models are not enough to explain amplitude information alone. Attenuation may have an important contribution to surface-wave amplitudes whereas body waves are more affected by scattering effects. Lastly, we proposed new misfit functions based on instantaneous phase and cross-correlation measurements for full waveform inversion. In addition, we qualitatively compared them to classical ones such as waveform and travel-time misfits by computing the finite-frequency sensitivity kernels using adjoint methods based upon a spectral element method. We observed that instantaneous phase measurements provide complementary information to the other misfit functions and are promising to exploit more information from a single seismogram
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