In this thesis we present all three stages of the inversion approach proposed by Kennett and Yoshizawa (2002). The three stage inversion approach consists of obtaining fundamental and higher mode Love and Rayleigh wave phase velocity measurements through waveform fitting in the first stage, combining them into multimode phase velocity models using the path average assumption in the second stage and an inversion for local shear wave speed properties to obtain a three-dimensional shear wave velocity model in the third stage. We first present a fully automated Monte Carlo modelspace search approach to measure fundamental and higher mode Love and Rayleigh wave phase velocities. The advantage of this approach is that we do not only obtain the best fitting model but the whole ensemble of models with their corresponding fit. This allows us to obtain mutually consistent uncertainties for the fundamental and higher mode phase velocity measurements. Our phase velocity measurements agree remarkably well with previous studies, but we have been able to enlarge the available dataset dramatically (>350,000 measurements). Surface waves are well suited to observe anisotropy since they carry information about both radial and azimuthal anisotropy. The presence of anisotropy is well established in the Earth's uppermost mantle, but it is more ambiguous in the deeper mantle. Since we use higher mode phase velocities which have a larger sensitivity to deeper structure compared to the fundamental mode, we improve our understanding of anisotropy into the deeper mantle. In the second stage, we thus invert the phase velocity measurements to obtain isotropic and azimuthally anisotropic phase velocity maps. Prior to inversion, we determine the optimum relative weighting for the isotropic and azimuthally anisotropic terms. We found that all fundamental and higher mode measurements require anisotropy. Special care was taken to obtain the posterior model uncertainties, needed to obtain the radial anisotropic shear wave velocity model. The azimuthal anisotropic phase velocity maps give indications of anisotropy at larger depths but a more detailed depth inversion using finite frequency kernels will provide more information on the depth extend of azimuthal anisotropy. Finally, we inverted the local azimuthally averaged phase velocity maps for radial shear wave anisotropy taking the full non-linearity into account using a Monte Carlo modelspace search approach. For the anisotropic model, we decided to compute the total probability of radial anisotropy and likewise that the amplitude of radial anisotropy is above 1% or 2%. We find a lithosphere dominated by fast horizontally polarized shear wave anisotropy (horizontal flow), an asthenosphere dominated by fast vertically polarized shear wave anisotropy (vertical flow) and a transition zone also dominated by fast vertically polarized shear wave anisotropy (vertical flow). The amplitude of anisotropy is likely large (>2%) in the lithosphere and asthenosphere and smaller in the transition zone (1%-2%). The lower mantle is most likely isotropic (or anisotropic with a very small amplitude
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