The first years of my research have dealt with how to measure fundamental and higher mode phase velocities for Love and Rayleigh waves. We use a model space search approach to obtain the phase velocity measurements. The advantage of this approach is that this method will provide us not only with one 'best' (phase velocity) model but the whole ensemble of models. From this ensemble of models we infer Bayesian statistics such as one- and two-dimensional marginals. For the phase velocities, the one-dimensional marginals are Gaussian and therefore we can represent them by a mean and a standard deviation. We invert the fundamental and higher mode Love and Rayleigh phase velocity measurements for isotropic and azimuthally anisotropic phase velocity maps. Due to the consistent uncertainties for the measurements, we obtain the phase velocity maps including consistent uncertainties. The source of anisotropy is the lattice preffered orientation of mantle minerals under strain in the mantle. Since higher modes are much more sensitive to deeper structure, we expect to be able to find out more about mantle dynamics in the transition zone and lower mantle.