3D transdimensional seismic tomography of the Earth's inner core using body waves and normal modes

Since the discovery of the inner core almost 100 years ago, the seismological community has found that the inner core contains significant heterogeneity in its elastic structure. This observation is significant and in many ways unexpected; we believe the inner core to be (relatively) chemically homogeneous consisting primarily of iron and nickel. Yet we observe that seismic waves which pass through the inner core travel faster in a north-south direction than an east-west direction and that the spectra of whole Earth oscillations are anomalously split in a way which is consistent with the same velocity difference. This difference in velocity between two directions through the inner core is called anisotropy, and from mineral physics we have reason to believe that this anisotropy is caused by the alignment of iron crystals which are themselves anisotropic at inner core temperatures and pressures. The primary goal of this thesis is to constrain, as well as possible, the elastic structure of the inner core. We expand upon the body wave dataset by adding new observations of paths which travel almost parallel to Earth's axis of rotation, giving us improved sensitivity to velocity in the north-south direction in the inner core. We combine our new data with other body wave datasets to produce a 3D seismic tomographic model of the inner core. This model utilised a transdimensional Markov chain Monte Carlo methodology which not only determines the best fitting anisotropy structure in the inner core, but also the uncertainties in our model and it does not require any prior assumptions on the parameterization of the inner core. The advantage of this method is significant, especially because the relatively poor sampling of the inner core means that prior assumptions on the parameterization may significantly affect the final model. In the transdimensional approach the parameterization is a part of the inversion. In our new transdimensional model we confirmed many previous observations, including an isotropic layer of 100 km thickness at the top of the inner core and that the inner core is split broadly into a western region and an eastern region. We are now able to make new robust observations, seeing for the first time that the western anisotropic zone is isolated to the northern hemisphere and that the inner most inner core exists but primarily in the eastern region. These observations are significant as it provides new insight into the mechanisms of inner core formation and dynamics, and we discuss the potential implications for inner core geodynamics. It is important in deep Earth research to bring together as many sources of information as possible. We have also measured 18 normal modes sensitive to the inner core. We used a splitting function approximation and a grid search methodology to constrain the uncertainties in the measurement. The data were then used to produce a preliminary 1D transdimensional model of inner core anisotropy using polynomial basis functions and find a model which agrees reasonably well with the spherical average of compressional anisotropy from the body wave model.