Summary We measure the seismic anisotropy of the inner core using PKPbc-PKPdf and PKPab-PKPdf differential travel times, as a function of the angle ζ between the Earth’s rotation axis and the ray path in the inner core. Previous research relied heavily on body waves originating in the South Sandwich Islands (SSI) and traveling to seismic stations in Alaska to sample inner core velocities with low ζ (polar paths). These SSI polar paths are problematic because they have anomalous travel time anomalies, there are no ultra polar SSI paths with ζ < 20o and they only cover a small part of the inner core. Here we improve constraints on inner core anisotropy using recently installed seismic stations at high latitudes, especially in the Antarctic, allowing us to measure ultra polar paths with ζ ranging from 20o − 5o. Our new data shows that the South Sandwich Island’s polar events are fast but still within the range of velocities measured from raypaths originating elsewhere. We further investigate the effect of mantle structure on our data set finding that the SSI data is particularly affected by fast velocities underneath the SSI originating from the subducted South Georgia slab which is currently located just above the CMB. This fast velocity region results in mantle structure being misinterpreted as inner core structure and we correct for this using a P-wave tomographic model. We also analyse the effect of velocity changes on the raypaths within the inner core and find that faster velocities significantly change the raypath resulting in the ray travelling deeper into the inner core and spending more time in the inner core. To remove this effect we propose a simple but effective method to correct each event-station pair for the velocity dependent raypath changes in the inner core, producing a more reliable fractional travel time measurement. Combining the new ultra polar data with mantle and raypath corrections results in a more reliable inner core anisotropy measurement and an overall measured anisotropy of 1.9%-2.3% for the whole inner core. This is lower than previous body wave studies ( 3% anisotropy) and in better agreement with the value of inner core anisotropy measured by normal modes ( 2% anisotropy). We also identify regional variation of anisotropic structure in the top 500 km of the inner core which appears to be more complex than simple hemispherical variations. These regional variations are independent of the SSI data and are still present when these data are excluded. We also find a potential innermost inner core with a radius of 690 km and stronger anisotropy.

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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.

<p>The inner core contains strong seismic heterogeneity, both laterally and from the surface to the centre. Accurately resolving the seismic structure of the inner core is key to unravelling the evolution of the core. Seismic models of inner core structure are often limited by their parameterization, which means it is difficult to interpret which features of the inner core are real (e.g. hemispheres or the inner most inner core). To overcome this we conduct seismic tomography using transdimensional inversion on a high quality data set of 5296 differential and 2344 absolute P-wave travel times. By taking a transdimensional approach we allow the data to define how the model space is parameterized and this provides us with both the mean structure of the inner core but also the probability distributions of each model parameter. This allows us to identify which regions of the model space are well constrained and likewise which regions are poorly constrained. We compare results from a static MCMC model and a transdimensional MCMC model, this provides confidence in our results as both models show clear similarities in structure. From no prior assumptions on inner core structure we recover many first order observations: such as anisotropic hemispheres and an isotropic outer inner core (OIC) along with potential observations of an inner most inner core. With higher resolution than previous inner core tomography we can provide more detailed interpretation of inner core structure and draw conclusions with greater confidence. We also conduct transdimensional inversions on a subset of our data which does not contain South Sandwich Islands (SSI) events which are considered by many to be unreliable or contaminated with mantle structure. The overall inner core structure remains largely the same however, showing that the SSI data does not significantly alter our final interpretations.</p>

<p>The Earth's inner core displays strong seismic anisotropy and 3D heterogeneity, which are most likely formed as a result of growth processes and post solidification deformation. Thus, accurately resolving seismic anomalies is key to understanding the formation and dynamic mechanisms of the inner core. Our ultimate aim is to improve current constraints on seismic anomalies in the inner core by combining normal mode data and body wave data in a joint tomographic inversion. While the body wave data is sensitive to regional scale seismic P-wave anisotropy in the inner core, normal modes provide long wavelength information on density, P-wave anisotropy and S-wave anisotropy. </p><p>We have produced a high resolution 3D seismic model of inner core isotropic and anisotropic velocity variations using a transdimensional methodology with body waves. In the transdimensional approach, the inversion itself determines the parameterization. It is encouraging to find many well know features, such as a hemispherical differences between a slow and strongly anisotropic western region and a fast and only weakly anisotropic eastern hemisphere, without a priori imposing those in our parameterization. We are now interested to see if the features seen using body waves are consistent with those seen by normal modes. We measure inner core sensitive normal modes using the splitting function approximation in a way which thoroughly explores the splitting function measurement model space. This then allows us to quantify the uncertainty in individual splitting function coefficients for each mode. We then combine these new normal mode measurements and uncertainty estimates with our body wave data in a joint probabilistic inversion for seismic structure in the inner core.</p>