Constraints on core-mantle boundary topography from normal mode splitting

The frequencies of Earth's normal modes are split by rotation, ellipticity, and internal structure of the Earth. Thus, models of mantle heterogeneity and discontinuity topography generate splitting that may be tested against observations. We insert maps of core-mantle boundary (CMB) topography, which are derived via either a purely seismic or a joint tomographic/geodynamic inversion of body waves data, on top of tomographic model S20RTS. We then calculate synthetic splitting functions for normal modes that have been shown to be sensitive to CMB topography and compare these to observed normal mode splitting data. The CMB topography maps obtained via geodynamically constrained tomography fit normal mode data better than purely seismic maps, in particular when the geodynamic constraint also accounts for the presence of post-perovskite in the D-'' region. We test the significance of the reduction in misfit using the concept of observability which suggests that normal modes are able to observe the difference between the different CMB topography maps. In addition, we find that the statistical significance, assessed by checking what fraction of 1000 randomly generated CMB models achieve a comparatively good fit as the desired model, is higher than 92% for degree 2 and 98% for all degrees. In summary, we have identified a model of CMB topography that fits body wave data and improves, at least to some extent, the fit to normal mode data, and is coherent with the large-scale pattern of deep mantle heterogeneity expected on the basis of convection modeling.