Reliable mantle density error bars: an application of the neighbourhood algorithm to normal‐mode and surface wave data

Summary We demonstrate the feasibility and reliability of a new approach to seismic modelling of long‐wavelength mantle structure. In doing so, we present new estimates of mantle model uncertainties that successfully explain apparent discrepancies in earlier 3D seismic density models and justify a new generation of model building. The characteristics of good models and of modelling error are described by model space ‘maps’ that display the data fit of a representative set of potential models. The neighbourhood algorithm (NA), recently developed by Malcolm Sambridge, allows efficient production of such maps for the long‐wavelength model parametrizations used in imaging the mantle density using normal‐mode data. We observe that when NA is applied to our global modelling problem the results are not only self‐consistent and consistent with independent resolution tests, but also explain discrepancies in the results of damped inversions. Synthetic ‘mapping’ experiments using the sensitivity kernels and measurement errors of several data catalogues allow us to determine the resolution of these data sets. Such resolution tests let us know which model parametrizations and data sets, if any, can yield meaningful results in inversions of real data. The new resolution tests reveal that recent density models from damped inversions of normal‐mode data are not robust. However, we also show that the addition of the most recent long‐wavelength data will, for the first time, reduce model covariances enough to achieve robust constraints on the depth and size of long‐wavelength density heterogeneity throughout the mantle.