Summary Observations of seismic anisotropy provide useful information to infer directions of mantle flow. However, existing global anisotropic tomography models are not consistent, particularly in the lower mantle. Therefore, the interpretation of seismic anisotropy in terms of mantle dynamics and evolution remains difficult. While surface and body waves are commonly used to build radially anisotropic tomography models, they provide heterogeneous data coverage and the radial anisotropy structure retrieved using these data may be biased by the use of imperfect crustal corrections. Normal modes, the free oscillations of the Earth, automatically provide global data coverage and their sensitivity to shear-wave (vs) and compressional-wave (vp) velocity makes them suitable to study both vs and vp anisotropy in the mantle. In this study, we assess whether current normal mode splitting data have sufficient sensitivity to lower mantle anisotropy to potentially constrain it. We consider the uncertainties in the data and the effect of inaccuracies in crustal thickness corrections and the assumed scaling between vp and vs. We perform forward modelling of normal mode data using six different 3-D global radially anisotropic tomography models to document how strong and widespread anisotropy has to be to be observable in current normal mode data. We find that, on average 50 per cent of the spheroidal and 55 per cent of the toroidal modes investigated show significant sensitivity to vs anisotropy, while roughly 57 per cent of the spheroidal modes also have strong sensitivity to vp anisotropy. Moreover, we find that the normal mode data fit varies substantially for the various anisotropic tomography models considered, with the addition of anisotropy not always improving the data fit. While we find that crustal thickness corrections do not strongly impact modes that are sensitive to the lower mantle, we observe a trade-off between radial anisotropy and vp scaling for these modes. As long as this is taken into consideration, our findings suggest that existing normal mode data sets can provide valuable information on both vs and vp anisotropy in the mantle.

<p>Seismic tomography provides valuable insights into the structure, composition and evolution of the mantle. However, the origin of structures like the Large-Low-Velocity-Provinces (LLVPs) in the lowermost mantle remains debated. Their velocity anomalies have been interpreted to be due to purely thermal or also compositional variations, with implications for mantle circulation, the evolution of the core and the Earth’s heat budget.</p> <p>To uniquely interpret seismic structures such as the LLVPs, it is crucial to constrain the relationships between different seismic observables, e.g. the ratio between shear-wave velocity (Vs) and compressional-wave velocity (Vp) variations. Joint inversions of seismic velocities have been performed, but their velocity amplitudes may be biased, uncertainties are typically not provided, and the resolution of Vs and Vp structures generally differs in existing models.</p> <p>To overcome these issues, we make use of the recently developed <em>SOLA method </em>(Zaroli, 2016), which is based on a Backus-Gilbert philosophy. Instead of finding a model with a particular data fit, we aim to construct model averages of the true Earth with uncertainties, whilst having a control on the model resolution. This direct control on resolution enables us to build Vs and Vp models that sample the same parts of the mantle, and therefore to robustly constrain the Vs/Vp ratio.</p> <p>Here, we test this philosophy by applying the SOLA method to normal modes. These free oscillations of the Earth are particularly useful to study the relationships between seismic velocities as they are directly sensitive to multiple physical parameters, including Vs, Vp as well as density. We illustrate our approach and discuss the trade-off between uncertainties and resolution using synthetic tests for both Vs and Vp, before showing real data inversions. Finally, we discuss the implications of our results for the Vs/Vp ratio in terms of mantle temperature and composition.</p>

<p>Seismic tomography is a powerful tool to study the deep Earth, given the lack of direct observations. Seismic structures can be interpreted together with constraints from other disciplines, such as geodynamics and mineral physics, to provides valuable information about the structure, dynamics and evolution of the mantle. Nevertheless, a robust physical interpretation of seismic images remains challenging as tomographic models typically lack uncertainty information and may have biased amplitudes due to uneven data coverage and regularisation.</p><p>We aim to build tomographic models of the mantle with associated uncertainties and unbiased amplitudes. For this, we use the SOLA method (Zaroli, 2016) applied to normal mode data, the Earth’s free oscillations. SOLA is based on a Backus-Gilbert approach, which explicitly constrains the amplitudes to be unbiased and inherently computes the model uncertainty and resolution. This approach enables us to perform meaningful physical interpretations of the imaged structures. By applying this method to normal modes, we obtain valuable insights on the long wavelength structure of the mantle. The use of normal modes also has several advantages: these data are sensitive to multiple parameters, including both Vs and Vp anisotropy as well as density, and they provide global data coverage.</p><p>Here, we report on our progress towards a new 3-D mantle model based on the inversion of normal mode splitting function data. We discuss initial results from synthetic tests and isotropic inversions in terms of model estimates, uncertainties and resolution.</p>

<p>For a thorough understanding of the impact of mantle convection on vertical motions of the lithosphere, computational modeling plays a crucial role. Mantle circulation can be modeled by solving the equations of motion of a fluid using Earth-like input parameters assimilating plate motions at the surface in discrete steps through time. Thus, a realistic Earth model relies on the robustness of the inserted information. However, apart from the general difficulty of inferring deep Earth’s properties, also the plate tectonic model introduces uncertainty. Especially the linking of relative plate motions to absolute position relies on controversial assumptions such as fixity of structures in the mantle (e.g., plumes or Large-Low-Shear-Velocity Provinces) or the association between subducted plates at depth and high velocity regions in tomographic images. The latter specifically are restricted by non-uniqueness and the need to regularize the inversions, distorting structures and damping heterogeneity amplitudes.</p> <p>In order to infer secondary results from an MCM, it is thus important to validate the model against independent observations. Here, we employ Earth’s free oscillations that feature global sensitivity to 3-D structure for model assessment, complementing our earlier work using seismic body wave data. To this end, the temperature field of a published MCM is converted to seismic velocity with the help of a thermodynamic model of mantle mineralogy. An effective forward approach for the computation of normal mode data from synthetic Earth models is the calculation of splitting functions, describing the distortion of characteristic frequency peaks in the spectrum induced by even degree structural heterogeneity. A general problem is that the sensitivity of normal modes with depth often shows oscillatory behaviour preventing a straight forward relation of frequency shifts to structure in a certain depth range. This can be mitigated by combining kernels of several modes via a Backus-Gilbert approach to obtain focused sensitivity in pre-specified depth ranges of the mantle. For testing the significance of relevant model differences in splitting function data, geometrical alterations mimicking changes in the absolute reference frame and viscosity were applied to a pre-computed MCM. Current results indeed indicate that normal mode data are sensitive to such model changes within their respective uncertainty ranges.</p>