Mantle tomography and its relation to temperature and composition

We propose a new method to constrain lateral variations of temperature and composition in the lower mantle from global tomographic models of shear- and compressional-wave speed. We assume that the mantle consists of a mixture of perovskite and magnesio-wüstite. In a first stage, we directly invert V_P and V_S anomalies for variations of temperature and composition, using the appropriate partial derivatives (or sensitivities) of velocities to temperature and composition. However, uncertainties in the tomographic models and in the sensitivities are such that variations in composition are completely unconstrained. Inferring deterministic distributions of temperature and composition being currently not possible, we turn to a statistical approach, which allows to infer several robust features. Comparison between synthetic and predicted ratios of the relative shear- to compressional-velocity anomalies indicates that the origin of seismic anomalies cannot be purely thermal, but do not constrain the amplitude of the variations of temperature and composition. We show that we can estimate these variations using histograms of the relative V_P and V_S anomalies at a given depth. We computed histograms for a large variety of cases and found that at the bottom of the mantle, variations in the volumic fraction of perovskite from ?14 to 10% are essential to explain seismic tomography. In the mid-mantle, anomalies of perovskite are not required, but moderate variations (up to 6%) can explain the observed distributions equally well. These trade-offs between anomalies of temperature and composition cannot be resolved by relative velocity anomalies alone. An accurate determination of temperature and composition requires the knowledge of density variations as well. We show that anomalies of iron can then also be resolved.