One of the most powerful approaches for understanding the 3‐D thermo‐chemical structure of the lower mantle is to link tomographic models with mineral physics data. This is not straightforward because of strong trade‐offs between thermal and chemical structures and their influence on seismic structures. They can be reduced by mapping simultaneously perturbations of wave speeds and density anomalies and by the quantitative assessment of the accuracy and uniqueness of seismic and mineralogical data. Here, we present new tomographic maps of low order even‐degree seismic structures which are an improvement on earlier models. They satisfy constraints from body wave, surface wave and normal mode data simultaneously, thereby enhancing the spatial resolution. Furthermore, the seismic structure at a given location is represented by a probability density function (pdf) which takes into account the uncertainty and non‐uniqueness of the solution due to modeling and data restrictions. Following a robust statistical procedure, we fit heterogeneity of wave speeds and density from hypothetical thermo‐chemical models to those of our tomographic maps. We thereby constrain lateral variations of temperature as well as iron, silica and post‐perovskite concentration in terms of pdfs. Our work shows that large scale chemical variations are likely everywhere in the lower mantle. In most of the D″ region post‐perovskite is most abundant in the Circum‐Pacific belt, but near the core its lateral variation is more complex. Furthermore, post‐perovskite concentration trades off with the amplitudes of temperature and silicate variations, but not with their lateral distribution. This might be the reason why temperature and silicate variations appear not constrained by our data in the lowermost few hundred km of the mantle.

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[1] Equation-of-state (EOS) modeling, whereby the seismic properties of a specified thermochemical structure are constructed from mineral physics constraints, and compared with global seismic data, provides a potentially powerful tool for distinguishing between plausible mantle structures. However, previous such studies at lower mantle depths have been hampered by insufficient evaluation of mineral physics uncertainties, overestimation of seismic uncertainties, or biases in the type of seismic and/or mineral physics data used. This has led to a wide, often conflicting, variety of models being proposed for the average lower mantle structure. In this study, we perform a thorough reassessment of mineral physics and seismic data uncertainties. Uncertainties in both the type of EOS, and mineral elastic parameters, used are taken into account. From this analysis, it is evident that the seismic variability due to these uncertainties is predominantly controlled by only a small subset of the mineral parameters. Furthermore, although adiabatic pyrolite cannot be ruled out completely, it is problematic to explain seismic velocities and gradients at all depth intervals with such a structure, especially in the interval 1660-2000 km. We therefore consider a range of alternative thermal and chemical structures, and map out the sensitivity of average seismic velocities and gradients to deviations in temperature and composition. Compositional sensitivity is tested both in terms of plausible end-member compositions (e.g., MORB, chondrite), and via changes in each of the five major mantle oxides, SiO 2 , MgO, FeO, CaO, and Al 2 O 3 . Fe enrichment reduces both P and S velocities significantly, while Si enrichment (and Mg depletion) increases P and S velocities, with a larger increase in P than in S. Using purely thermal deviations from adiabatic pyrolite, it remains difficult to explain simultaneously all seismic observations. A superadiabatic temperature gradient does improve the seismic fit in the lowermost mantle, but should be accompanied by concurrent bulk chemistry changes. Our results suggest that the most plausible way to alter bulk chemistry in the lowermost mantle, simultaneously fitting density, bulk velocity and shear velocity constraints, is an increasing contribution of a hot, basalt-enriched component with depth.

S U M M A R YA 1-D reference model for the mantle that is physically meaningful would be invaluable both in geodynamic modelling and for an accurate interpretation of 3-D seismic tomography. However, previous studies have shown that it is difficult to reconcile the simplest possible 1-D physical model-1300 • C adiabatic pyrolite-with seismic observations. We therefore generate a set of alternative 1-D thermal and chemical mantle models, down to 900 km depth, and compare their properties with seismic data. We use several different body and surface wave data sets that provide complementary constraints on mantle structure. To assess the agreement between our models and seismic data, we take into account the large uncertainties in both the elastic/anelastic parameters of the constituent minerals, and the thermodynamic procedures for calculating seismic velocities. These uncertainties translate into substantial differences in seismic structure. However, in spite of such differences, subtle trends remain. We find that models which attain (1) higher velocity gradients between 250 and 350 km; (2) higher velocity gradients in the lower transition zone; and (3) higher average velocities immediately beneath the 660-discontinuity, than 1300 • C adiabatic pyrolite-either via a temporary shift to lower temperatures, and/or a change to a seismically faster chemical composition-provide a significantly better fit to the seismic data than adiabatic pyrolite. This is compatible with recent thermochemical dynamic models by Tackley et al. in which average thermal structure is smooth and monotonous, but average chemical structure deviates substantially from pyrolite above, in, and below the transition zone. Our results suggest that 1-D seismic reference models are being systematically biased by a complex 3-D chemical structure. This bias should be taken into account when attempting quantitative interpretation of seismic anomalies, since those very anomalies contribute to the 1-D average signal.