S U M M A R YWe have developed model S40RTS of shear-velocity variation in Earth's mantle using a new collection of Rayleigh wave phase velocity, teleseismic body-wave traveltime and normalmode splitting function measurements. This data set is an order of magnitude larger than used for S20RTS and includes new data types. The data are related to shear-velocity perturbations from the (anisotropic) PREM model via kernel functions and ray paths that are computed using PREM. Contributions to phase delays and traveltimes from the heterogeneous crust are estimated using model CRUST2.0. We calculate crustal traveltimes from long-period synthetic waveforms rather than using ray theory. Shear-velocity perturbations are parametrized by spherical harmonics up to degree 40 and by 21 vertical spline functions for a total of 35 301 degrees of freedom. S40RTS is characterised by 8000 resolved unknowns. Since we compute the exact inverse, it is straightforward to determine models associated with fewer or more unknowns by adjusting the model damping. S40RTS shares many characteristics with S20RTS because it is based on the same data types and similar modelling procedures. However, S40RTS shows more clearly than S20RTS the abrupt change in the pattern of shear-velocity heterogeneity across the 660-km phase transition and it presents a more complex patern of shear-velocity heterogeneity in the lower mantle. Utilities to visualise S40RTS and software to analyse the resolution of S40RTS (or models for different damping parameters) are made available.

We present the new model SP12RTS of isotropic shear-wave (V S) and compressional-wave (V P) velocity variations in the Earth's mantle. SP12RTS is derived using the same methods as employed in the construction of the shear-wave velocity models S20RTS and S40RTS, and the same data types. SP12RTS includes additional traveltime measurements of P-waves and new splitting measurements: 33 normal modes with sensitivity to the compressional-wave velocity and 9 Stoneley modes with sensitivity primarily to the lowermost mantle. Contrary to S20RTS and S40RTS, variations in V S and V P are determined without invoking scaling relationships. Lateral velocity variations in SP12RTS are parametrised using spherical harmonics up to degree 12, to focus on long-wavelength features of V S and V P and their ratio R. Large-lowvelocity provinces (LLVPs) are observed for both V S and V P. SP12RTS also features an increase of R up to 2500 km depth, followed by a decrease towards the core-mantle boundary. A negative correlation between the shear-wave and bulk-sound velocity variations is observed for both the LLVPs and the surrounding mantle. These characteristics can be explained by the presence of post-perovskite or large-scale chemical heterogeneity in the lower mantle.

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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.

SS and PP precursors are currently the only body wave data types that have significant coverage in both oceanic and continental regions to study the existence and characteristics of mantle discontinuities on a global scale. Here, the techniques used by global seismologists to observe SS and PP precursors are reviewed. Seismograms, aligned on SS or PP, are stacked using normal move out (NMO) techniques to obtain common depth point gathers. Bootstrap methods are employed to determine 95% confidence levels of the stacks and robustness of the observations. With these relatively simple techniques, a range of discontinuities has been found in the mantle up to 1,200 km depth. The stacks are dominated by the transition zone discontinuities at 410, 520 and 660 km depth, but additional discontinuities at 220, 300-350, 800-900 and 1,100-1,200 km depth are also seen in certain regions. An overview is given of the most recent observational results with a discussion of their mineral physical interpretation and geodynamical significance. Both seismology and mineral physics agree on the level of complexity at the transition discontinuities: a simple 410, a more complicated 520 and a highly complicated 660-km discontinuity are consistently found in both disciplines.