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In previous publications, we presented a general framework, which we called ‘box tomography’, that allows the coupling of any two different numerical seismic wave propagation solvers, respectively outside and inside a target region, or ‘box’. The goal of such hybrid wavefield computations is to reduce the cost of computations in the context of full-waveform inversion for structure within the target region, when sources and/or receivers are located at large distances from the box. Previously, we had demonstrated this approach with sources and receivers outside the target region in a 2-D acoustic spherical earth model, and demonstrated and applied this methodology in the 3-D spherical elastic Earth in a continental scale inversion in which all stations were inside the target region. Here we extend the implementation of the approach to the case of a 3-D global elastic earth model in the case where both sources and stations are outside the box. We couple a global 3-D solver, SPECFEM3D_GLOBE, for the computation of the wavefield and Green’s functions in a reference 3-D model, with a regional 3-D solver, RegSEM, for the computation of the wavefield within the box, by means of time-reversal mirrors. We briefly review key theoretical aspects, showing in particular how only the displacement is needed to be stored at the boundary of the box. We provide details of the practical implementation, including the geometrical design of the mirrors, how we deal with different sizes of meshes in the two solvers, and how we address memory-saving through the use of B-spline compression of the recorded wavefield on the mirror. The proposed approach is numerically efficient but also versatile, since adapting it to other solvers is straightforward and does not require any changes in the solver codes themselves, as long as the displacement can be recovered at any point in time and space. We present benchmarks of the hybrid computations against direct computations of the wavefield between a source and an array of stations in a realistic geometry centred in the Yellowstone region, with and without a hypothetical plume within the ‘box’, and with a 1-D or a 3-D background model, down to a period of 20 s. The ultimate goal of this development is for applications in the context of imaging of remote target regions in the deep mantle, such as, for example, Ultra Low Velocity Zones.

Global variations in the propagation of fundamental-mode and overtone surface waves provide unique constraints on the low-frequency source properties and structure of the Earth’s upper mantle, transition zone and mid mantle. We construct a reference data set of multimode dispersion measurements by reconciling large and diverse catalogues of Love-wave (49.65 million) and Rayleigh-wave dispersion (177.66 million) from eight groups worldwide. The reference data set summarizes measurements of dispersion of fundamental-mode surface waves and up to six overtone branches from 44 871 earthquakes recorded on 12 222 globally distributed seismographic stations. Dispersion curves are specified at a set of reference periods between 25 and 250 s to determine propagation-phase anomalies with respect to a reference Earth model. Our procedures for reconciling data sets include: (1) controlling quality and salvaging missing metadata; (2) identifying discrepant measurements and reasons for discrepancies; (3) equalizing geographic coverage by constructing summary rays for travel-time observations and (4) constructing phase velocity maps at various wavelengths with combination of data types to evaluate inter-dataset consistency. We retrieved missing station and earthquake metadata in several legacy compilations and codified scalable formats to facilitate reproducibility, easy storage and fast input/output on high-performance-computing systems. Outliers can be attributed to cycle skipping, station polarity issues or overtone interference at specific epicentral distances. By assessing inter-dataset consistency across similar paths, we empirically quantified uncertainties in traveltime measurements. More than 95 per cent measurements of fundamental-mode dispersion are internally consistent, but agreement deteriorates for overtones especially branches 5 and 6. Systematic discrepancies between raw phase anomalies from various techniques can be attributed to discrepant theoretical approximations, reference Earth models and processing schemes. Phase-velocity variations yielded by the inversion of the summary data set are highly correlated (R ≥ 0.8) with those from the quality-controlled contributing data sets. Long-wavelength variations in fundamental-mode dispersion (50–100 s) are largely independent of the measurement technique with high correlations extending up to degree ∼25. Agreement degrades with increasing branch number and period; highly correlated structure is found only up to degree ∼10 at longer periods (T > 150 s) and up to degree ∼8 for overtones. Only 2ζ azimuthal variations in phase velocity of fundamental-mode Rayleigh waves were required by the reference data set; maps of 2ζ azimuthal variations are highly consistent between catalogues ( R = 0.6–0.8). Reference data with uncertainties are useful for improving existing measurement techniques, validating models of interior structure, calculating teleseismic data corrections in local or multiscale investigations and developing a 3-D reference Earth model.

A major goal in Earth Science has been to understand how geochemical characteristics of lavas at the Earth's surface relate to the location and formation history of specific regions in the Earth's interior. For example, some of the strongest evidence for the preservation of primitive material comes from low⁴He/³He ratios in ocean island basalts, but the location of the primitive helium reservoir(s) remains unknown. Here we combine whole‐mantle seismic tomography, simulations of mantle flow, and a global compilation of new and existing measurements of the⁴He/³He ratios in ocean island basalts to constrain the source location of primitive⁴He/³He material. Our geodynamic simulations predict the present‐day surface expression of plumes to be laterally offset from their lower mantle source locations. When this lateral offset is accounted for, a strong relationship emerges between minimum⁴He/³He ratios in oceanic basalts and seismically slow regions, which are generally located within the two large low shear‐wave velocity provinces (LLSVPs). Conversely, no significant relationship is observed between maximum²⁰⁸Pb^*/²⁰⁶Pb^*ratios and seismically slow regions in the lowermost mantle. These results indicate that primitive materials are geographically restricted to LLSVPs, while recycled materials are more broadly distributed across the lower mantle. The primitive nature of the LLSVPs indicates these regions are not composed entirely of recycled slabs, while complementary xenon and tungsten isotopic anomalies require the primitive portion of the LLSVPs to have formed during Earth's accretion, survived the Moon‐forming giant impact, and remained relatively unmixed during the subsequent 4.5 billion years of mantle convection.