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In global-scale seismic tomography, teleseismic P and PP waves mainly constrain structures in the upper two thirds of the mantle, whereas core-diffracted waves (Pdiff) constrain the lower third. This study is the first to invert a very large data set of Pdiff waves, up to the highest possible frequencies. This results in tomographic resolution matching and exceeding that of global S -wave tomographies, which have long been the models of choice for interpreting lowermost mantle structure. We present three new global tomography models of 3-D isotropic P -wave velocity in the earth's mantle. Multifrequency cross-correlation traveltimes are measured on all phases in passbands from 30 s dominant period to the highest frequencies that produce satisfactory fits (≈3 s). Model DETOX-P1 fits ≈2.5 M traveltimes from teleseismic P waves. DETOX-P2 fits the same data, plus novel measurements of ≈1.4 M traveltimes of Pdiff waves. DETOX-P3 fits the same data as DETOX-P2, plus ≈ 1.2 M PP traveltimes. Synthetics up to 1 s dominant period are computed by full wave propagation in a spherically symmetric earth using the spectral-element method AxiSEM. Traveltimes are linked to 3-D velocity perturbations (d VP / VP) by finite-frequency Fréchet kernels, parametrized on an adaptive tetrahedral grid of ≈400 000 vertices spaced by ≈80 km in the best-sampled regions. To complete spatial coverage, the waveform cross-correlation measurements are augmented by ≈5.7 million analyst-picked, teleseismic P arrival times. P , Pdiff and PP traveltimes are jointly inverted for 3-D isotropic P -velocity anomalies in the mantle and for events corrections, by least squares solution of an explicit matrix–vector equation. Inclusion of Pdiff traveltimes (in DETOX-P2, -P3) improves the spatial sampling of the lowermost mantle 100- to 1000-fold compared to teleseismic P waves (DETOX-P1). Below ≈2400 km depth, seismically slow anomalies are clustered at southern and equatorial latitudes, in a dozen or more intensely slow patches of 600–1400 km diameter. These features had long been classed into two large low shear velocity provinces (LLVP), which now appears questionable. Instead, patches of intensely slow anomalies in the lowermost mantle seem to form a nearly continuous, globe-spanning chain beneath the southern hemisphere, according to our increased resolution of LLVP-internal subdivisions and newly imaged patches beneath South America. Our tomography also supports the existence of whole-mantle plumes beneath Iceland, Ascension, Afar, Kerguelen, Canary, Azores, Easter, Galapagos, Hawaii, French Polynesia and the Marquesas. Seismically fast structure in the lowermost mantle is imaged as narrowly elongated belts under Eastern Asia and the Americas, presumably reflecting the palaeo-trench geometries of subduction zones and arcs that assembled Eastern Asia and the American Cordilleras in Palaeozoic and early Mesozoic times. Mid-mantle structure is primarily constrained by teleseismic P waves, but Pdiff data have a stabilizing effect, for example, sharpening the geometries of subducted slabs under the Americas, Eurasia and the Northern Pacific in the upper 2000 km. PP traveltimes contribute complementary constraints in the upper and mid mantle, but they also introduce low-velocity artefacts beneath the oceans, through downward smearing of lithospheric structure. Our three new global P -wave models can be accessed and interactively visualized through the SubMachine web portal (http://submachine.earth.ox.ac.uk/). [ABSTRACT FROM AUTHOR]

We present a novel numerical method to simulate global seismic wave propagation in realistic aspherical 3-D earth models across the observable frequency band of global seismic data. Our method, named AxiSEM3D, is a hybrid of spectral element method (SEM) and pseudospectral method. It describes the azimuthal dimension of global wavefields with a substantially reduced number of degrees of freedom via a global Fourier series parametrization, of which the number of terms can be locally adapted to the inherent azimuthal complexity of the wavefields. AxiSEM3D allows for material heterogeneities, such as velocity, density, anisotropy and attenuation, as well as for finite undulations on radial discontinuities, both solid–solid and solid–fluid, and thereby a variety of aspherical Earth features such as ellipticity, surface topography, variable crustal thickness, undulating transition zone and core–mantle boundary topography. Undulating discontinuities are honoured by means of the 'particle relabelling transformation', so that the spectral element mesh can be kept spherical. The implementation of the particle relabelling transformation is verified by benchmark solutions against a discretized 3-D SEM, considering ellipticity, topography and bathymetry (with the ocean approximated as a hydrodynamic load) and a tomographic mantle model with an undulating transition zone. For the state-of-the-art global tomographic models with aspherical geometry but without a 3-D crust, efficiency comparisons suggest that AxiSEM3D can be two to three orders of magnitude faster than a discretized 3-D method for a seismic period at 5 s or below, with the speed-up increasing with frequency and decreasing with model complexity. We also verify AxiSEM3D for localized small-scale heterogeneities with strong perturbation strength. With reasonable computing resources, we have achieved a corner frequency of up to 1 Hz for 3-D mantle models. [ABSTRACT FROM AUTHOR]