We present a methodology to compute 3-D global seismic wavefields for realistic earthquake sources in visco-elastic anisotropic media, covering applications across the observable seismic frequency band with moderate computational resources. This is accommodated by mandating axisymmetric background models that allow for a multipole expansion such that only a 2-D computational domain is needed, whereas the azimuthal third dimension is computed analytically on the fly. This dimensional collapse opens doors for storing space–time wavefields on disk that can be used to compute Fréchet sensitivity kernels for waveform tomography. We use the corresponding publicly available AxiSEM (www.axisem.info) open-source spectral-element code, demonstrate its excellent scalability on supercomputers, a diverse range of applications ranging from normal modes to small-scale lowermost mantle structures, tomographic models, and comparison with observed data, and discuss further avenues to pursue with this methodology.

We present SubMachine, a collection of web‐based tools for the interactive visualization, analysis, and quantitative comparison of global‐scale data sets of the Earth's interior. SubMachine focuses on making regional and global‐scale seismic tomography models easily accessible to the wider solid Earth community, in order to facilitate collaborative exploration. We have written software tools to visualize and explore over 30 tomography models—individually, side‐by‐side, or through statistical and averaging tools. SubMachine also serves various nontomographic data sets that are pertinent to the interpretation of mantle structure and complement the tomographies. These include plate reconstruction models, normal mode observations, global crustal structure, shear wave splitting, as well as geoid, marine gravity, vertical gravity gradients, and global topography in adjustable degrees of spherical harmonic resolution. By providing repository infrastructure, SubMachine encourages and supports community contributions via submission of data sets or feedback on the implemented toolkits.

SUMMARY: 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 (dVP/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/).

We present a new method and implementation (Instaseis) to store global Green's functions in a database which allows for near-instantaneous (on the order of milliseconds) extraction of arbitrary seismograms. Using the axisymmetric spectral element method (AxiSEM), the generation of these databases, based on reciprocity of the Green's functions, is very efficient and is approximately half as expensive as a single AxiSEM forward run. Thus, this enables the computation of full databases at half the cost of the computation of seismograms for a single source in the previous scheme and allows to compute databases at the highest frequencies globally observed. By storing the basis coefficients of the numerical scheme (Lagrange polynomials), the Green's functions are 4th order accurate in space and the spatial discretization respects discontinuities in the velocity model exactly. High-order temporal interpolation using Lanczos resampling allows to retrieve seismograms at any sampling rate. AxiSEM is easily adaptable to arbitrary spherically symmetric models of Earth as well as other planets. In this paper, we present the basic rationale and details of the method as well as benchmarks and illustrate a variety of applications. The code is open source and available with extensive documentation at www.instaseis.net .

The geoscience community is increasingly utilizing seismic tomography to interpret mantle heterogeneity and its links to past tectonic and geodynamic processes. To assess the robustness and distribution of positive seismic anomalies, inferred as subducted slabs, we create a set of vote maps for the lower mantle with 14 global P-wave or S-wave tomography models. Based on a depth-dependent threshold metric, an average of 20% of any given tomography model depth is identified as a potential slab. However, upon combining the 14 models, the most consistent positive wavespeed features are identified by an increasing vote count. An overall peak in the most robust anomalies is found between 1000–1400 km depth, followed by a decline to a minimum around 2000 km. While this trend could reflect reduced tomographic resolution in the middle mantle, we show that it may alternatively relate to real changes in the time-dependent subduction flux and/or a mid-lower mantle viscosity increase. An apparent secondary peak in agreement below 2500 km depth may reflect the degree-two lower mantle slow seismic structures. Vote maps illustrate the potential shortcomings of using a limited number or type of tomography models and slab threshold criteria.

Plate reconstructions since the breakup of Pangaea are mostly based on the preserved spreading history of ocean basins, within absolute reference frames that are constrained by a combination of age‐progressive hotspot tracks and paleomagnetic data. The evolution of destructive plate margins is difficult to constrain from surface observations as much of the evidence has been subducted. Seismic tomography can directly constrain paleotrench locations by imaging subducted lithosphere in the mantle. This new evidence, combined with the geological surface record of subduction, suggests that several intraoceanic arcs existed between the Farallon Ocean and North America during late Mesozoic times—in contrast to existing quantitative models that typically show long‐lived subduction of the Farallon plate beneath the continental margin. We present a continuously closing plate model for the eastern Pacific basin from 170 Ma to present, constrained using “tomotectonic analysis”—the integration of surface and subsurface data. During the Middle to Late Jurassic, we show simultaneous eastward and westward subduction of oceanic plates under an archipelago composed of Cordilleran arc terranes. As North America drifts westward, it diachronously overrides the archipelago and its arcs, beginning in the latest Jurassic. During and post‐accretion, Cordilleran terranes are translated thousands of kilometers along the continental margin, as constrained by paleomagnetic evidence. Final accretions to North America occur during the Eocene, ending ~100 Myr of archipelago override. This model provides a detailed, quantitative tectonic history for the eastern Pacific domain, paving the way for tomotectonic analysis to be used in other paleo‐oceanic regions.