We present REVEAL, a global‐scale, transversely isotropic full‐waveform inversion model. REVEAL builds upon the earlier construction of the long‐wavelength Earth (LOWE) model by lowering the minimum period from 100 to 33 s and by more than doubling the number of included earthquakes to 2366. In the course of 305 quasi‐Newton iterations, REVEAL assimilated a total of 6,005,727 unique three‐component waveforms. The inversion method rests on the combination of a stochastic mini‐batch optimization and wavefield‐adapted spectral‐element meshes. Although the former naturally exploits redundancies in the data set, the latter reduces the cost of wavefield simulations by reducing the effective dimension of the numerical mesh. As a consequence, the average cost of an iteration in this inversion is only around 0.62% of an iteration that uses the complete data set with a standard cubed‐sphere‐type mesh. We calculated 3D synthetic seismograms using a graphics processing unit‐accelerated spectral‐element wave propagation solver, accommodating the effects of anelasticity, topography, bathymetry, ocean loading, and ellipticity. For a diverse range of global wavepaths, REVEAL predicts complete three‐component seismograms at 33 s period that have not been included in the inversion. This generalization to unseen data suggests applications of REVEAL in event location and characterization, as well as in ground‐motion modeling.

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