While the downward mass flux in the Earth's deep interior is well constrained by seismic tomography, the upward flux is still poorly understood and debated. Recent tomography studies suggest that we are now starting to resolve deep mantle plume structures. However, a lack of uncertainty quantification impedes a full assessment of their significance and whether they are statistically distinct from noise. This work uses a spherical wavelet transform and random noise realizations to quantify the probability of deep plume‐like features in six recent global tomographic models. We find that out of 50 possible mantle deep plumes, 12 are highly likely, with probabilities larger than 80%, and 12 are likely, with probability between 70% and 80%. Objective, quantitative approaches as proposed in this study should be used for model interpretation. The five most likely deep mantle plumes are Tahiti, Macdonald, East Africa, Pitcairn, and Marquesas, which have some of the largest buoyancy fluxes estimated in a previous study that used hotspot swell volumes. This could resolve past discrepancies between deep mantle plumes inferred by visual analysis of tomography models and flux estimations from hotspot swell data. In addition, a notable unlikely deep mantle plume is Yellowstone, with probability lower than 50%. We also identify a likely deep mantle plume associated with the Amsterdam‐St Paul hotspot, a region scarcely discussed in previous studies and that deserves future investigation. Hence, our automated, objective approach is a valuable alternative approach for the quantitative interpretation of tomographic models.

Many problems across computer vision and the natural sciences require the analysis of spherical data, for which representations may be learned efficiently by encoding equivariance to rotational symmetries. We present a generalized spherical CNN framework that encompasses various existing approaches and allows them to be leveraged alongside each other. The only existing non-linear spherical CNN layer that is strictly equivariant has complexity OpC 2 L 5 q, where C is a measure of representational capacity and L the spherical harmonic bandlimit. Such a high computational cost often prohibits the use of strictly equivariant spherical CNNs. We develop two new strictly equivariant layers with reduced complexity OpCL 4 q and OpCL 3 log Lq, making larger, more expressive models computationally feasible. Moreover, we adopt efficient sampling theory to achieve further computational savings. We show that these developments allow the construction of more expressive hybrid models that achieve state-of-the-art accuracy and parameter efficiency on spherical benchmark problems.

SUMMARY Determining the crustal structure of ocean island volcanoes is important to understand the formation and tectonic evolution of the oceanic lithosphere and tectonic swells in marine settings, and to assess seismic hazard in the islands. The Azores Archipelago is located near a triple junction system and is possibly under the influence of a mantle plume, being at the locus of a wide range of geodynamic processes. However, its crustal structure is still poorly constrained and debated due to the limited seismic coverage of the region and the peculiar linear geometry of the islands. To address these limitations, in this study we invert teleseismic Rayleigh wave ellipticity measurements for 1-D shear wave speed (VS) crustal models of the Azores Archipelago. Moreover, we test the reliability of these new models by using them in independent moment tensor inversions of local seismic data and demonstrate that our models improve the waveform fit compared to previous models. We find that data from the westernmost seismic stations used in this study require a shallower Moho depth (∼10 km) than data from stations in the eastern part of the archipelago (∼13–16 km). This apparent increase in the Moho depth with increasing distance from the mid-Atlantic ridge (MAR) is expected. However, the rate at which Moho deepens away from the MAR is greater than that predicted from a half-space cooling model, suggesting that local tectonic perturbations have modified crustal structure. The 1-D VS models obtained beneath the westernmost seismic stations also show higher wave speeds than for the easternmost stations, which correlates well with the ages of the islands except Santa Maria Island. We interpret the relatively low VS profile found beneath Santa Maria Island as resulting from underplating, which agrees with previous geological studies of the island. Compared to a recent receiver function study of the region, the shallow structure (top ∼2 km) in our models shows lower shear wave speed, which may have important implications for future hazard studies of the region. More generally, the new seismic crustal models we present in this study will be useful to better understand the tectonics, seismicity, moment tensors and strong ground motions in the region.

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