Two Effective Degrees of Freedom Can Represent the Dominant Features of Global Rayleigh Wave Dispersion Maps

Objectively exploring global variations in crust and upper mantle structure helps constrain fundamental aspects of Earth's plate tectonic and convective processes. Here we adopted a Variational Auto-Encoder to explore the degrees of freedom of global Rayleigh wave dispersion maps at 4-40 mHz. We found that two latent variables sufficiently represent the global variations, suggesting inherent coupling between crustal and mantle seismic properties. We propose that the two extracted latent variables mostly correspond with crustal thickness and upper mantle thermal structure. The first variable shows low values for continental mountain belts and ocean spreading ridges, contrasted by high values for abyssal plains. The second variable shows low values for most oceanic lithosphere and Phanerozoic continental areas, contrasted by high values for Archean cratons. Latent space correlations indicate that continental lithosphere has more strongly coupled depth features than beneath the oceans, which might be a consequence of its longevity. Rayleigh wave dispersion maps measure the speed of surface waves, which sample Earth's elastic structure over depth intervals that increase with the wave period. Maps of variability in surface wave speeds allow us to evaluate coupling between crust and mantle properties. Using a recently developed neural network technique, we found that two free variables sufficiently represent the global variation of Rayleigh wave dispersion maps. The number of free variables found is much smaller than typically assumed in tomographic imaging and suggests that crust and mantle in different locations share many major features. The spatial distributions of the two variables correlate well with plate tectonic boundaries and geologic provinces. The first variable outlines thick crust and spreading regions with low values, contrasted by high values for ancient oceanic plates. The second variable presents Archean cratons with the highest values and shows widespread low values in oceanic regions. We propose that the two extracted variables are related to variations of crust thickness and upper mantle thermal structure. Moreover, the two variables from the continents show higher correlation coefficients than those from the oceans, suggesting that structural properties of continental lithosphere are more strongly coupled at different depths. Global Rayleigh wave dispersion sampled at dozens of frequencies can be sufficiently represented by two latent variables The variables are more correlated in continental than oceanic regions, indicating a stronger depth coupling below continents The two variables jointly outline the dominant thermal structures linked to tectonics and mantle convection