Comparing the Dynamics of Free Subduction in Cartesian and Spherical Domains

Abstract

The effects of sphericity are regularly neglected in numerical and laboratory studies that examine the factors controlling subduction dynamics. Most existing studies have been executed in a Cartesian domain, with the small number of simulations undertaken in a spherical shell incorporating plates with an oversimplified rheology, limiting their applicability. Here, we simulate free-subduction of composite visco-plastic plates in 3-D Cartesian and spherical shell domains, to examine the role of sphericity in dictating the dynamics of subduction, and highlight the limitations of Cartesian models. We identify two irreconcilable differences between Cartesian and spherical models, which limit the suitability of Cartesian-based studies: (i) the presence of sidewall boundaries in Cartesian models, which modify the flow regime; and (ii) the reduction of space with depth in spherical shells, alongside the radial gravity direction, which cannot be captured in Cartesian domains. Although Cartesian models generally predict comparable subduction regimes and slab morphologies to their spherical counterparts, there are significant quantitative discrepancies. We find that simulations in Cartesian domains that exceed Earth's dimensions overestimate trench retreat. Conversely, due to boundary effects, simulations in smaller Cartesian domains overestimate the variation of trench curvature driven by plate width. Importantly, spherical models consistently predict higher sinking velocities and a reduction in slab width with depth, particularly for wider subduction systems, enhancing along-strike slab buckling and trench curvature. Results imply that sphericity must be considered when simulating Earth's subduction systems, and that it is essential for accurately predicting the dynamics of subduction zones of width ˜2400 km or more.