Rheological Controls on the Plate-Mantle System: Self-Consistent vs. Kinematically Constrained Models

Earth’s interior plays a fundamental role in the long-term evolution of the surface, climate, and biosphere. However, Earth's mantle evolution remains largely ambiguous, as imaging techniques are limited to present-day observations and geochemical or geological constraints apply to a non-global scale. Plate tectonic reconstructions coupled with convection models could provide constraints on the evolution of mantle structure. In this study, we employ both fully self-consistent and kinematically constrained mantle convection models^[1]. The mantle rheology is temperature-, pressure-, phase-, and stress-dependent, with the latter represented through pseudo-plasticity. The novelty of this work lies in employing a composite rheology with “realistic” rheological parameters^[2] in a fully three-dimensional geometry. By using both fully self-consistent models and plate-driven models, we aim to address the discrepancies in terms of long-term convective and tectonic behaviour that arise when forcing plate velocities onto the surface. The latter is done by imposing time-dependent surface velocity boundary conditions provided by a plate tectonic reconstruction^[3].

To evaluate the extent to which the models reproduce plate-like tectonics, we explore several independent constraints. In particular, we compute slab sinking rates and compare them to estimates inferred from seismic tomography^[4]. Slab sinking rates in self-consistent models provide insight into the mantle’s rheology. For example, sinking rates that are lower than those based on tomographic and geological data may indicate an overly viscous mantle. Our results show that the slab sinking rate is generally higher in models with imposed plate velocities compared to fully self-consistent models. Furthermore, a tessellation algorithm^[5] will be applied to the surface of the models to detect plates in the self-consistent models with plate-like behaviour. Based on these results, a plate-size frequency distribution can be calculated and compared to present-day Earth^[6]. Results show that low yield stresses generate too many small plates, and too few large plates [Fig. 1]. In order to generate Earth-like plate tectonics, yield stress needs to be sufficiently high to reproduce the plate-size frequency distribution of present-day Earth, but also sufficiently low to facilitate a long-term mobile lid regime.

^[1] Tackley, P. J. (2008). Phys. Earth Planet. Inter. 171, 1–4.

^[2] Tackley, P. J., Ammann, M., Brodholt, J. P., Dobson, D. P., & Valencia, D. (2013). Icarus 225, 50–61.

^[3] Merdith, A. S., Williams, S. E., Collins, A. S., et al. (2021). Earth-Sci. Rev. 214, 103477.

^[4] Van der Meer, D. G., van Hinsbergen, D. J. J., & Spakman, W. (2018). Tectonophysics 723, 309–448.

^[5] Janin, A., Coltice, N., Chamot-Rooke, N., & Tierny, J. (2025). Nat. Geosci. 18, 1041–1047.

^[6] Bird, P. (2003). Geochem. Geophys. Geosyst. 4, 2001GC000252.