Seismic observations showing that the asthenosphere can flow faster than, and in a different direction than, the plate above motivated mantle convection models in which tectonic plates are driven partly by pressure-driven (Poiseuille-type) asthenosphere flow rather than by slab pull alone. Semple and Lenardic (2020) showed in self-consistent 3D spherical convection models with dynamically generated weak plate margins that pressure-driven asthenosphere flow survives the presence of plate margins and that a non-Newtonian upper mantle permits bistability (hysteresis) between single-plate (stagnant-lid-like) and plate-tectonic (mobile-lid) modes at identical parameter conditions. Their models used a power-law stress exponent of 2 — below the rock-like value of roughly 3.5 for olivine dislocation creep, chosen per the source's own description to keep computation manageable — and omitted temperature-dependent viscosity; whether the slab-pull/pressure-driven-flow balance survives at rock-like stress exponents with experimentally consistent activation parameters, and how combining non-Newtonian rheology with temperature-dependent viscosity reshapes the parameter space that permits tectonic bistability, therefore remain open. No study combining both realism upgrades is known; later work either uses different rheological frameworks (pseudoplastic, composite, grain-size, or analytic models) or explicitly notes that the pressure-driven component and realistic activation parameters remain to be incorporated. The problem is open.

Background

Since the plate-tectonic revolution, the canonical answer to what drives tectonic plates has been slab pull — the negative buoyancy of cold subducting plates — with ridge push as a secondary force. This view has been challenged by seismic observations beneath the Pacific plate (Lin et al., 2016), which revealed two distinct zones of seismic anisotropy (direction-dependent seismic wave speed, produced by alignment of olivine crystals): one at the base of the plate and another roughly 200 km deeper. These observations indicate that the asthenosphere — the weak, slowly flowing upper-mantle layer beneath the rigid lithosphere — can flow faster than, and in a different direction from, the plate above, which purely slab-driven flow cannot explain. In the language of channel flow, flow dragged by a moving plate is Couette flow, while flow driven by horizontal pressure gradients (for example, from rising plumes or subduction-related return flow) is Poiseuille flow; Poiseuille flow can in principle exert a driving traction on the plate above instead of merely resisting it. Analytical and numerical studies (Höink & Lenardic, 2010; Höink et al., 2011; Coltice et al., 2019; Stotz et al., 2018) argued that the asthenosphere can indeed transition from offering low resistance to plate motion to actively driving plates. Semple and Lenardic (2018) then showed, in 3D spherical mantle convection models with a non-Newtonian upper mantle, that pressure gradients can channelize flow into a plug-flow configuration (fast interior with shear concentrated at the top and bottom of the channel), consistent with the seismic anisotropy observations. 'Non-Newtonian' here means the effective viscosity decreases as strain rate rises, parameterized by a power law with stress exponent n; dislocation creep of olivine, the dominant upper-mantle deformation mechanism in laboratory rock experiments, corresponds to n ≈ 3.5, while n = 1 is linear (Newtonian) viscosity. Semple and Lenardic (2020) extended these models by allowing weak plate margins to form: where stresses exceed a yield stress σy, local viscosity drops and platelike surface mobility emerges. Their findings were: (1) weak margins increase the globally averaged ratio of slab-driven to pressure-driven asthenosphere flow, but pressure-driven flow remains active and its relative strength grows with margin strength; (2) locally, asthenosphere flow still exceeds plate velocity and rotates with depth away from plate-motion direction; (3) a non-Newtonian upper mantle permits hysteresis — single-plate (stagnant-lid-like, immobile-surface) and plate-tectonic (mobile-lid) states can both exist at the same parameter conditions, selected by initial conditions — echoing earlier bistability results obtained with temperature-dependent viscosity (Weller & Lenardic, 2012; Lenardic et al., 2016). Two idealizations remained. First, the power-law exponent was n = 2, below the rock-like n ≈ 3.5, chosen per the source's own description to keep resolution and run-time requirements manageable; stronger non-Newtonian behavior localizes shear more sharply and is computationally far more expensive. Second, temperature-dependent viscosity (the Arrhenius-type stiffening of cold material central to the earlier hysteresis studies) and grain-size-dependent viscosity were omitted, to isolate the interaction between the non-Newtonian asthenosphere and plate margins; independent assessments confirm that the 2020 models did not employ temperature-dependent viscosity (Arnould et al., 2023) and used an idealized, layered viscosity structure with activation parameters smaller than experimental values (Patočka et al., 2024). Whether the reported force-partition conclusions and the bistability window survive these two realism upgrades is the open question.

Problem Statement

In self-consistent 3D mantle convection models that dynamically generate weak plate margins (platelike surface behavior), determine how the stress exponent of a non-Newtonian upper-mantle/asthenosphere rheology raised to rock-like values (n up to ≈ 3.5, with experimentally consistent activation parameters), the plate-margin yield strength, and temperature-dependent viscosity jointly control: (1) the partitioning between slab-pull-driven and pressure-driven asthenosphere flow — specifically, whether the conclusions of Semple & Lenardic (2020) survive, namely that pressure-driven flow remains an active component that grows with margin strength, that local asthenosphere velocity can exceed plate velocity, and that asthenosphere flow direction can rotate with depth away from plate motion; and (2) the extent and hysteresis of the bistable window in which single-plate (stagnant-lid-like, immobile-surface) and plate-tectonic (mobile-lid) modes coexist at identical parameter conditions, selected by initial conditions, when the non-Newtonian rheology is combined with temperature-dependent viscosity. The models are spherical-shell configurations with a radially stratified lithosphere, a power-law asthenosphere, and a yield-stress plate-margin law in which local viscosity drops where stress exceeds σy. The sweep must span the stress exponent from the 2020 value of 2 up to rock-like values (≈ 3.5), the plate-margin yield strength across both the weak- and strong-margin regimes, and the activation parameters from the 2020 idealized, layered values to experimentally consistent values (cf. Patočka et al., 2024), at a resolution sufficient to bracket the mobile-lid/stagnant-lid transitions on both the up-ramp and down-ramp branches. The investigation determines the quantified flow/force partition as a function of stress exponent, yield stress, and viscosity-contrast (activation) parameters, the regime map — with up-ramp and down-ramp initial-condition branches — establishing where bistability exists and where it does not, and whether the 2020 force-partition conclusions (pressure-driven flow remaining active and growing with margin strength, local asthenosphere speed exceeding plate speed, depth-dependent flow rotation) and the 2020 bistability claim survive under the combined realistic rheology.

References

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