Masaki Yoshida

Viscosity is a fundamental physical property of fluids and plays a crucial role in both materials science and the natural sciences. However, discussions of viscosity rarely address its upper bound, because extremely high-viscosity materials are typically rock-forming minerals, which are not usually treated within the framework of fluid dynamics. Here, I focus on the upper bound of viscosity for solid-Earth materials. This study estimates this upper bound under temperature and pressure conditions relevant to natural systems by integrating constraints from different timescales of the solid Earth: geodetic observations over years to decades, laboratory rock-deformation experiments over hours to years, and geological processes such as lithospheric bending and subduction driven ultimately by mantle convection over millions of years. The results show that the maximum viscosity of stable lithospheric regions, inferred from geodetic observations, is approximately consistent with the maximum viscosities of major rock-forming minerals estimated from flow-law parameters obtained in laboratory deformation experiments. This study suggests that the upper bound of viscosity is 1030±2 Pa s, based on the physical definition of viscosity as resistance to flow over finite timescales ranging from human-observable to Earth-history timescales. These results may provide a broader rheological perspective on high-viscosity non-Newtonian fluids, glassy materials, soft matter, and related systems, rather than being confined to geophysical contexts.

The Pacific plate, which is the largest oceanic plate on Earth, has implications for the general understanding of plate dynamics, including the origin of intraplate stress and the driving force for plate motion. However, this is currently limited by the scarcity of geophysical and geological observational data. In this study, an instantaneous global mantle flow calculation was performed to predict the intraplate stress field and stress regimes on the Pacific plate using a geodynamic model based on the density anomaly structure of the mantle converted from a seismic tomography model incorporating subducting plates. The numerical results demonstrate that the southern part of the Pacific plate is dominated by a normal faulting regime. In contrast, the northern part is dominated by a thrust faulting regime, in which the tensional stress axes in the older and stable part of the Pacific plate tend to be oblique to the direction of plate motion. This suggests that the stress state of the Pacific plate is almost neutral (i.e., neither compressional nor tensional) along the direction of plate motion. Furthermore, shallow positive buoyancy-induced asthenospheric flow is essential for reproducing the observed plate motion of the Pacific plate.

A series of numerical simulations of mantle convection in 3D spherical-shell geometry were performed to evaluate the intraplate stress regime from numerically obtained velocity and stress fields. The intraplate stress regime was quantitatively classified into nine types by analyzing the principal deviatoric stress axes and the “stress ratio,” which is a continuous parameter accounting for the stress regimes. From the viewpoint of global geodynamics, this study analyzed the depth profile of the stress ratio across the entire depth of the mantle. The results demonstrated that the radial viscosity structure of the mantle interior strongly affected intraplate stress regimes, and the combination of increased viscosity in the lower mantle and the low-viscosity asthenosphere enhanced the pure strike-slip faulting regime within moving plates as indicated using visco-plastic rheology. The temporally averaged toroidal-poloidal ratio (T/P ratio) at the top surface of mantle convection with surface plate-like motion and the mantle’s viscosity stratification may be comparable to the observed T/P ratio of present-day and past Earth. The normal faulting (or strike-slip) regime with a strike-slip (or normal faulting) component, as well as the pure strike-slip faulting regime, were broadly found in the stable parts of the plate interiors. However, the significant dominance of these stress regimes was not observed in the depth profile of the toroidal-poloidal ratio as a remarkable peak magnitude near the top surface of the lithosphere. This result implies that the strike-slip component analyzed in this study does not directly relate to the formation of strike-slip faults that are infinitely narrow plate boundaries compared with the finite low-viscosity boundary obtained from a mantle convection model with visco-plastic rheology. Nonetheless, this first analysis of the stress ratio may contribute to an improved understanding of the intraplate stress reproduced by future numerical studies of mantle convection with further realistic conditions.

The influence of the continental lithosphere and its root (or keel) on the continental drift of Earth is a key element in the history of plate tectonics. Previous geodynamic studies of mantle flow suggested that the cratonic root is moderately mechanically coupled with the underlying mantle, and stable continental drift on Earth's timescales occurs when the effective viscosity contrast between the continental lithosphere and the underlying mantle is approximately 10³. Both geodynamics and seismological studies indicate that mechanically weak mobile belts (i.e., orogenic or suture zones) that surround cratons may play a role in the longevity of the cratonic lithosphere over geologically long timescales (i.e., over 1,000 million years) because they act as a buffer region against the high-viscosity cratons. Low-viscosity asthenosphere, characterized by slow seismic velocities, reduces the basal drag force acting on the cratonic root, which may also contribute to the longevity of the cratonic lithosphere. ▪ The role of the continental lithosphere and its root on the continental drift is reviewed from recent geodynamic and seismological studies. ▪ The cratonic root is moderately mechanically coupled with the underlying mantle and deformed by mantle flow over geological timescales. ▪ Orogenic belts or suture zones that surround cratons act as a buffer to protect cratons and are essential for their longevity. ▪ Low-viscosity asthenosphere may reduce the basal drag acting on the cratonic root and also contribute to its stability and longevity.

This paper reports on results for the thermal and mechanical states at the interface of two-layer thermal convection in two-dimensional (2-D) spherical geometry solved by numerical calculations. The two-layer system was composed of a highly viscous layer (HVL) and a low-viscosity layer (LVL) underneath. The two end-member convection regimes were studied by varying two free model parameters, which control the degree of layering in HVL convection and separate the HVL into the upper and lower parts. One of the regimes was a nearly whole-layer convection regime in which the upwelling and downwelling plumes easily penetrated into another layer in the HVL, while the other was a so-called hybrid convection regime, which represented a transitional regime between the whole-layer convection and the double-layer convection. The spatiotemporal analyses of convection behavior showed that the lateral scale of HVL convection and the resultant lateral scale of thermal heterogeneity beneath the HVL–LVL interface tended to be larger in the hybrid convection regime than those in the whole-layer convection regime. On the other hand, the fluctuation of shear-stress at the HVL–LVL interface was more time-dependent in the hybrid convection regime, whereas the mechanical heterogeneity near the HVL–LVL interface was larger in the whole-layer convection regime. The present results on the differences in the scale of dynamically determined thermal and mechanical states beneath the HVL–LVL interface between the two end-member convection regimes may apply to issues on the relationship between thermal and mechanical conditions at the Earth’s core–mantle boundary and the strength of the geomagnetic field.