Masanori Kameyama

Thermal-mechanical effects of low-temperature plasticity (the Peierls mechanism) on the deformation of a viscoelastic shear zone

We studied for the first time the effects of low-temperature plasticity on the formation of shear zones. A thermal-mechanical model has been developed for describing the shear deformation of Maxwell viscoelastic material with a rheology close to dry olivine. We employed a one-dimensional model with a half-width of L deforming under a constant velocity U at the boundary, and the spatially-averaged strain rate U/L was set to O(10−14) s−1. In addition to diffusion and power-law creep, we included deformation by low-temperature plasticity, called the Peierls mechanism, which is significant at low temperatures and has a strong exponential dependence on the stress. When a sufficient magnitude of heat is generated by the rapid conversion from elastically-stored energy into viscous dissipation, thermal instability takes place and the deformation localizes in a narrow region. By comparing the condition for thermal instability, we found that the low-temperature plasticity inhibits the development of thermal instability in shear zones in case of constant strain rate. The Peierls mechanism enhances deformation at a significantly lower stress compared to the rheology with solely diffusion creep and power-law creep. The enhanced deformation by low-temperature plasticity produces lower amount of dissipative heating, and thus stabilizes the shear zone. Comparing the stability between constant strain-rate and constant stress boundary conditions, we found that the Peierls mechanism exerts an opposite destabilizing effect in the case of constant stress. For dry olivine rheology and realistic magnitude of the strain rate, the effect of low-temperature plasticity is significant for temperatures between around 800 K and 1000 K. This finding suggests that the low-temperature plasticity may be crucial in determining the thermal-mechanical stability in the shallow portion of slabs.

The interaction of viscous heating with grain‐size dependent rheology in the formation of localized slip zones

The formation of localized shear zones is important for understanding many local and global processes in geodynamics. We have developed a self-consistent thermal-mechanical model together with a rheology which depends on temperature, strain-rate and grain-size distribution. The grain-size distribution has contributions from both dynamic recrystallization and grain-growth processes, and is governed locally by a nonlinear ordinary differential equation. A one-dimensional model with 104 points is employed to resolve all of the scales involving grain-size and temperature. We found that grain-growth inhibits the development of shear zones, and that there is a delicate interplay between viscous heating and grain-growth process in determining whether narrow fault zones are developed quickly. For realistic parameters of rheology and grain-boundary processes for wet olivine, the magnitude of the rate of grain-growth is crucial to determine whether shear zones are stable or unstable at temperature T ≃ 1000 K or shear stress σ ≃ 100 MPa.

Transitions in thermal convection with strongly temperature-dependent viscosity in a wide box

Numerical models are systematically presented for time-dependent thermal convection of Newtonian fluid with strongly temperature-dependent viscosity in a two-dimensional rectangular box of aspect ratio 3 at various values of the Rayleigh number Rab defined with viscosity at the bottom boundary up to 1.6×108 and the viscosity contrast across the box rη up to 108. We found that there are two different series of bifurcations that take place as rη increases. One series of bifurcations causes changes in the behavior of the thermal boundary layer along the surface boundary from small-viscosity-contrast (SVC) mode, through transitional (TR) mode, to stagnant-lid (ST) mode, or from SVC mode directly to ST mode, depending on Rab. Another series of bifurcations causes changes in the aspect ratio of convection cells; convection with an elongated cell can take place at moderate rη (103–105.5 at Rab=6×106), while only convection of aspect ratio close to 1 takes place at small rη and large rη. The parameter range of rη and Rab for elongated-cell convection overlaps the parameter range for SVC and ST modes and include the entire parameter range for TR mode. In the elongated-ST regime, the lid of highly viscous fluid along the top boundary is not literally ‘stagnant’ but can horizontally move at a velocity high enough to induce a convection cell with aspect ratio much larger than 1.

Multigrid iterative algorithm using pseudo-compressibility for three-dimensional mantle convection with strongly variable viscosity

A numerical algorithm for solving mantle convection problems with strongly variable viscosity is presented. Equations for conservation of mass and momentum for highly viscous and incompressible fluids are solved iteratively by a multigrid method in combination with pseudo-compressibility and local time stepping techniques. This algorithm is suitable for large-scale three-dimensional numerical simulations, because (i) memory storage for any additional matrix is not required and (ii) vectorization and parallelization are straightforward. The present algorithm has been incorporated into a mantle convection simulation program based on the finite-volume discretization in a three-dimensional rectangular domain. Benchmark comparisons with previous two- and three-dimensional calculations including the temperature- and/or depth-dependent viscosity revealed that accurate results are successfully reproduced even for the cases with viscosity variations of several orders of magnitude. The robustness of the numerical method against viscosity variation can be significantly improved by increasing the pre- and post-smoothing calculations during the multigrid operations, and the convergence can be achieved for the global viscosity variations up to 10^1^0.

Effects of temperature-dependent thermal diffusivity on shear instability in a viscoelastic zone: Implications for faster ductile faulting and earthquakes in the spinel stability field

The introduction of a new model of thermal diffusivity has motivated us to reinvestigate a one-dimensional viscoelastic shear zone model with realistic rheology, temperature-dependent thermal diffusivity (κ(T)) and viscous dissipation. Although thermal diffusivity in the shear zone is spatially heterogeneous with κ(T) and viscous heating, the spatial distribution of κ(T) does not affect shear zone evolution for the mesh resolution used in the model. As temperatures increase above room temperature, thermal diffusivity decreases. The lower thermal diffusivity causes a slight spatial thinning of the shear zone and an acceleration of the onset of instability relative to cases using a room temperature value of thermal diffusivity. Increasing the nonlinearity of κ(T) enhances shear zone thinning and speed-up of instability; the amount of enhancement depends on temperature, mineralogy and the rate of shear heating. The rheology of spinel creates a more unstable situation for the shear zone than that of olivine, but the boundary separating instability and stability is sensitive to changes in material properties. A decrease in the grain size does not influence the timescale of instability, unless grain size reduction causes diffusion creep to be the dominant deformation mechanism. Viscoelastic thermal–mechanical instabilities occur on timescales ranging from a few hundred to several thousand years. In most slabs, no instability is found to occur in spinel regions at temperatures above 1200 K. Likewise, shear instability in olivine at upper mantle depths will not occur at temperatures greater than 1100 K.

Deformation of a seamount subducting beneath an accretionary prism: Constraints from numerical simulation

We examined the process of seamount subduction via a numerical simulation using the finite element method, applying a frictional force on the plate interface that is proportional to the normal stress. We calculate the incremental stress due to infinitesimal deformation of the seamount associated with subduction, and consider the implications for stress buildup and fracturing of the seamount itself. Our results show that the maximum shear stress concentrates at both flanks of the seamount, which suggests that fracturing will start there. We can surmise that, eventually, the seaward flank may be more apt to break than the landward flank at shallow depth if the confining pressure there is sufficiently low. We consider this to be a possible scenario for the generation of a thrust fault imaged at the seaward flank of the Muroto seamount, which is subducting under the Nankai trough accretionary prism.

DYNAMICS OF SUPERPLUMES IN THE LOWER MANTLE

Superplumes in the lower mantle have been inferred for a long time by the presence of two very large provinces with slow seismic wave velocities. These extensive structures are not expected from numerical and laboratory experiments nor are they found in thermal convection with constant physical properties under high Rayleigh number conditions. Here we summarize our dynamical understanding of superplume structures within the framework of thermal convection. The numerical studies involve both two- and threedimensional models in Cartesian and spherical-shell geometries. The theoretical approach is based on models with increasing complexity, starting with the incompressible Boussinesq model and culminating with the anelastic compressible formulation. We focus here on the (1) depth-dependence of variable viscosity and thermal coefficient of expansion (2) radiative thermal conductivity and (3) both upper- and deep-mantle phase transitions. All these physical factors in thermal convection help to create conditions favorable for the formation of partially-layered convection and large-scale upwelling structures in the lower mantle.

A 15.2 TFlops Simulation of Geodynamo on the Earth Simulator

For realistic geodynamo simulations, one must solve the magnetohydrodynamic equations to follow time development of thermal convection motion of electrically conducting fluid in a rotating spherical shell. We have developed a new geodynamo simulation code by combining the finite difference method with the recently proposed spherical overset grid called Yin-Yang grid. We achieved performance of 15.2 Tflops (46% of theoretical peak performance) on 4096 processors of the Earth Simulator.

A thermo-chemical regime in the upper mantle in the early Earth inferred from a numerical model of magma-migration in a convecting upper mantle

Abstract A numerical model of mantle magmatism in a convecting upper mantle has been developed to study the thermo-chemical evolution of the upper mantle of the early Earth. The solid-state convection in the upper mantle is modeled by a convection of a binary eutectic material with a Newtonian temperature-dependent rheology in a two-dimensional rectangular box placed on a heat bath as a model of the lower mantle. The density depends on the chemical composition and melt-content as well as temperature of the material. The material contains heat-producing elements that are incompatible and exponentially decay with time. Mantle magmatism is modeled by a permeable flow of melt generated by a pressure-release melting induced by the solid-state convection through matrix. The permeable flow is driven by a buoyancy due to the density difference between the melt and the matrix. The thermo-chemical evolution in the box occurs in two stages if the deeper part of the box is not so strongly depleted in heat-producing elements in spite of the upward migration and concentration of heat-producing elements into a crustal layer along the top surface boundary due to magmatism. In the earlier stage, active magmatism occurs because of a strong internal heating due to the heat-producing elements, a chemically stratified structure develops well in the box with dense magmatic products in the deeper part and less dense residual materials in the shallower part, and the temperature distribution becomes strongly superadiabatic over the entire box. The temperature at the base of the box becomes as high as the solidus temperature. The chemically stratified structure is, however, suddenly destroyed by convective mixing and the temperature in the deeper part of the box suddenly drops by several hundred degrees when the internal heat source becomes too weak owing to the decay of heat-producing elements which sustain the active magmatism and hence keep the effect of chemical differentiation due to the magmatism stronger than the effect of convective mixing. In the later stage of the evolution, the box becomes chemically homogeneous and magmatism occurs only mildly. If heat-producing elements are efficiently transported into the crustal layer and the deeper part of the box becomes strongly depleted in heat-producing elements owing to the magmatism, only a mild magmatism occurs even at the beginning, a chemically stratified structure does not develop well, and the temperature in the box rapidly decreases to a stationary value. The regime of hot and chemically stratified upper mantle suggested from the earlier stage of the case with mild depletion of heat-producing elements at depth fits in with many observations of the Archean continental crust.

ON THE VIGOR OF MANTLE CONVECTION IN SUPER-EARTHS

Numerical models are presented to clarify how adiabatic compression affects thermal convection in the mantle of super-Earths ten times the Earths mass. The viscosity strongly depends on temperature, and the Rayleigh number is much higher than that of the Earths mantle. The strong effect of adiabatic compression reduces the activity of mantle convection; hot plumes ascending from the bottom of the mantle lose their thermal buoyancy in the middle of the mantle owing to adiabatic decompression, and do not reach the surface. A thick lithosphere, as thick as 0.1 times the depth of the mantle, develops along the surface boundary, and the efficiency of convective heat transport measured by the Nusselt number is reduced by a factor of about four compared with the Nusselt number for thermal convection of incompressible fluid. The strong effect of adiabatic decompression is likely to inhibit hot spot volcanism on the surface and is also likely to affect the thermal history of the mantle, and hence, the generation of magnetic field in super-Earths.