Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

<title>Abstract</title>In this paper, we carried out a series of linear analyses on the onset of thermal convection of highly compressible fluids whose physical properties strongly vary in space in convecting vessels either of a three-dimensional spherical shell or a two-dimensional spherical annulus geometry. The variations in thermodynamic properties (thermal expansivity and reference density) with depth are taken to be relevant for the super-Earths with ten times the Earth’s mass, while the thermal conductivity and viscosity are assumed to exponentially depend on depth and temperature, respectively. Our analysis showed that, for the cases with strong temperature dependence in viscosity and strong depth dependence in thermal conductivity, the critical Rayleigh number is on the order of 10⁸–10⁹, implying that the mantle convection of massive super-Earths is most likely to fall in the stagnant-lid regime very close to the critical condition, if the properties of their mantle materials are quite similar to the Earth’s. Our analysis also demonstrated that the structures of incipient flows of stagnant-lid convection in the presence of strong adiabatic compression are significantly affected by the depth dependence in thermal conductivity and the geometries of convecting vessels, through the changes in the static stability of thermal stratification of the reference state. When the increase in thermal conductivity with depth is sufficiently large, the thermal stratification can be greatly stabilized at depth, further inducing regions of insignificant fluid motions above the bottom hot boundaries in addition to the stagnant lids along the top cold surfaces. We can therefore speculate that the stagnant-lid convection in the mantles of massive super-Earths is accompanied by another motionless regions at the base of the mantles if the thermal conductivity strongly increases with depth (or pressure), even though their occurrence is hindered by the effects the spherical geometries of convecting vessels.

DOI： 10.1186/s40623-021-01499-w

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DOI： 10.1186/s40623-020-01195-1

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DOI： 10.3389/feart.2020.00117

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGEROPEN  

We present two-dimensional numerical models of thermal convection of a compressible fluid in the mantles of super-Earths calculated under the truncated anelastic liquid approximation to discuss how adiabatic compression affects the thermal convection, depending on planetary mass. The convection is driven by basal heating, the viscosity depends on temperature, and the thermal expansivity and the reference density depend on the depth. We varied all of the magnitude of adiabatic heating, the Rayleigh number, the depth profile of the thermal expansivity, and that of the reference density in accordance with the planetary mass. The effects on thermal convection become substantial, when the planetary mass normalized by the Earth's mass Mp exceeds a threshold Mc, about 4. Hot plumes ascending from the core-mantle boundary become thinner with increasing Mp; they become almost invisible except around the core-mantle boundary, when Mp > Mc. The lithosphere that develops along the surface boundary due to the temperature dependence of viscosity becomes thicker with increasing Mp and is about twice as thick as that at Mp = 1 when Mp = 9.4. The convective velocity is almost independent of Mp. These results are in a striking contrast with earlier predictions that are made based on the models where the effects of adiabatic compression are neglected; it is important to take account of the effects of adiabatic compression properly in the exploration of mantle dynamics such as plate tectonics and hot spot volcanisms in massive super-Earths. Further researches are necessary to clarify the dependence of Mc on the surface temperature and the material properties of the convecting mantle.

DOI： 10.1186/s40623-018-0975-5

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Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier B.V.  

We conduct a series of numerical experiments of thermal convection of highly compressible fluids in a two-dimensional rectangular box, in order to study the mantle convection on super-Earths. The thermal conductivity and viscosity are assumed to exponentially depend on depth and temperature, respectively, while the variations in thermodynamic properties (thermal expansivity and reference density) with depth are taken to be relevant for the super-Earths with 10 times the Earth's. From our experiments we identified a distinct regime of convecting flow patterns induced by the interplay between the adiabatic temperature change and the spatial variations in viscosity and thermal conductivity. That is, for the cases with strong temperature-dependent viscosity and depth-dependent thermal conductivity, a “deep stratosphere” of stable thermal stratification is formed at the base of the mantle, in addition to thick stagnant lids at their top surfaces. In the “deep stratosphere”, the fluid motion is insignificant particularly in the vertical direction in spite of smallest viscosity owing to its strong dependence on temperature. Our finding may further imply that some of super-Earths which are lacking in mobile tectonic plates on their top surfaces may have “deep stratospheres” at the base of their mantles.

DOI： 10.1016/j.pepi.2017.11.001

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Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：MDPI AG  

In this study, we conduct numerical simulations of thermochemical mantle convection in a 2D spherical annulus with a highly viscous lid drifting along the top surface, in order to investigate the interrelation between the motion of the surface (super)continent and the behavior of chemical heterogeneities imposed in the lowermost mantle. Our calculations show that assembly and dispersal of supercontinents occur in a cyclic manner when a sufficient amount of chemically-distinct dense material resides in the base of the mantle against the convective mixing. The motion of surface continents is significantly driven by strong ascending plumes originating around the dense materials in the lowermost mantle. The hot dense materials horizontally move in response to the motion of continents at the top surface, which in turn horizontally move the ascending plumes leading to the breakup of newly-formed supercontinents. We also found that the motion of dense materials in the base of the mantle is driven toward the region beneath a newly-formed supercontinent largely by the horizontal flow induced by cold descending flows from the top surface occurring away from the (super)continent. Our findings imply that the dynamic behavior of cold descending plumes is the key to the understanding of the relationship between the supercontinent cycle on the Earth’s surface and the thermochemical structures in the lowermost mantle, through modulating not only the positions of chemically-dense materials, but also the occurrence of ascending plumes around them.

DOI： 10.3390/geosciences7040126

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DOI： 10.1186/s40623-017-0630-6

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：OXFORD UNIV PRESS  

We explore thermal convection of a fluid with a temperature-dependent viscosity in a basally heated 3-D spherical shell using linear stability analyses and numerical experiments, while considering the application of our results to terrestrial planets. The inner to outer radius ratio of the shell f assumed in the linear stability analyses is in the range of 0.11-0.88. The critical Rayleigh number R-c for the onset of thermal convection decreases by two orders of magnitude as f increases from 0.11 to 0.88, when the viscosity depends sensitively on the temperature, as is the case for real mantle materials. Numerical simulations carried out in the range of f = 0.11-0.55 show that a thermal boundary layer (TBL) develops both along the surface and bottom boundaries to induce cold and hot plumes, respectively, when f is 0.33 or larger. However, for smaller f values, a TBL develops only on the bottom boundary. Convection occurs in the stagnant-lid regime where the root mean square velocity on the surface boundary is less than 1 per cent of its maximum at depth, when the ratio of the viscosity at the surface boundary to that at the bottom boundary exceeds a threshold that depends on f. The threshold decreases from 10(6.5) at f = 0.11 to 10(4) at f = 0.55. If the viscosity at the base of the convecting mantle is 10(20)-10(21) Pa s, the Rayleigh number exceeds R-c for Mars, Venus and the Earth, but does not for the Moon and Mercury; convection is unlikely to occur in the latter planets unless the mantle viscosity is much lower than 10(20) Pa s and/or the mantle contains a strong internal heat source.

DOI： 10.1093/gji/ggw226

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Authorship：Last author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER GEOPHYSICAL UNION  

Recent geological observations support the subduction of some oceanic arcs into the mantle. For example, the Izu-Bonin arc is considered to be partially subducting underneath the island of Honshu, Japan, despite its lower density than that of surrounding mantle, after the vertical collision with Honshu at similar to 17Ma. Seismological surveys have clarified the internal structure of the arc, which consists of the basaltic and boninitic upper crust, the felsic middle crust, the intermediate upper-lower crust, and the mafic lower crust. This structure extends and moves northward toward Honshu. Among these components, part of the middle, the intermediate upper-lower, and the lower crust is thought to be subducting. Here in order to estimate the subduction rate of granitic materials in oceanic arcs to the deep mantle, we have conducted numerical simulations of the subduction of arcs based on the finite element method and investigated the effect of arcs' sizes and shapes and slab temperature. The results show that the subduction rate heavily depends on the geometry of the arcs or temperature profiles of the subducting slabs. When the size of the arc or the temperature of the slab is smaller, the subduction rate grows larger owing to competition between upward buoyancy and downward viscous drag from slabs. The results also show that about 20% of the felsic crust materials in oceanic arcs that are comparable in size to the Izu-Bonin arc can be subducted into the deep mantle when the temperature of the subducting slab is of the usual value.

DOI： 10.1002/2016JB013119

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：OXFORD UNIV PRESS  

A series of our linear analysis on the onset of thermal convection was applied to that of highly compressible fluids in a planar layer whose thermal conductivity and viscosity vary in space, in order to study the influences of spatial variations in physical properties expected in the mantles of massive terrestrial planets. The thermal conductivity and viscosity are assumed to exponentially depend on depth and temperature, respectively, while the variations in thermodynamic properties (thermal expansivity and reference density) with depth are taken to be relevant for the super-Earths with 10 times the Earth's. Our analysis demonstrated that the nature of incipient thermal convection is strongly affected by the interplay between the adiabatic compression and spatial variations in physical properties of fluids. Owing to the effects of adiabatic compression, a 'stratosphere' can occur in the deep mantles of super-Earths, where a vertical motion is insignificant. An emergence of 'stratosphere' is greatly enhanced by the increase in thermal conductivity with depth, while it is suppressed by the decrease in thermal expansivity with depth. In addition, by the interplay between the static stability and strong temperature dependence in viscosity, convection cells tend to be confined in narrow regions around the 'tropopause' at the interface between the 'stratosphere' of stable stratification and the 'troposphere' of unstable stratification. We also found that, depending on the variations in physical properties, two kinds of stagnant regions can separately develop in the fluid layer. One is well-known 'stagnant-lids' of cold and highly viscous fluids, and the other is 'basal stagnant regions' of hot and less viscous fluids. The occurrence of 'basal stagnant regions' may imply that convecting motions can be insignificant in the lowermost part of the mantles of massive super-Earths, even in the absence of strong increase in viscosity with pressure (or depth).

DOI： 10.1093/gji/ggv507

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER GEOPHYSICAL UNION  

Numerical models of bottom-heated thermal convection of highly compressible fluid with strongly temperature-dependent viscosity are presented to understand how the Rayleigh number Ra and the temperature dependence of viscosity exert control over the regimes of thermal convection in massive super-Earths. Thermodynamic properties of mantle materials are pressure dependent, but other material properties including the viscosity are not. A stagnant lid develops along the surface of the planet, when the viscosity contrast across the mantle due to temperature dependence r exceeds 10(6) at high Rayleigh number relevant to super-Earths. The threshold in r, which increases with increasing Ra, is higher than that expected for the Earth from earlier Boussinesq models. The efficiency of convective heat transport measured by the Nusselt number Nu is considerably lower than that expected from Boussinesq models; Nu depends on Ra and r as Nu=59r(-0.23)(Ra/10(9))(0.27), when r10(5). Strong adiabatic compression significantly reduces the activity of hot ascending plumes especially at high r. At r relevant for super-Earths, hot ascending plumes lose their buoyancy on their way and hardly reach the surface boundary: hot spot volcanism due to ascending plumes is probably suppressed on super-Earths. The lithosphere is considerably thicker than that suggested by earlier Boussinesq models and is unlikely to show a plate-like behavior.

DOI： 10.1002/2015JE004793

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Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：OXFORD UNIV PRESS  

A series of linear analysis was performed on the onset of thermal convection of highly compressible fluids, in order to deepen the fundamental insights into the mantle convection of massive super-Earths in the presence of strong adiabatic compression. We consider the temporal evolution (growth or decay) of an infinitesimal perturbation superimposed to a highly compressible fluid which is in a hydrostatic (motionless) and conductive state in a basally heated horizontal layer. As a model of pressure-dependence in material properties, we employed an exponential decrease in thermal expansivity alpha and exponential increase in (reference) density rho with depth. The linearized equations for conservation of mass, momentum and internal (thermal) energy are numerically solved for the critical Rayleigh number as well as the vertical profiles of eigenfunctions for infinitesimal perturbations. The above calculations are repeatedly carried out by systematically varying (i) the dissipation number (Di), (ii) the temperature at the top surface and (iii) the magnitude of pressure-dependence in alpha and rho. Our analysis demonstrated that the onset of thermal convection is strongly affected by the adiabatic compression, in response to the changes in the static stability of thermal stratification in the fluid layer. For sufficiently large Di where a thick sublayer of stable stratification develops in the layer, for example, the critical Rayleigh number explosively increases with Di, together with drastic decreases in the length scales of perturbations both in vertical and horizontal directions. In particular, for very large Di, a thick 'stratosphere' occurs in the fluid layer where the vertical motion is significantly suppressed, resulting in a shrink of the incipient convection in a thin sublayer of unstable thermal stratification. In addition, when Di exceeds a threshold value above which a thermal stratification becomes stable in the entire layer, no perturbation is allowed to grow with time regardless of the Rayleigh number and/or the horizontal wavelength. We also found that the effect of adiabatic compression becomes prominent for higher temperature at the top surface of the fluid layer. These findings may imply the crucial importance of adiabatic compression in understanding the dynamics and evolution of the mantles of massive super-Earths, particularly for those orbiting their parent stars very closely.

DOI： 10.1093/gji/ggu457

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Language：English   Publishing type：Part of collection (book)   Publisher：Springer International Publishing  

The flows in the subduction channels with wet mantle wedge are calculated by 1-D finite difference method with fine numerical resolutions. The water content largely affects the viscosity of the mantle wedge. Previous simulation result using dry rheology on the mantle wedge shows that viscosity of the subduction channels controls the process and that the sustainable thickness of the channel in the deep mantle is ~2-3 km. However, little is known about the effect of the water content in the mantle wedge on the subduction channels. Here, in order to estimate the supply rate of continental materials to the deep mantle with water-rich environment on the mantle wedge, we have conducted a numerical simulation of a subduction channel. The results show that the water content controlsthe flux of the continental materials especially when temperature of mantle wedge is high. Therefore, the water content of the mantle wedge can be more important in the ancient mantle because of its high temperature.

DOI： 10.1007/978-3-319-15627-9_9

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER GEOPHYSICAL UNION  

The influence of MgSiO3 majorite on mantle convection has been investigated via 2-D numerical simulations that incorporate the stability field of majorite. According to a recent first principles study, wadsleyite decomposes into an assemblage of majorite plus periclase with a large negative Clapeyron slope. Since the stability field of majorite is limited to be greater than similar to 2200 K in a depth range of 500-660 km for Mg2SiO4, very hot upwelling plumes are expected to be strongly influenced by the phase transitions related to majorite. These hot upwellings are occasionally observed in simulations, even though the average temperature of hot plumes is far less than the stability field of majorite. The dynamics of these upwellings are controlled by the release and the absorption of latent heat induced by majorite's phase transitions as well as by the interruption of currents due to the large negative Clapeyron slope related to majorite.

DOI： 10.1002/2014GL061477

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

To understand how adiabatic compression influences mantle convection in super-Earths, we carried out linear stability analysis and non-linear numerical simulation of thermal convection for constant viscosity infinite Prandtl number fluid with both constant and pressure-dependent thermal expansivity. The mantle is basally heated and internal heating is not considered. In the case of constant thermal expansivity, thermal convection is totally inhibited in super-Earths of more than about 5 times the Earth's mass owing to the strong effect of adiabatic compression, when the surface temperature is sufficiently high. Pressure-dependence of thermal expansivity is crucial for the onset of convection in massive super-Earths. Even when the thermal expansivity depends on pressure, our numerical simulation shows that the effect of adiabatic compression reduces the efficiency of convective heat transport by up to about 60%, depending on the planetary mass and the surface temperature. The reduction in the efficiency of convective heat transport makes cooling of the mantle more difficult in massive super-Earths, especially when the surface temperature is high. The surface temperature of a planet may affect its thermal history not only through its effects on the mechanical properties of convecting mantle materials, but also through its influence on adiabatic compression of convecting materials. (C) 2014 Elsevier Inc. All rights reserved.

DOI： 10.1016/j.icarus.2013.12.022

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：CHINA UNIV GEOSCIENCES, BEIJING  

A series of linear stability analysis is carried out on the onset of thermal convection in the presence of spatial variations of viscosity, thermal conductivity and expansivity. We consider the temporal evolution of an infinitesimal perturbation superimposed to a static (motionless) and conductive state in a basally-heated planar layer. From the changes in flow patterns with increasing the amplitudes of temperature dependence of viscosity, we identified the transition into the "stagnant-lid" (ST) regime, where the convection occurs only beneath a thick and stagnant-lid of cold fluid at the top surface. Detailed analysis showed a significant increase of the aspect ratio of convection cells in ST regime induced by the spatial variations in thermal conductivity and/or expansivity: the horizontal length scale of ST convection can be enlarged by up to 50% with 10 times increase of thermal conductivity with depth. We further developed an analytical model of ST convection which successfully reproduced the mechanism of increasing horizontal length scale of ST regime convection cells for given spatial variations in physical properties. Our findings may highlight the essential roles of the spatial variation of thermal conductivity on the convection patterns in the mantle.

DOI： 10.1007/s12583-014-0405-y

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

Numerical models are presented to clarify how adiabatic compression affects thermal convection in the mantle of super-Earths ten times the Earth's mass. The viscosity strongly depends on temperature, and the Rayleigh number is much higher than that of the Earth's 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.

DOI： 10.1088/2041-8205/780/1/L8

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We examined in an analytical manner the stability of thermal stratification of highly compressible fluids with depth-dependent physical properties, to obtain the fundamental insights into the convective motion in the mantles of 'super-Earths'. We consider a stability in a horizontal layer of a highly compressible fluid,which is in a hydrostatic (motionless) state under a uniform gravitational field. As a model of pressure-dependence in material properties, we employed an exponential decrease in thermal expansivity and exponential increase in thermal conductivity with depth. By using the 'parcel method' as in meteorological studies, we investigated the change in the static stability of thermal stratification depending on the adiabatic compression as well as the depth-dependence of thermal expansivity and conductivity, with a special emphasis on the changes in the depth ranges (or the vertical extent) of unstable thermal stratifications. We found that a large thermal expansivity at depth tends to suppress the instability within the entire layer of compressible fluids, as opposed to the cases with incompressible ones. This means that the effect of adiabatic compression is of crucial importance in the understanding the mantle dynamics of super-Earths. We also found that, for the conditions relevant to super-Earths of 10 times mass of the Earth's, the stability of thermal stratification significantly varies. For example, the stratification is unstable in the entire layer only for a strong decrease in thermal expansivity with depth and/or low surface temperature. If this condition is not met, the fluid layer will be split into a 'troposphere' and 'stratosphere', depending on the stable or unstable thermal stratification. In addition, for the cases with extremely high surface temperature, a stratification can be stable even in the entire depth range of the fluid layer. The present findings may imply that the models of thermal evolution of super-Earths have to be carefully reconsidered by incorporating the effects of 'stratosphere' on the overall heat transfer within the planets. © The Authors 2013. Published by Oxford University Press on behalf of The Royal Astronomical Society.

DOI： 10.1093/gji/ggt321

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

Geological studies have suggested that a significant amount of crustal material has been lost from the surface due to delamination, continental collision, and subduction at oceanic-continental convergent margins. If so, then the subducted crustal materials are expected to be trapped in the mid-mantle due to the density difference from peridotitic materials induced by the phase transition from coesite to stishovite. In order to study the effect of the subducted granitic materials floating around the mantle transition zone, we conducted two-dimensional numerical experiments of mantle convection incorporating a continental drift with a heat source placed around the bottom of the mantle transition zone. The simulations deal with a time-dependent convection of fluid under the extended Boussinesq approximation in a model of a two-dimensional rectangular box with a height of 2900 km and a width of 11,600 km, where a continent with a length of 2900 km and heat source below the continent are imposed. We found that the addition of heat source in the mantle transition zone considerably enhances the onset of upwelling plumes in the upper mantle, which further reduces the time scale of continental drift. The heat source also causes massive mechanical mixing, especially in the upper mantle. The results suggest that the heat source floating around the mantle transition zone can be a possible candidate for inducing the supercontinent cycle. (C) 2013 International Association for Gondwana Research. Published by Elsevier B.V. All rights reserved.

DOI： 10.1016/j.gr.2013.02.001

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

In this paper we carried out numerical experiments of a time-dependent thermal convection in a two-dimensional Cartesian box of aspect ratio (width/height) of 6, in order to study the influences on the convecting flow patterns of the spatial variations in physical properties (viscosity eta, thermal conductivity k and expansivity alpha). A series of calculations by systematically varying the magnitude of spatial variations in these properties showed that the strongly temperature-dependent eta induces the change in flow pattern into the "stagnant lid" (ST) regime, regardless of the increase in k and/or decrease in alpha with depth, where the convection occurs only beneath a stagnant lid of cold fluid at the top surface. In particular, we found that the increase in thermal conductivity k with depth significantly affects the convecting flow patterns in the presence of strong temperature-dependence in eta. Compared with those with uniform k, the patterns of ST convection with non-uniform k are characterized by (i) thinner top thermal boundary layers or lids and (ii) larger horizontal length scales of convection cells beneath the stagnant lid. In addition, the variation in k with depth decreases the threshold values of the temperature-dependence in eta above which the ST-mode of convection takes place, which may also help stabilize the convection cells of large horizontal length scales beneath stagnant lids. Our results may highlight the potential importance of the increase in thermal conductivity with depth (or pressure) in controlling the planforms of thermal convection in the mantle of terrestrial planets. (C) 2013 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.pepi.2013.08.001

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

Geological studies have revealed that continental materials subduct from the Earth's surface via the following three mechanisms: tectonic erosion, sediment subduction, and direct subduction of immature oceanic arcs. Then, the continental materials are transported through subduction channels that are located between subducting slabs and mantle wedges. However, the depth that a subduction channel reaches and the magnitude of the flux of subducted materials at that depth are not clear. Here, in order to estimate the supply rate of continental materials to the deep mantle, we have conducted a numerical simulation of a subduction channel based on the finite difference method. We have found that a sustainable thickness of the channel in the deep mantle is similar to 2-3 km and its corresponding flux of continental materials integrated over the length of the current subduction zones is 2.2 km(3)/yr. These results indicate that almost all of the continental material that is subducted through the channel is capable of reaching the depth of the mantle transition zone. The total amount of continental materials conveyed to the deep mantle over 4 Gyr is estimated to be about 10(10) km(3), which is greater than the volume of the present continental crust at the surface of the Earth. (C) 2013 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.tecto.2013.02.001

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER  

A linear stability analysis was performed in order to study the onset of thermal convection in the presence of a strong viscosity variation, with a special emphasis on the condition for the stagnant-lid (ST) convection where a convection takes place only in a sublayer beneath a highly viscous lid of cold fluid. We consider the temporal evolution (growth or decay) of an infinitesimal perturbation superimposed to a Boussinesq fluid with an infinite Prandtl number which is in a static (motionless) and conductive state in a basally heated planar layer or spherical shell. The viscosity of the fluid is assumed to be exponentially dependent on temperature. The linearized equations for conservations of mass, momentum, and internal (thermal) energy are numerically solved for the critical Rayleigh number, Ra (c) , as well as the radial profiles of eigenfunctions for infinitesimal perturbations. The above calculations are repeatedly carried out by systematically varying (i) the magnitude of the temperature dependence of viscosity, E, and (ii) the ratio of the inner and outer radii of the spherical shell, gamma. A careful analysis of the vertical structure of incipient flows demonstrated that the dominance of the ST convection can be quantitatively identified by the vertical profile of Delta (h) (a measure of conversion between horizontal and vertical flows), regardless of the model geometries. We also found that, in the spherical shell relevant to the Earth's mantle (gamma = 0.55), the transition into ST convection takes place at the viscosity contrast across the layer . Taken together with the fact that the threshold value of r (eta) falls in the range of r (eta) for a so-called sluggish-lid convection, our finding suggests that the ST-mode of convection with horizontally elongated convection cells is likely to arise in the Earth's mantle solely from the temperature-dependent viscosity.

DOI： 10.1007/s00162-011-0250-x

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER GEOPHYSICAL UNION  

We conducted two-dimensional numerical experiments of mantle convection with imposed kinematic motions of cold slabs, in order to study the mechanism for the generation of ascending flows in the "Big Mantle Wedge" (BMW), which has been recently proposed in order to relate the stagnant Pacific slab with the intraplate volcanism in northeast Asia. Our calculations demonstrated that the BMW is expanded oceanward in response to the retreating motion of trench and slab, which strongly affects the flows in the region. In particular, the subducting and retreating motion of slab induces a local but strong circulation near the oceanward end (or a hinge) of the stagnant slab in the BMW. Our findings suggest that ascending flows in the BMW can be triggered most easily near the hinge of the stagnant slab, which is in good agreement with the occurrence of several active intraplate volcanoes above the stagnant Pacific slab. Citation: Kameyama, M., and R. Nishioka (2012), Generation of ascending flows in the Big Mantle Wedge (BMW) beneath northeast Asia induced by retreat and stagnation of subducted slab, Geophys. Res. Lett., 39, L10309, doi:10.1029/2012GL051678.

DOI： 10.1029/2012GL051678

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During an earthquake, fault strength decreases with slip over the slip-weakening distance, D-c, to a residual strength. The estimation of D-c is crucial for the evaluation of fault instability during earthquakes; however, it has been difficult to determine D-c from natural faults. We found geological evidence of thermal pressurization from the on-land analog of a subduction thrust exhumed from seismogenic depths; thermal pressurization was indicated by the fluidization of comminuted material and increase in the volume of fluid inclusions by frictional heating. Numerical analysis of thermal pressurization with the constraints on the thickness of the seismic slip zone, the temperature range of frictional heating, and ambient conditions of subduction thrusts indicates that the D-c of subduction thrusts ranges from 0.03 to 0.22 m, which is independent of initial pore-fluid pressure on subduction thrusts. The short D-c associated with the effect of thermal pressurization on subduction thrusts indicates the occurrence of rapid stress relief and high radiated energy during subduction earthquakes. (C) 2010 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.tecto.2010.01.002

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：WILEY-BLACKWELL PUBLISHING, INC  

P&gt;Benchmark comparisons are an essential tool to verify the accuracy and validity of computational approaches to mantle convection. Six 2-D Cartesian compressible convection codes are compared for steady-state constant and temperature-dependent viscosity cases as well as time-dependent constant viscosity cases. In general we find good agreement between all codes when comparing average flow characteristics such as Nusselt number and rms velocity. At Rayleigh numbers near 106 and dissipation numbers between 0 and 2, the results differ by approximately 1 per cent. Differences in discretization and use of finite volumes versus finite elements dominate the differences. There is a small systematic difference between the use of the anelastic liquid approximation (ALA) compared to that of the truncated ALA. In determining the onset of time-dependence, there was less agreement between the codes with a spread in the Rayleigh number where the first bifurcation occurs ranging from 7.79 x 105 to 1.05 x 106.

DOI： 10.1111/j.1365-246X.2009.04413.x

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

In this study, we propose a so-called fluid rope coiling to use as a validity test of our simulation scheme designed to solve the plate-mantle problem in the Eulerian frame of reference. In a plate-mantle unified system, a subducting plate is known to show various large and complex deformations. A numerical simulation for the plate-mantle problem is required to solve such plate motions properly without serious numerical errors. Fluid rope coiling, in which a coiling motion of viscous fluid is poured onto a horizontal plane from a certain height with the shape of a thin rope, is known to be one such motion. We reproduced the coiling rope of a Stokes flow by two different methods: a three-dimensional simulation and simplified one-dimensional solution. Quantitative comparison of these methods enables us to evaluate the accuracy of the simulation scheme for large non-linear deformation problems. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

DOI： 10.1016/j.pepi.2009.03.014

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

A new simulation code of mantle convection in a three-dimensional spherical shell is presented. Major innovation of the code comes from an combination of two numerical techniques, namely Yin-Yang grid and ACUTE algorithm, which we had developed for large-scale simulations of solid earth sciences Bench. mark comparisons for the steady convection for low Rayleigh numbers (Ra) with previous calculations revealed that accurate results are successfully reproduced not only for isoviscous cases but also for the cases where the mild temperature-dependence of viscosity is included. We also demonstrated that Our code can reproduce the change in convective flow patterns into the "sluggish-lid" regime with increasing the viscosity variation r(n) up to 10(4). (C) 2008 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.pepi.2008.06.025

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

Toward the unified simulation of the large deformation of a rigid viscoelastic material (plate) and the convection of a viscous fluid (mantle), an Eulerian scheme with a semi-Lagrangian method is developed. The scheme adopts the CIP-CSLR method for advection terms of staggered grid system in three dimensions. The positive transported profile of a positive quantity is assured by flux corrections in the dimensional splitting method. The Jaumann co-rotational effect of the stress tensor is also integrated into the semi-Lagrangian treatment. This co-rotated semi-Lagrangian method is combined with an exponential time differencing method in the time development of the Maxwell constitutive model. The large time step comparable to, or larger than, the Maxwell relaxation time is successfully realized. Validation tests are performed for the three-dimensional Rayleigh-Taylor instability of a viscoelastic material with jump discontinuity of the mass density and other material properties. (C) 2008 Elsevier Inc. All rights reserved.

DOI： 10.1016/j.jcp.2008.01.052

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The current availability of thousands of processors at many high performance computing centers has made it feasible to carry out, in near real time, interactive visualization of 3D mantle convection temperature fields, using grid configurations having 10-100 million unknowns. We will describe the technical details involved in carrying out this endeavor, using the facilities available at the Laboratory of Computational Science and Engineering (LCSE) at the University of Minnesota. These technical details involve the modification of a parallel mantle convection program, ACuTEMan
the usage of client-server socket based programs to transfer upwards of a terabyte of time series scientific model data using a local network
a rendering system containing multiple nodes
a high resolution PowerWall display, and the interactive visualization software, DSCVR. We have found that working in an interactive visualizastion mode allows for fast and efficient analysis of mantle convection results. © Springer-Verlag 2008.

DOI： 10.1007/s10069-007-0008-1

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We have developed a new strategy and espouse a novel paradigm for large-scale computing and real-time interactive visualization. This philosophy calls for intense interactive sessions for a couple of hours at a time at the expense of storing data on many disk drives during regular or heroic runs on massively parallel systems. We have already carried out successfully real-time volume-rendering visualization by employing hundreds of processors for a grid with over 25 million unknowns. Both Cartesian and spherical 3D mantle convection are visualized. The volume-rendered images are viewed on a large display device, with many panels holding around 13 million pixels. We will employ a software strategy involving an hierarchical rendering service, which will have as software an Ajax interface for interactive visualization of large data sets on many different platforms from desktop PC's to hand-held devices, such as the OQO and the Nokia N-800. An option for stereo viewing is also implemented. We have installed a user interface as web application, using Java and Ajax framework in order to achieve over the Internet reasonable accessibility to our ongoing runs. Our goal is to expand the array of interactive devices, which will make it feasible to carry out ubiquitous visualization and monitoring of large-scale simulations or onsite events and to allow for collaborations across oceans. © Springer-Verlag 2008.

DOI： 10.1007/s10069-008-0013-z

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

Burial depth, cumulative displacement, and peak temperature of frictional heat of a fault system are estimated by thermal analysis in the fold-thrust belt of the Western Foothills complex, western Taiwan based on the vitrinite reflectance technique. The regional thermal structure across the complex reveals that the rocks were exposed to maximum temperatures ranging from 100 degrees C to 180 degrees C, which corresponds to a burial depth of 3.7-6.7 km. A large thermal difference of 90 degrees C were observed at the Shuilikeng fault which make the eastern boundary of the fold-thrust belt where it is in contact with metarnorphic rock of Hsuehshan Range. The large thermal difference corresponds to cumulative displacernents on the Shuilikeng fault estimated to be in the range of 5.2-6.9 km. However, thermal differences in across the Shuangtung and Chelungpu faults cannot be determined apparently due to small vertical offsets. The large displacement observed across the Shuilikeng fault is absent at the other faults which are interpreted to be younger faults within the piggyback thrust system. Localized high temperatures adjacent to fault zones were observed in core samples penetrating the Chelungpu fault. Three major fracture zones were observed at core lengths of 225 m, 330 m, and 405 m and the two lower zones which comprise dark gray narrow shear zones. A value of vitrinite reflectance of 1.8%, higher than the background value of 0.8%, is limited at a narrow shear zone of I cm thickness at the fracture zone at 330 m. The estimated peak temperature in the range of 550-680 degrees C in the shear zone is far higher than the background temperature of 130 degrees C, and it is interpreted as due to frictional heating during seismic faulting. (C) 2007 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.tecto.2007.01.017

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER BASEL AG  

We have developed a two-dimensional dynamical model of asymmetric subduction integrated into the mantle convection without imposed plate velocities. In this model we consider that weak oceanic crust behaves as a lubricator on the thrust fault at the plate boundary. We introduce a rheological layer that depends on the history of the past fracture to simulate the effect of the oceanic crust. The thickness of this layer is set to be as thin as the Earth's oceanic crust. To treat 1-kilometer scale structure at the plate boundary in the 1000-kilometer scale mantle convection calculation, we introduce a new numerical method to solve the hydrodynamic equations using a couple of uniform and nonuniform grids of control volumes. Using our developed models, we have systematically investigated effects of basic rheological parameters that determine the deformation strength of the lithosphere and the oceanic crust on the development of the subducted slab, with a focus on the plate motion controlling mechanism. In our model the plate subduction is produced when the friction coefficient (0.004-0.008) of the modeled oceanic crust and the maximum strength (400 MPa) of the lithosphere are in plausible range inferred from the observations on the plate driving forces and the plate deformation, and the rheology experiments. In this range of the plate strength, yielding induces the plate bending. In this case the speed of plate motion is controlled more by viscosity layering of the underlying mantle than by the plate strength. To examine the setting of the overriding plate, we also consider the two end-member cases in which the overriding plate is fixed or freely-movable. In the case of the freely-movable overriding plate, the trench motion considerably changes the dip angle of the deep slab. Especially in the case with a shallow-angle plate boundary, retrograde slab motion occurs to generate a shallow-angle deep slab.

DOI： 10.1007/s00024-007-0197-4

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Language：English   Publishing type：Part of collection (book)   Publisher：Springer Netherlands  

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. © 2007 Springer.

DOI： 10.1007/978-1-4020-5750-2_9

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Language：English   Publishing type：Part of collection (book)   Publisher：Blackwell Publishing Ltd  

The discovery of post-perovskite phase transition near the core-mantle boundary (CMB) has turned our heads to the potentially important role played by the increasing complexity of the physical properties in the lower-mantle models. In this study we have investigated the influences on lower mantle dynamics by the strongly depth-dependent coefficient of thermal expansion and radiative thermal conductivity together with the post-perovskite transition within the framework of isochemical models. We have carried out the simulations in both 2-D and 3-D Cartesian geometries. First, we review the basic connection between the temperature profile and the Clapeyron slope, calling attention to the special relationship between the temperature intercept of the post-perovskite phase change and the temperature at the core-mantle boundary. Double-crossing of the post-perovskite boundary takes place only, when the temperature of the CMB is greater than the temperature intercept of the phase change. We find that mantle plumes become multiscale in nature because of the combined effects exerted by variable mantle viscosity, strongly depth-dependent thermal expansivity, radiative thermal conductivity at the bottom of the mantle, the spinel to perovskite phase transition and the perovskite to post-perovskite phase change in the deep mantle. Both radiative thermal conductivity and strongly decreasing thermal expansivity in the lower mantle can help to induce partially layered convection with slabs stagnating in the transition zone. In our isochemical models a second low viscosity zone is created under the transition zone accompanied by intense shear heating. Secondary mantle plumes emerge from this region at the base of the transition zone. Large-scale upwellings in the lower mantle are induced mainly by both the style of lower-mantle stratification and the decrease in thermal expansivity. They control the location and the local dynamics of the upper-mantle plumes. In these models with variable thermal conductivity and viscosity, an increase in the temperature of the CMB causes a greater tendency for layered convection. From the same depth-dependent thermal expansivity, we can deduce the 3-D density anomalies from the seismic velocity anomalies inferred from seismic tomographic inversion. Using these density distributions, we can calculate the viscous responses of the Earth due to these density anomalies for a given viscosity structure. We then focus on the lateral viscosity variations of the deep mantle on the solution of the inverse problem involving the inferences of the viscosity from the long-wavelength geoid. Our solution for the large-scale lateral viscosity structure in the lowermost mantle shows that the region underneath hot spots have significantly higher viscosity in the deep mantle than the region below subduction regions. Recent inferences from firstprinciples calculations and laboratory experiments on analogue post-perovskite material also surmise the rheology of post-perovskite would be dominated by dislocation mechanism and be softer than perovskite. We put forth a hypothetical scenario in which the bottom portions of the superplumes in the deep mantle are stiffer than the adjacent post-perovskite mantle and are held fixed by the surrounding horizontal flow of post-perovskite.

DOI： 10.1029/174GM17

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER GEOPHYSICAL UNION  

The influences of the post-perovskite (PPV) phase transition on the thermal state in the lower mantle are studied with a three-dimensional model of mantle convection in a Cartesian domain under the extended Boussinesq approximation with variable viscosity and temperature-dependent thermal conductivity. We have varied (i) the intensity of latent heat exchange associated with the PPV transition by increasing the density change and (ii) the temperature at the core-mantle boundary (CMB) which determines the stability field of the PPV phase through the relative positioning with the phase transition temperature at the CMB. We found that the actual PPV transition hardly affects the thermal structure in the lower mantle, although it has a tendency to bend the vertical temperature profile toward the equilibrium thermodynamic conditions of the transition in extreme cases with enhanced latent heat exchange and CMB temperature lower than that of phase transition.

DOI： 10.1029/2006GL025744

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File： JES4_21Kameyama.pdf

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

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(10). (c) 2005 Elsevier Inc. All rights reserved.

DOI： 10.1016/j.jcp.2004.11.030

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Institute of Electrical and Electronics Engineers Inc.  

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.

DOI： 10.1109/SC.2004.1

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

We investigated the similarity between thermal-viscous coupling (TVC) and frictional sliding, proposed by Kameyama and Kaneda [Pure Appl. Geophys. 159 (2002) 2011]. We consider a one-dimensional layer composed of viscous material, which is sandwiched and sheared by two thick elastic layers. The rate of viscous deformation depends on the temperature T, in the viscous layer as well as shear stress T. The temperature T-c changes owing to heating by viscous dissipation and conductive cooling. We carried out velocity-stepping tests for the steady-state deformation both numerically and analytically, and compared the temporal evolution of small perturbations with that of the spring-block model with rate- and state-dependent friction (RSF). We found that, as is the case of frictional slip stability, the manner of temporal evolution is classified into four regimes depending on whether it is stable or not and whether it is monotonous or oscillatory with time. By further interpreting TVC in terms of general RSF theory by Ruina [J. Geophys. Res. 88 (1983) 10359], we obtained the relations between the parameters appearing in the phenomenological RSF law and the nondimensional parameters which characterize the nature of TVC. A further improvement of this approach might be important for estimating the actual values of frictional constitutive parameters at the deeper portion of seismogenic faults of interplate or inland earthquakes where a ductile deformation is expected to be significant. (C) 2003 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.tecto.2003.09.012

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER BASEL AG  

We propose a thermal-mechanical model of shear deformation of a viscoelastic material to describe the temperature-dependence of friction law. We consider shear deformation of one-dimensional layer composed of a Maxwell linear viscoelastic material under a constant velocity V and temperature T, at the boundary. The strain rate due to viscous deformation depends both on temperature and shear stress. The temperature inside the layer changes owing to frictional heating and conductive cooling. Steady-state calculations show that the sign of dsigma(ss)/dV, where sigma(ss) is steady-state stress, changes from positive to negative as V increases, and that the threshold velocity above which the sign of dsigma(ss)/dV is negative increases with increasing T-w. These results are in accordance with the conjecture that the downdip limit of seismogenic zones is marked by the transition in the sign of dsigma(ss)/dV due to temperature rise with depth. We also find that the response of steady state to a step change in V is quite similar to the response of frictional slip with constitutive laws which employ state variables. These findings suggest that by further improving the present model a model of constitutive relations along faults or plate boundaries can be developed which contains temperature-dependence in a physically-sound manner.

DOI： 10.1007/s00024-002-8720-0

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER GEOPHYSICAL UNION  

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.

DOI： 10.1029/2000GL012266

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Language：Japanese   Publishing type：Research paper (bulletin of university, research institution)   Publisher：東京大学  

We develop a thermal-mechanical model for describing the formation of shear zones. We consider shear deformation of a two-dimensional rectangular region composed of a viscous fluid under a constant velocity at the boundary. Viscosity of the material is assumed to depend only on temperature for simplicity. In order to enhance the shear deformation, we included a small inclusion whose viscosity differs from that of the surrounding material. We carried out time-marching simulations and monitored the evolution of temperature and strain around the inclusion. Our results show that the deformation localizes in a narrow region when sufficient heat is generated by viscous dissipation. In the zone of localized deformation, temperature increases by several hundred degrees owing to strong dissipative heating. We found that the zone of localized deformation develops in the region where the greatest heat is generated at the initial stage of evolution. The zone of localized deformation pierces the inclusion when the inclusion is weaker than the surrounding material, while it develops away from the inclusion when the inclusion is stiffer than the surrounding material. These findings, though qualitatively, suggest that heating by viscous dissipation may play an important role in the formation of decollements around subducted seamounts.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

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 (kappa&gt;(*) over bar * (T)) and viscous dissipation. Although thermal diffusivity in the shear zone is spatially heterogeneous with kappa&gt;(*) over bar * (T) and viscous heating, the spatial distribution of kappa&gt;(*) over bar * (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 kappa&gt;(*) over bar * (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. (C) 2000 Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S0012-821X(00)00239-9

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

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 Ra-b defined with viscosity at the bottom boundary up to 1.6 x 10(8) and the viscosity contrast across the box r(eta) up to 10(8). We found that there are two different series of bifurcations that take place as r(eta) 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 Ra-b. Another series of bifurcations causes changes in the aspect ratio of convection cells; convection with an elongated cell can take place at moderate r(eta) (10(3)-10(5.5) at Ra-b = 6 x 10(6)), while only convection of aspect ratio close to 1 takes place at small r(eta) and large r(eta). The parameter range of r(eta) and Ra-b 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. (C) 2000 Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S0012-821X(00)00171-0

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

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 defor mation 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. (C) 1999 Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S0012-821X(99)00040-0

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Blackwell Publishing Ltd  

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 a ≃ 100 MPa. Copyright 1997 by the American Geophysical Union.

DOI： 10.1029/97GL02648

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

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.

DOI： 10.1016/0031-9201(95)03102-2

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Language：Japanese   Publisher：日本惑星科学会  

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Language：Japanese   Publisher：可視化情報学会  

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Language：English   Publisher：SPRINGER-VERLAG BERLIN  

We have designed a new system for real-time interactive visualization of results taken directly from large-scale simulations of 3-D mantle convection and other large-scale simulations. This approach allows for intense visualization sessions for a couple of hours as opposed to storing massive amounts of data in a storage system. Our data sets consist of 3-D data for volume rendering with sets ranging as high as over 1.0 million unknowns at; each timestep. Large scale visualization on a display wall holding around 1.3 million pixels has already been accomplished with extension to hand-held devices, such as the OQO and Nokia N800. We are developing web-based software in Java, to extend the use of this system across long distances. The software is aimed at creating an interactive and functional application capable of running on multiple browsers by taking advantage of two AJAX-enabled web frameworks: Echo2 and Google Web Toolkit.

DOI： 10.1007/978-3-540-89646-3_101

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Language：English   Publisher：Institute of Electrical and Electronics Engineers Inc.  

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.

DOI： 10.1109/SC.2004.1

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Language：Japanese   Publisher：The Japanese Society for Planetary Sciences  

The viscosity of the mantle is the strongly dependence of the temperature. We simulate the thermal convection with temperature dependent viscosity in the cylindrical polar coordiate. The model is considered basal-heating and time-dependent convection model of the Boussinesq approximation, infinite Prandtl number and Newtonian fluid. The viscosity of modelled mantle is the function of exponential to the temperature. The ratio across inner and outer boundary is used 0.5. The Rayleigh number is used 6×10^6. The viscosity contrast is used up to 10^5. The result of our calculation is similar to 2D box model: we find three styles of convection, which is Whole layer mode, Sluggish lid mode and Stagnant lid mode. Appearance of the Stagnant lid mode, cylindical annulus case is lower viscosity contrast compared with 2D box model. In this presentation, we discuss about temperature dependence of viscosity required the numerical modelling of mantle convection with geometry and dynamics of the lithosphere based on our simulation result.

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Language：Japanese   Publisher：The Japanese Society for Planetary Sciences  

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The viscosity of the mantle is the strongly dependence of the temperature. We simulate the thermal convection with temperature dependent viscosity in the cylindrical polar coordiate. The model is considered basal-heating and time-dependent convection model of the Boussinesq approximation, infinite Prandtl number and Newtonian fluid. The viscosity of modelled mantle is the function of exponential to the temperature. The ratio across inner and outer boundary is used 0.5. The Rayleigh number is used 6×10^6. The viscosity contrast is used up to 10^5. The result of our calculation is similar to 2D box model: we find three styles of convection, which is Whole layer mode, Sluggish lid mode and Stagnant lid mode. Appearance of the Stagnant lid mode, cylindical annulus case is lower viscosity contrast compared with 2D box model. In this presentation, we discuss about temperature dependence of viscosity required the numerical modelling of mantle convection with geometry and dynamics of the lithosphere based on our simulation result.

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Language：Japanese  

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Language：Japanese  

researchmap

Language：Japanese  

researchmap

Language：Japanese  

researchmap

Language：Japanese  

researchmap

Language：Japanese  

researchmap

Language：Japanese  

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Language：English   Presentation type：Oral presentation (general)  

Venue：幕張メッセ(千葉県千葉市美浜区)  

researchmap

Language：Japanese  

researchmap

Language：English   Presentation type：Oral presentation (general)  

Venue：幕張メッセ(千葉県千葉市美浜区)  

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Language：Japanese   Presentation type：Oral presentation (invited, special)  

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Language：Japanese   Presentation type：Oral presentation (general)  

Venue：幕張メッセ(千葉県千葉市美浜区)  

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Language：Japanese   Presentation type：Poster presentation  

Venue：幕張メッセ(千葉県千葉市美浜区)  

researchmap

Language：Japanese   Presentation type：Oral presentation (general)  

researchmap

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：幕張メッセ(千葉県千葉市美浜区)  

researchmap