Mantle rheology: radial and lateral viscosity variations inferred from microphysical creep laws

Inferences on the rheology of the mantle based on theoretical and experimental rate equations for steady state creep are discussed and compared with results from geophysical models. The radial increase of viscosity by one to three orders of magnitude across the mantle, required by inversion of postglacial rebound and geodynamic data, is confirmed by microphysical models based on the estimation of continuous and discontinuous changes of creep parameters with depth. The upper mantle (viscosity 10²⁰–10²¹ Pa s) is likely to show non-Newtonian rheology (power-law creep) for average grain sizes larger than 0.1 mm as an order of magnitude. Given the variability of both grain size and stress conditions, local regions of linear rheology can be present. The rheology of transition zone and lower mantle (viscosity 10²²–10²⁴ Pa s) cannot be definitely resolved at present. Estimation of creep parameters leads to possible nonlinear or mixed rheology, if grain sizes are not lower than 0.1 mm and flow conditions can be approximated by a constant strain rate of about 10⁻¹⁵ s⁻¹. This conclusion can be modified by different flow conditions (e.g. a decrease in strain rate or constant viscous dissipation). Furthermore, experiments on fine-grained garnetites and perovskite analogues have shown that diffusion creep is predominant at laboratory conditions. However, the pressure dependence of creep in these phases is unknown, and therefore direct extrapolation to lower mantle conditions is necessarily speculative. Lateral variations of viscosity, largest in the upper and lowermost mantle (up to 2–4 orders of magnitude) are predicted by models based on lateral temperature anomalies derived from seismic tomographic models.     

One-dimensional modelling of mantle flow

A one-dimensional model of flow between a fixed boundary at the bottom and a moving one on top with no net flow through vertical sections is tested for geophysically interesting mantle viscosity-depth functions. Such a model, although simplistic, may help in answering the question to what depth the return flow extends, at least in the case of moving plates measuring many thousand kilometers across, such as the Pacific plate.It the viscosity in the asthenosphere is less than three orders of magnitude smaller than that of the mantle below, the return flow extends to great depth and the asthenosphere is a zone of concentrated shear. If the viscosity contrast is greater, the return flow is concentrated in the asthenosphere. For a wide range of model parameters typical flow velocities below the asthenosphere are about one-tenth of the plate velocity. The pressure gradient required by the mantle flow may be manifest in gravity trends across moving plates, but no excessive gravity anomalies are required by the model if the absolute viscosity values conform to those inferred from post-glacial rebound data. A thinner and lower-viscosity layer is favored over a thicker and more viscous layer if both fit glacial rebound evidence. The present model may not be applicable if down to the core the viscosity is as low as about 10²¹ N s m^–2 with a free-slip bottom boundary.     

On the interaction between small- and large-scale convection and postglacial rebound flow in a power-law mantle

Some consequences arising from the superposition of flows of two different kinds or scales in a non-Newtonian mantle are discussed and applied to the cases mantle convection plus postglacial rebound flow as well as small- plus large-scale mantle convection. If the two flow types have similar magnitude, the apparent rheology of both flows becomes anisotropic and the apparent viscosity for one flow depends on the geometry of the other. If one flow has a magnitude significantly larger than the other, the apparent viscosity for the weak flow is linear but develops direction-dependent variations about a factorn (n being the power exponent of the rheology). For the rebound flow lateral variations of the apparent viscosity about at least 3 are predicted and changes in the flow geometry and relaxation time are possible. On the other hand, rebound flow may weaken the apparent viscosity for convection. Secondary convection under moving plates may be influenced by the apparent anisotropic rheology. Other mechanisms leading to viscous anisotropy during shearing may increase this effect. A linear stability analysis for the onset of convection with anisotropic linear rheology shows that the critical Rayleigh number decreases and the aspect ratio of the movement cells increases for decreasing horizontal shear viscosity (normal viscosity held constant). Applied to the mantle, this model weakens the preference of convection rolls along the direction of plate motion. Under slowly moving plates, rolls perpendicular to the plate motion seem to have a slight preference. These results could be useful for resolving the question of Newtonian versus non-Newtonian or isotropic versus anisotropic mantle rheology.     

Small-scale convection under the back-arc occurring in the low viscosity wedge

Water released from subducting slabs through a dehydration reaction may lower the viscosity of the mantle significantly. Thus, we may expect a low viscosity wedge (LVW) above the subducting slabs. The LVW coupled with a large-scale flow induced by the subducting slabs may allow the existence of roll-like small-scale convection whose axis is normal to the strike of the plate boundary. Such a roll structure may explain the origin of along-arc variations of mantle temperature proposed recently in northeast Japan. We study this possibility using both 2D and 3D models with/without pressure- and temperature-dependent viscosity. 2D models without pressure and temperature dependence of viscosity show that, with a reasonable geometry of the LVW and subduction speed, small-scale convection is likely to occur when the viscosity of the LVW is less than 10¹⁹ Pa s. Corresponding 3D model studies reveal that the wavelength of rolls depends on the depth of the LVW. The inclusion of temperature-dependent viscosity requires the existence of further low viscosity in the LVW, since temperature dependence suppresses the instability of the cold thermal boundary layer. Pressure (i.e. depth) dependence coupled with temperature dependence of the viscosity promotes short wavelength instabilities. The model, which shows a relatively moderate viscosity decrease in the LVW (most of the LVW viscosity is 10¹⁸∼10¹⁹ Pa s) and a wavelength of roll ∼80 km, has a rather small activation energy and volume (∼130 kJ/mol and ∼4 cm³/mol) of the viscosity. This small activation energy and volume may be possible, if we regard them as an effective viscosity of non-linear rheology.     

Viscosity distribution in the mantle convection models

Viscosity is a fundamental property of the mantle which determines the global geodynamical processes. According to the microscopic theory of defects and laboratory experiments, viscosity exponentially depends on temperature and pressure, with activation energy and activation volume being the parameters. The existing laboratory measurements are conducted with much higher strain rates than in the mantle and have significant uncertainty. The data on postglacial rebound only allow the depth distributions of viscosity to be reconstructed. Therefore, spatial distributions (along the depth and lateral) are as of now determined from the models of mantle convection which are calculated by the numerical solution of the convection equations, together with the viscosity dependences on pressure and temperature (PT-dependences). The PT-dependences of viscosity which are presently used in the numerical modeling of convection give a large scatter in the estimates for the lower mantle, which reaches several orders of magnitude. In this paper, it is shown that it is possible to achieve agreement between the calculated depth distributions of viscosity throughout the entire mantle and the postglacial rebound data. For this purpose, the values of the volume and energy of activation for the upper mantle can be taken from the laboratory experiments, and for the lower mantle, the activation volume should be reduced twice at the 660-km phase transition boundary. Next, the reduction in viscosity by an order of magnitude revealed at the depths below 2000 km by the postglacial rebound data can be accounted for by the presence of heavy hot material at the mantle bottom in the LLSVP zones. The models of viscosity spatial distribution throughout the entire mantle with the lithospheric plates are presented.     

Convective instabilities in a variable viscosity fluid cooled from above

Whether in the mantle or in magma chambers, convective flows are characterized by large variations of viscosity. We study the influence of the viscosity structure on the development of convective instabilities in a viscous fluid which is cooled from above. The upper and lower boundaries of the fluid are stress-free. A viscosity dependence with depth of the form ν₀ + ν₁ exp(?γ.z) is assumed. After the temperature of the top boundary is lowered, velocity and temperature perturbations are followed numerically until convective breakdown occurs. Viscosity contrasts of up to 10⁷ and Rayleigh numbers of up to 10⁸ are studied.For intermediate viscosity contrasts (around 10³), convective breakdown is characterized by the almost simultaneous appearance of two modes of instability. One involves the whole fluid layer, has a large horizontal wavelength (several times the layer depth) and exhibits plate-like behaviour. The other mode has a much smaller wavelength and develops below a rigid lid. The “whole layer” mode dominates for small viscosity contrasts but is suppressed by viscous dissipation at large viscosity contrasts.For the “rigid lid” mode, we emphasize that it is the form of the viscosity variation which determines the instability. For steep viscosity profiles, convective flow does not penetrate deeply in the viscous region and only weak convection develops. We propose a simple method to define the rigid lid thickness. We are thus able to compute the true depth extent and the effective driving temperature difference of convective flow. Because viscosity contrasts in the convecting region do not exceed 100, simple scaling arguments are sufficient to describe the instability. The critical wavelength is proportional to the thickness of the thermal boundary layer below the rigid lid. Convection occurs when a Rayleigh number defined locally exceeds a critical value of 160–200. Finally, we show that a local Rayleigh number can be computed at any depth in the fluid and that convection develops below depth z_r (the rigid lid thickness) such that this number is maximum.The simple similarity laws are applied to the upper mantle beneath oceans and yield estimates of 5 × 10¹⁵?5 × 10¹⁶ m² s^?1 for viscosity in the thermal boundary layer below the plate.     

Thermal histories of the core and mantle

Recognition that the cooling of the core is accomplished by conduction of heat into a thermal boundary layer (D″) at the base of the mantle, partly decouples calculations of the thermal histories of the core and mantle. Both are controlled by the temperature-dependent rheology of the mantle, but in different ways. Thermal parameters of the Earth are more tightly constrained than hitherto by demanding that they satisfy both core and mantle histories. We require evolution from an early state, in which the temperatures of the top of the core and the base of the mantle were both very close to the mantle solidus, to the present state in which a temperature increment, estimated to be ～ 800 K, has developed across D″. The thermal history is not very dependent upon the assumption of Newtonian or non-Newtonian mantle rheology. The thermal boundary layer at the base of the mantle (i.e., D″) developed within the first few hundred million years and the temperature increment across it is still increasing slowly. In our preferred model the present temperature at the top of the core is 3800 K and the mantle temperature, extrapolated to the core boundary without the thermal boundary layer, is 3000 K. The mantle solidus is 3860 K. These temperatures could be varied within quite wide limits without seriously affecting our conclusions. Core gravitational energy release is found to have been remarkably constant at ～ 3 × 10¹¹ W. nearly 20% of the core heat flux, for the past 3 × 10⁹ y, although the total terrestrial heat flux has decreased by a factor of 2 or 3 in that time. This gravitational energy can power the “chemical” dynamo in spite of a core heat flux that is less than that required by conduction down an adiabatic gradient in the outer core; part of the gravitational energy is used to redistribute the excess heat back into the core, leaving 1.8 × 10¹¹ W to drive the dynamo. At no time was the dynamo thermally driven and the present radioactive heating in the core is negligibly small. The dynamo can persist indefinitely into the future; available power 10¹⁰ y from now is estimated to be 0.3 × 10¹¹ W if linear mantle rheology is assumed or more if mantle rheology is non-linear. The assumption that the gravitational constant decreases with time imposes an implausible rate of decrease in dynamo energy. With conventional thermodynamics it also requires radiogenic heating of the mantle considerably in excess of the likely content of radioactive elements.     

Lower mantle dynamics with the post-perovskite phase change, radiative thermal conductivity, temperature- and depth-dependent viscosity

The new post-perovskite phase near the core-mantle boundary has important ramifications on lower mantle dynamics. We have investigated the dynamical impact arising from the interaction of temperature- and depth-dependent viscosity with radiative thermal conductivity, up to a lateral viscosity contrast of 10⁴, on both the ascending and descending flows in the presence of both the endothermic phase change at 670 km depth and an exothermic post-perovskite transition at 2650 km depth. The phase boundaries are approximated as localized zones. We have employed a two-dimensional Cartesian model, using a box with an aspect-ratio of 10, within the framework of the extended Boussinesq approximation. Our results for temperature- and depth-dependent viscosity corroborate the previous results for depth-dependent viscosity in that a sufficiently strong radiative thermal conductivity plays an important role for sustaining superplumes in the lower mantle, once the post-perovskite phase change is brought into play. This aspect is especially emphasized, when the radiative thermal conductivity is restricted only to the post-perovskite phase. These results revealed a greater degree of asymmetry is produced in the vertical flow structures of the mantle by the phase transitions. Mass and heat transfer between the upper and lower mantle will deviate substantially from the traditional whole-mantle convection model. Streamlines revealed that an overall complete communication between the top and lower mantle is difficult to be achieved.     

Critical phenomena in thermal conductivity: Implications for lower mantle dynamics

Microscopic mechanisms for heat transport in dense minerals (phonon scattering and photon attenuation) exhibit aspects of threshold behavior, discussed qualitatively here. For all minerals examined so-far using laser-flash analysis, the lattice component of the thermal conductivity of the mantle asymptotes to a constant above a critical temperature of ∼1500 K. Radiative transfer calculated from absorption spectra has thresholds in both grain-size and Fe content, and a rather complex dependence on temperature. These critical phenomena impact convection of the lower mantle, because the lattice contribution tends to destabilize the cold boundary layers, whereas radiative transfer mostly promotes stability in the lower mantle, unless the grains are large and Fe-rich, which makes convection chaotic and time-dependent. The specific behavior suggests that flow in the lower mantle is sluggish, whereas flow in the upper mantle-transition zone is time-dependent. The decrease in k_rad as Fe/(Fe + Mg) increases beyond ∼0.1 may be connected with formation of lower mantle, thermo-chemical plumes through positive feedback.     

Large aspect ratio cells in two-dimensional thermal convection

Numerical experiments have been carried out on two-dimensional thermal convection, in a Boussinesq fluid with infinite Prandtl number, at high Rayleigh numbers. With stress free boundary conditions and fixed heat flux on upper and lower boundaries, convection cells develop with aspect ratios (width/depth) λ? 5, if heat is supplied either entirely from within or entirely from below the fluid layer. The preferred aspect ratio is affected by the lateral boundary conditions. If the temperature, rather than the heat flux, is fixed on the upper boundary the cells haveλ ≈ 1. At Rayleigh numbers of 2.4 × 10⁵ and greater, small sinking sheets are superimposed on the large aspect ratio cells, though they do not disrupt the circulation. Similar two-scale flows have been proposed for convection in the earth's mantle. The existence of two scales of flow in two-dimensional numerical experiments when the viscosity is constant will allow a variety of geophysically important effects to be investigated.     

Rheology of the mantle and tectonics of the oceanic lithospheric plates

The modern concepts of the rheology of viscous mantle and brittle lithosphere, as well as the results of the numerical experiments on the processes in a heated layer with a viscosity dependent on pressure, temperature, and shear stress, are reviewed. These dependences are inferred from the laboratory studies of olivine and measurements of postglacial rebound (glacial isostatic adjustment) and geoid anomalies. The numerical solution of classical conservation equations for mass, heat, and momentum shows that thermal convection with a highly viscous rigid lithosphere develops in the layer with the parameters of the mantle with the considered rheology under a temperature difference of 3500 K, without any special additional conditions due to the self-organization of the material. If the viscosity parameters of the lithosphere correspond to dry olivine, the lithosphere remains monolithic (unbroken). At a lower strength (probably due to the effects of water), the lithosphere splits into a set of separate rigid plates divided by the ridges and subduction zones. The plates submerge into the mantle, and their material is involved in the convective circulation. The results of the numerical experiment may serve as direct empirical evidence to validate the basic concepts of the theory of plate tectonics; these experiments also reveal some new features of the mantle convection. The probable structure of the flows in the upper and lower mantle (including the asthenosphere), which shows the primary role of the lithospheric plates, is demonstrated for the first time.     

全球地表热流的产生与分布

全球地表热流是反映地球内部热与动力学过程的一种主要能流.本文在三维球坐标框架下，就几个不同的粘度模型分别研究地幔内部密度异常(基于全球地震层析结果)以及板块运动激发的地幔流动的热效应及其对于观测地表热流产生和分布特征的贡献.由于地幔动力系统具有较高的Pe数，可以期望由板块运动激发的地幔流动将强烈地扰动地幔内部初始传导状态下的温度场以及地表热的热流分布.结果表明，与地幔内部密度异常产生的热效应相比，运动的板块及其激发的地幔流动在全球地表观测热流的产生和分布特征上起着更为重要的作用.观测到的大洋中脊处的高热流在很大程度上可以归因于板块激发的地幔流动的热效应.计算的平均温度剖面较好地揭示了岩石圈和D″层的温度特征，即温度随深度的剧烈变化，这与我们目前通过其他手段对岩石圈和D″层的温度结构了解是一致的.一个下地幔粘度比上地幔高出30倍的粘度结构(文中使用的粘度模型2)较之其余模型的拟合程度似乎更好.     

Rheology of the lower crust beneath the northern part of North China: Inferences from lower crustal xenoliths from Hannuoba basalts, Hebei Province, China

Lower crustal xenoliths brought up rapidly by basaltic magma onto the earth surface may provide di-rect information on the lower crust. The main purpose of this research is to gain an insight into the rheology of the lower crust through the detailed study of lower crustal xenoliths collected from the Hannuoba basalt, North China. The lower crustal xenoliths in this area consist mainly of two pyroxene granulite, garnet granulite, and light-colored granulite, with a few exception of felsic granulite. The equilibration temperature and pressure of these xenoliths are estimated by using geothermometers and geobarometers suitable for lower crustal xenoliths. The obtained results show that the equilibration temperature of these xenoliths is within the range of 785―900℃, and the equilibrium pressure is within the range of 0.8―1.2 GPa, corresponding to a depth range of 28―42 km. These results have been used to modify the previously constructed lower crust-upper mantle geotherm for the studied area. The dif-ferential stress during the deformation process of the lower crustal xenoliths is estimated by using recrystallized grain-size paleo-piezometer to be in the range of 14―20 MPa. Comparing the available steady state flow laws for lower crustal rocks, it is confirmed that the flow law proposed by Wilks et al. in 1990 is applicable to the lower crustal xenoliths studied in this paper. The strain rate of the lower crust estimated by using this flow law is within the range of 10-13―10-11 s-1, higher than the strain rate of the upper mantle estimated previously for the studied area (10-17―10-13 s-1); the equivalent viscosity is estimated to be within the range of 1017―1019Pa·s, lower than that of the upper mantle (1019―1021 Pa·s). The constructed rheological profiles of the lower crust indicate that the differential stress shows no significant linear relation with depth, while the strain rate increases with depth and equivalent vis-cosity decrease with depth. The results support the viewpoint of weak lower continental crust.     

Heat flow and depth versus age for the Mesozoic northwest Atlantic Ocean: results from the Sohm abyssal plain and implications for the Bermuda Rise

Heat flow in the Sohm abyssal plain is measured to be 53 mW/m² at an age of 163 Ma. This is 25% higher than predicted by conductive cooling models, even though the sediment-corrected basement depth of 6.5 km at this location is normal for its age. An analysis of existing heat flow, depth and geoid anomalies in the northwest Atlantic shows that there is little correlation between heat flow and depth throughout the entire region. Depth and geoid are clearly related to the Bermuda swell while the associated heat flow anomaly, once adjusted for variations with age, is limited to 5 mW/m² and only decays to the south. This means that the Bermuda swell is probably not caused by extensive thermal reheating within the lithosphere, but instead by dynamic uplift at its lower boundary due to the convective upwelling of a mantle plume. The regionally high heat flow in the northwest Atlantic may be a thermal remanent of previous plumes which passed beneath this region early in its history. Therefore, depth and heat flow anomalies from this region cannot be used to provide constraints on steady-state parameters of the lithosphere, such as the presence or absence of a long-term boundary layer at its base.     

Tectonic stress controls on ascent and emplacement of magmas

The tectonic stresses can significantly affect the propagation of a magma-filled crack. It has been pointed out that the rheological boundaries control the emplacement of magmas through the effect of stress. However, it has not been clarified how the role of rheological boundaries depends on the regional tectonic and thermal states. We have evaluated the role of rheological boundaries under various tectonic and thermal conditions and found that the level of magma emplacement may jump according to the changes in the tectonic force or the surface heat flow. The stress profiles were estimated by a simple model of lithospheric deformation. We employed a three-layer model of the lithosphere; the upper crust, the lower crust and the upper mantle have different rheological properties. A constant horizontal force is applied to the lithosphere, and the horizontal strain is assumed to be independent of depth. When realistic tectonic forces (>10¹¹ N/m) are applied, the rheological boundaries mainly control the emplacement of magma. The emplacement is expected at the MOHO, the upper–lower crust boundary, and the brittle–ductile boundary. For lower tectonic forces (<10¹¹ N/m), the tectonic stress no longer plays an important role in the emplacement of magmas. When the tectonic stress controls the emplacement, the roles of rheological boundaries strongly depend on the surface heat flow. When the surface heat flow is relatively high (>80 mW/m²), the stress in the mantle is quite low and the MOHO cannot trap ascending magmas. For relatively low heat flow (<80 mW/m²), on the other hand, the MOHO acts as a magma trap, and the upper–lower crust boundary acts as a magma trap only when the magma supply rate is sufficiently high. Our results suggest that the emplacement depth can change responding to the change in the tectonic force and/or that in the surface heat flow. This may provide us a key to understand the relation between the evolution of a volcanic region and its tectonic and/or thermal history.     

Study on the rheology of subducting slabs

We calculate thermal and phase structures of subducting slabs for different subducting velocities by a modified coupling code of the kinetic phase-transformation equations and the heat-diffusion equation with latent-heat release. Whereafter, we estimate their rheology structures based on the thermal and phase structures from the mineral physical point of view. At shallow depth, the upper layer has a high effective viscosity greater than 10³⁴Pa · s; while the lower layer has a relatively low effective viscosity, which is greater than 10²⁶Pa · s nevertheless. The effective viscosities below the kinetic phase boundary of olivine to wadsleyite decrease obviously, and reach a minimum of 10²²Pa · s. Small areas with higher effective viscosities exist above the depth of about 700 km in subducting slabs, which are produced by lower temperatures that are related with endothermic phase transformation of spinel to perovskite and magnesiowustite. The 1% and 99% isograds of spinel proportion delineate tortuous belts with low effective viscosities, which would affect the geodynamic behavior of subducting slabs.     

The dynamical and thermal structure of deep mantle plumes

If the interpretation of the D″ layer at the base of the mantle as a thermal boundary layer, with a temperature increment in the order of 800 K, is correct, then the formation of deep-mantle plumes to vent material from it appears inevitable. We demonstrate quantitatively that the strong temperature dependence of viscosity guides the upward flow into long-lived chimneys that are ～ 20 km in diameter near the base of the mantle and decrease in width with progressive upward softening and partial melting of plume material. The speed of flow up the axis of the plume is correspondingly fast; 1.6 m y^?1 at the base and 4.8 m y^?1 at 670 km depth. Thermal diffusive spreading of a heated plume is compensated by a slow horizontal convergence of mantle material toward the chimney in response to the lower pressure there. This convergence, which contributes only a small increment to the flux of material up the plume, also serves to throttle the flow in the chimney. The global plume mass flux necessary to transport 1.6 × 10¹² W of core heat upward through the mantle is 1.8 × 10⁶ kg s^?1. At its base, plume material is probably still significantly below its solidus or eutectic temperature, but substantial partial melting is very likely as it rises. We speculate that a small fraction of this fluid component eventually emerges at the surface in “hot spots”, with the fate of the remainder being unknown. The behaviour and properties of D″ and of plumes are closely coupled. Not only are plumes a necessary consequence of a thermal boundary layer, but their existence is impossible without that layer.     

Critical phenomena in thermal conductivity: Implications for lower mantle dynamics

Microscopic mechanisms for heat transport in dense minerals (phonon scattering and photon attenuation) exhibit aspects of threshold behavior, discussed qualitatively here. For all minerals examined so-far using laser-flash analysis, the lattice component of the thermal conductivity of the mantle asymptotes to a constant above a critical temperature of 1500 K. Radiative transfer calculated from absorption spectra has thresholds in both grain-size and Fe content, and a rather complex dependence on temperature. These critical phenomena impact convection of the lower mantle, because the lattice contribution tends to destabilize the cold boundary layers, whereas radiative transfer mostly promotes stability in the lower mantle, unless the grains are large and Fe-rich, which makes convection chaotic and time-dependent. The specific behavior suggests that flow in the lower mantle is sluggish, whereas flow in the upper mantle-transition zone is time-dependent. The decrease in k_rad as Fe/(Fe + Mg) increases beyond 0.1 may be connected with formation of lower mantle, thermo-chemical plumes through positive feedback.     

Thermal Structure of the Ionian Slab

We propose a thermal model of the subducting Ionian microplate. The slab sinks in an isothermal mantle, and for the boundary conditions we take into account the relation between the maximum depth of seismicity and the thermal parameter L_th of the slab, which is a product of the age of the subducted lithosphere and the vertical component of the convergence rate. The surface heat-flux dataset of the Ionian Sea is reviewed, and a convective geotherm is calculated in its undeformed part for a surface heat flux of 42 mW m^–2, an adiabatic gradient of 0.6 mK m^–1, a mantle kinematic viscosity of 10¹⁷ m² s^–1 and an asthenosphere potential temperature of 1300°C. The calculated temperature-depth distribution compared to the mantle melting temperature indicates the decoupling limit between lithosphere and asthenosphere occurs at a depth of 105 km and a temperature of 1260°C. A 70–km thick mechanical boundary layer is found. By considering that the maximum depth of the seismic events within the slab is 600 km, a L_th of 4725 km is inferred. For a subduction rate equal to the spreading rate, the corresponding assimilation and cooling times of the microplate are about 7 and 90 Myr, respectively. The thermal model assumes that the mantle flow above the slab is parallel and equal to the subducting plate velocity of 6 cm yr^–1, and ignores the heat conduction down the slab dip. The critical temperature, above which the subduced lithosphere cannot sustain the stress necessary to produce seismicity, is determined from the thermal conditions governing the rheology of the plate. The minimum potential temperature at the depth of the deepest earthquake in the slab is 730°C.     

Post-glacial rebound and present-day three-dimensional deformations

The WEGENER^† activities related to the study of post-glacial rebound are presented together with a review of the present state-of-the-art in this study field. Post-glacial rebound research is an unique tool for studying the viscoelastic behaviour of the Earth's mantle on time scales of thousands of years. The viscosity structure of the Earth's mantle determined from an inversion of observations of glacially induced deformations is a basic requirement for modelling long-term phenomena such as the convection in the Earth's mantle, and for better understanding unsolved questions such as the nature of the mantle discontinuities or the vertical scale of convection.First, an introduction to the scientific background is given, and the three principal ingredients for post-glacial rebound studies, namely the ice model, the Earth model, and the observations are briefly considered. For the ice model, the uncertainties due to a trade-off between ice model and Earth rheology are outlined. The different approaches used to model the Earth and its deformations in post-glacial rebound studies are discussed emphasising the preliminary nature of the derived rheologies and depth dependencies. The observations, in particular the relative sea-level changes and three-dimensional surface deformations, are described with special emphasis on observational gaps. Based on the discussion of the ingredients, an outline of the future developments in post-glacial rebound research is attempted with particular emphasis on the Earth model and the theory of deformations.For several decades extreme efforts have been made to precisely monitor the land uplift in Scandinavia. However, for the height component the existing data still are associated with large uncertainties while reliable data on the horizontal component are practically nil. The ongoing long-term (longer than ten years) spacegeodetic measurements are likely to provide the three-dimensional deformations with the spatial resolution and accuracy required in order to substantially contribute to post-glacial rebound studies. Thus, present-day three-dimensional deformations of the Earth's surface beneath and around the former ice sheets as a constraint for the mantle rheology and viscosity structure will increasingly become important as they become known from space-geodetic measurements with high spatial resolution and an accuracy approaching the mm/a-level.