地幔的蠕变性质

地幔的蠕变特性是地球物理学中一个普遍关心的问题。本文以地球模型和地球热模型为基础,结合理论导出的蠕变方程和岩石蠕变实验的结果,考虑到温度、压力、晶粒直径及相变过程对地幔流变特性的影响,计算了整个地幔的蠕变性质和等效粘滞性。 结果表明,当晶粒直径d≤1毫米时,扩散蠕变是主要的,地幔行为与牛顿流体相似。当d≥10毫米时,幂函数蠕变成为主要的形变机制,地幔呈非牛顿粘滞性。从得出的结果来看,并不存在高粘的下地幔。     

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.     

Convection in a variable-viscosity fluid: Newtonian versus power-law rheology

A number of finite-element calculations of convection in a variable-viscosity fluid have been carried out to investigate the effects of non-Newtonian flow when rheology is also subject to a strong temperature and pressure influence. A variety of cases has been studied in the range of effective Rayleigh numbers between 10⁴ and 10⁶, including different modes of heating and a range of values for activation energy and activation volume. Power-law creep with a stress exponent of 3 turns out to lead to considerably different flow pattern and heat transfer properties than Newtonian rheology. In general, the effect is to reduce viscosity contrasts imposed by p,T dependence, which can lead in some circumstances to the mobilisation of otherwise stagnant regions within the cell. The properties of non-Newtonian flow can be closely imitated by a Newtonian fluid with a reduced value of the activation enthalpy bH^* with b?0.3–0.5. It appears possible that non-Newtonian rheology plays a key role in determining the convective style in a planetary mantle.     

Viscosity and conductivity of the lower mantle; an experimental study on a MgSiO3 perovskite analogue,KZnF3

We have investigated the high-temperature rheological and electrical behaviour of single-crystal KZnF₃ fluoperovskite, an analogue of the MgSiO₃ perovskite in the lower mantle.The crystals flow by Newtonian dislocation creep (Harper-Dorn creep), predominantly on {100} planes. Below the melting point, solid-electrolyte behaviour appears, accompanied by a weakening of the mechanical properties. Geophysical implications are examined: the lower mantle can convect by Newtonian dislocation creep and an asthenosphere may exist at the bottom of the mantle. Electromagnetic interactions between the core and solid-electrolyte lower mantle may also be important.     

Evidence for low viscosity garnet-rich layers in the upper mantle

The rheological properties of upper mantle rocks play an important role in controlling the dynamics of the lithosphere and mantle convection. Experimental studies and microstructures in naturally deformed mantle rocks usually imply that olivine controls the upper mantle rheology. Here we show for the first time evidence from the geometry of folded compositional layers in mantle rocks from Western Norway that garnet-rich rocks can have lower solid-state viscosities than olivine-rich rocks. Modeling of melt-free and dry rheology of garnet and olivine confirms that the reversed viscosity contrast between garnet-rich and olivine-rich layers for this folding event can be achieved over a relatively wide range of temperatures at low stress conditions when the fine-grained garnet deforms by diffusion creep while the coarse-grained olivine deforms by dislocation creep and/or diffusion creep.In general, modeling of the fold viscosity contrast shows that in the stable subcontinental lithospheric mantle or convecting mantle such a reversed viscosity contrast can be formed due to diffusion creep processes in fine-grained garnets in a dry mantle environment or at conditions where the garnet-pyroxene layer is partially molten, i.e. close to solidus–liquidus conditions in the upper mantle. Alternatively in cold plate tectonic settings, e.g. in subduction zones, some water-weakening is a feasible mechanism to create the reversed viscosity contrast between garnet and olivine.     

Transient creep of the lithosphere and its role in geodynamics

Laboratory experiments with samples of rocks show that at small strains there is transient creep, at which the strain grows with time, and the strain rate decreases. Plate tectonics allows only small strains in the lithospheric plates, so that the lithosphere creep is transient. In geodynamics, the lithosphere is regarded as a cold boundary layer formed by mantle convection. If we assume that the lithosphere has a steady-state creep, which is described by power-law non-Newtonian rheological model, the low effective viscosity of the lower layers of the lithosphere, obtained by data on small-scale postglacial flows, is possible only at high strain rates in these layers. However, the high strain rates in the lithosphere induce large strains that contradict plate tectonics. Transient creep of the lithosphere leads to its mobility at small strains, removing the discrepancy between thermal convection in the mantle and plate tectonics, which holds in the case of power-law rheological model of the lithosphere.     

Rheology of the lower mantle

The rheology of the lower mantle of the Earth is examined from the viewpoint of solid state physics. Recent developments in high-pressure research suggest that the lower mantle contains a considerable amount of (Mg, Fe)O with Fe/Mg + Fe = 0.2–0.3. The pressure and temperature dependences of diffusion in (Mg, Fe)O are estimated by the theory of diffusion in ionic solids. Of the materials composing the lower mantle, (Mg, Fe)O may be the “softest”, and therefore the rheology of the lower mantle may be that of (Mg, Fe)O, unless the framework effect is important.Temperatures in the lower mantle are inferred from the depths of phase transitions and the melting temperatures of the core materials. A thermal boundary layer at the base of the mantle is suggested. The physical mechanisms of creep are examined based on a grain size-stress relation and non-Newtonian flow is shown to be the dominant flow mechanism in the Earth's mantle.The effective viscosity for the temperature models, with and without the thermal boundary layer, is calculated for constant stress and constant strain rate (with depth). For constant strain rate, which may be appropriate for discussing the mechanics of descending slabs, the increase in effective viscosity with depth is smaller than for the constant-stress case, which may be appropriate for discussing the flow induced by the surface motion of plates.The relatively small depth gradient of viscosity, for constant strain rate, suggests that the lower mantle could also participate in convection. The effective viscosity increases with depth, however, by at least 10² to 10³ from the top to the bottom of the lower mantle, for a reasonable range of activation volumes and temperatures. There will be a low-viscosity layer at the base of the mantle, in contrast to the high-viscosity layer at the top of the mantle (plates), if a thermal boundary layer is present. The constant Newtonian viscosity inferred from rebound data may be an apparent feature resulting from the difference in deformation mechanisms between isostatic rebound and large-scale flow.     

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.     

地幔对流的数值模拟及其与表面观测的关系

本文从基本的热对流方程出发,并结合地幔对流特点,特别考虑到自重及非线性影响,探讨地幔对流及其与表面观测的关系,发展了相应的数值方法.结果表明,计算得到的长波大地水准面、地表地形、板块速度场水平散度与观测值符合程度较好.上、下地幔的非绝热温度异常与由地震层析得到的地震波速异常显示一定的相关性.地幔内部的流动呈现复杂形态,反映了高瑞利数对流的特征.     

Attenuation of seismic waves and the universal rheological model of the Earth’s mantle

Analysis of results of laboratory studies on creep of mantle rocks, data on seismic wave attenuation in the mantle, and rheological micromechanisms shows that the universal, i.e., relevant to all time scales, rheological model of the mantle can be represented as four rheological elements connected in series. These elements account for elasticity, diffusion rheology, high temperature dislocation rheology, and low temperature dislocation rheology. The diffusion rheology element is described in terms of a Newtonian viscous fluid. The high temperature dislocation rheology element is described by the rheological model previously proposed by the author. This model is a combination of a power-law non-Newtonian fluid model for stationary flows and the linear hereditary Andrade model for flows associated with small strains. The low temperature dislocation rheology element is described by the linear hereditary Lomnitz model.     

Continental growth and volatile exchange during Earth''s evolution

We investigate the thermal and degassing history of the Earth with the help of a parameterized mantle convection model including the volatile exchange between mantle and surface reservoirs. The weakening of mantle silicates by dissolved volatiles is described by a functional relationship between creep rate and water fugacity. We use flow law parameters of diffusion creep in olivine under dry and wet conditions. The mantle degassing rate is considered as directly proportional to the seafloor spreading rate, which is also dependent on the mantle heat flow and the continental area. To calculate the spreading rate, we assume three different continental growth models: constant growth, delayed growth, and the one proposed by Reymer and Schubert (1984, Tectonics, 3: 63–77). The rate of regassing also depends on the seafloor spreading rate, as well as on other factors. Both mechanisms (degassing and regassing) are coupled self-consistently with the help of a parameterized convection model under implementation of a temperature and volatile-content dependent mantle viscosity. We calculate time series for the Earth's evolution over 4.6 Gyr for the average mantle temperature, the mantle heat flow, the mantle viscosity, the Rayleigh number, the Urey ratio, the volatile loss, and the seafloor spreading rate. In those numerical simulations with continental growth from the beginning and a high initial average mantle temperature water is outgassed rapidly. In the delayed continental growth model there is a very early outgassing event and the delayed continental growth has no remarkable influence on the thermal and outgassing history. A similar situation is found for the linear continental growth model but not for the Reymer and Schubert (1984) model.     

Tectonic episodicity and convective feedback mechanisms

The evolution of the Earth is characterized by irreversible processes: radioactive decay of the major heat-producing elements, thermal convection and chemical segregation. The prevailing heating from within and the temperature dependence of the viscosity are essential for thermal convection. In the present paper, the chemical and thermal evolution of the mantle and the generation of the continent material are represented by a two-dimensional and finite-difference Boussinesq convection model. We have incorporated the above-mentioned principal features in this model, a geochemical paper by Hofmann (1988, Earth Planet. Sci. Lett., 90: 297–314) constituting our starting point for the distribution of the radionuclides. The concentration of the radionuclides and the viscosity are functions of the location and time developing according to our system of differential equations. Although the real Earth is a much more complex system, we have dared to make a comparison with observed geophysical and geological data; we obtain a depleted upper mantle and acceptable values for the heat flow on the surface of the Earth as well as for the distribution of temperature, viscosity and of the velocity of creep in the mantle. The ups and downs of the convective vigour of the model roughly resemble the supercontinental cycles, the world-wide distribution of mineral dates in time, the sea-level variations and the variations of a number of geochemical parameters.     

Convection model of post-glacial uplift

A new approach to analytical and numerical study of the process of the post-glacial uplifting of the Earth’s surface was proposed within the framework of a viscous model. Displacement of the Earth’s surface is considered as the motion of the density boundary due to chemico-density convection. It is shown that the incorporation of the non-Newtonian rheology at observed velocities of post-glacial uplifts requires an obligatory presence of faults in the lithosphere and gives rise to quasi-uniform motion of the mantle material, whose viscosity under the lithosphere is, on the average, sufficiently small and amounts to ～10¹⁹ Pa. The study of the stability of the constructed model of the post-glacial uplift considered as the chemico-density convection relative to the thermal convection shows that the velocity of thermal convection developing in the presence of a quasiuniform mantle flow related to the post-glacial recovery is ～1 m/yr.     

Influence of the Load Wavelength on the Permeability of a Viscosity Interface in the Mantle

Assuming a radially stratified Newtonian mantle in a steady-state approximation, we demonstrate that the permeability of a viscosity interface at 660-km depth strongly depends on the wavelength of buoyancy forces driving the flow. The flow induced by long-wavelength loads penetrates through the boundary freely even if the viscosity increases by two orders. In contrast, the boundary is practically impermeable for short-wavelength loads located in the upper mantle. Thus, a stepwise increase of viscosity is a significant obstacle for small descending features in the upper mantle, but huge upper mantle downwellings, or upwellings formed in the-lower mantle can overcome it easily. This indicates that certain care is necessary in interpreting the seismic structure of the mantle by means of flow models. The global tomographic image includes only the first few degrees of the harmonic series and, consequently, its interpretation in terms of a present-day flow field results in a predominantly whole-mantle circulation even for extreme viscosity contrasts.     

The mantle convection model with non-Newtonian rheology and phase transitions: The flow structure and stress fields

The mantle convection model with phase transitions, non-Newtonian viscosity, and internal heat sources is calculated for two-dimensional (2D) Cartesian geometry. The temperature dependence of viscosity is described by the Arrhenius law with a viscosity step of 50 at the boundary between the upper and lower mantle. The viscosity in the model ranges within 4.5 orders of magnitude. The use of the non-Newtonian rheology enabled us to model the processes of softening in the zone of bending and subduction of the oceanic plates. The yield stress in the model is assumed to be 50 MPa. Based on the obtained model, the structure of the mantle flows and the spatial fields of the stresses σ_xz and σ_xx in the Earth’s mantle are studied. The model demonstrates a stepwise migration of the subduction zones and reveals the sharp changes in the stress fields depending on the stage of the slab detachment. In contrast to the previous model (Bobrov and Baranov, 2014), the self-consistent appearance of the rigid moving lithospheric plates on the surface is observed. Here, the intense flows in the upper mantle cause the drift and bending of the top segments of the slabs and the displacement of the plumes. It is established that when the upwelling plume intersects the boundary between the lower and upper mantle, it assumes a characteristic two-level structure: in the upper mantle, the ascending jet of the mantle material gets thinner, whereas its velocity increases. This effect is caused by the jump in the viscosity at the boundary and is enhanced by the effect of the endothermic phase boundary which impedes the penetration of the plume material from the lower mantle to the upper mantle. The values and distribution of the shear stresses σ_xz and superlithostatic horizontal stresses σ_xx are calculated. In the model area of the subducting slabs the stresses are 60–80 MPa, which is by about an order of magnitude higher than in the other mantle regions. The character of the stress fields in the transition region of the phase boundaries and viscosity step by the plumes and slabs is analyzed. It is established that the viscosity step and endothermic phase boundary at a depth of 660 km induce heterogeneities in the stress fields at the upper/lower mantle boundary. With the assumed model parameters, the exothermic phase transition at 410 km barely affects the stress fields. The slab regions manifest themselves in the stress fields much stronger than the plume regions. This numerically demonstrates that it is the slabs, not the plumes that are the main drivers of the convection. The plumes partly drive the convection and are partly passively involved into the convection stirred by the sinking slabs.     

Seismic Anisotropy in the Deep Mantle, Boundary Layers and the Geometry of Mantle Convection

—An attempt is made to explore the geodynamical significance of seismic anisotropy in the deep mantle on the basis of mineral physics. The mineral physics observations used include the effects of deformation mechanisms on lattice and shape preferred orientation, the effects of pressure on elastic anisotropy and the nature of lattice preferred orientation in deep mantle minerals in dislocation creep regime. Many of these issues are still poorly constrained, but a review of recent results shows that it is possible to interpret deep mantle seismic anisotropy in a unified fashion, based on the solid state processes without invoking partial melting. The key notions are (i) the likely regional variation in the magnitude of anisotropy as deformation mechanisms change from dislocation to diffusion creep (or superplasticity), associated with a change in the stress level and/or grain-size in the convecting mantle with a high Rayleigh number, and (ii) the change in elastic anisotropy with pressure in major mantle minerals, particularly in (Mg, Fe)O. The results provide the following constraints on the style of mantle convection (i) the SH > SV anisotropy in the bottom transition zone and the SV > SH anisotropy in the top lower mantle can be attributed to anisotropy structures (lattice preferred orientation and/or laminated structures) caused by the horizontal flow in this depth range, suggesting the presence of a mid-mantle boundary layer due to (partially) layered convection, (ii) the observed no significant seismic anisotropy in the deep mantle near subduction zones implies that deformation associated with subducting slabs is due mostly to diffusion creep (or superplasticity) and therefore slabs are weak in the deep mantle and hence easily deformed when encountered with resistance forces, and (iii) the SH > SV anisotropy in the cold thick portions of the D" layer is likely to be due to horizontally aligned shape preferred orientation in perovskite plus magnesiowüstite aggregates formed by strong horizontal shear motion in the recent past.     

Nonlinear free thermal convection in a spherical shell:A variable viscosity model

Introduction The velocity field of surface plate motion can be split into a poloidal and a toroidal parts.At the Earth′s surface,the toroidal component is manifested by the existence of transform faults,and the poloidal component by the presence of convergence and divergence,i.e.spreading and subduc-tion zones.They have coupled each other and completely depicted the characteristics of plate tec-tonic motions.The mechanism of poloidal field has been studied fairly clearly which is related to …     

Deformation mechanism maps for polycrystalline galena

A deformation mechanism map, depicting the fields of stress and temperature in which modes of plastic flow are dominant (i.e. provide the fastest strain rate) has been calculated for polycrystalline, stoichiometric galena for each of two grain sizes; namely, 10 and 10³ μm. The deformation mechanisms considered were dislocation glide, dislocation creep (i.e. creep involving dislocation climb), Nabarro-Herring creep and Coble creep.During folding and related tectonic deformation in the earth's crust steady-state flow of galena may occur by either dislocation or diffusion creep at very low differential stresses (typically ranging from 100 bars down to 10^?2 bar, or less). The dislocation creep field will be enlarged at the expense of that for diffusion creep, however, if (a) the stress dependence of strain rate for dislocation creep decreases at low stresses and if the grain size is greater than 10 μm, or (b) diffusion creep rates decline at high strains due to the presence of second-phase particles in the grain boundaries. It is probable that dislocation glide will be the dominant deformation mechanism in galena only at low temperatures and fast strain rates and it is unlikely to be the dominant mechanism during folding. Kinking may have some potential as an indicator of these temperatures and strain rates.