Orogenic volcanism caused by thermal runaways?

Summary. Quartz eclogite as source rock seems capable of explaining the chemistry of calc-alkaline volcanics. This model requires partial melting of quartz eclogite in the depth range 100–200 km. Shear heating of the subducting crust is one of the most debated models. The problem may be treated with two different boundary conditions: constant strain rate or constant shear stress. In the former case an increase in temperature tends to reduce the heat production thus stabilizing the shear flow; the result is a moderate increase in temperature which will remain constant during flow. The latter case may lead to a thermal feedback instability and thus temperature and strain rate may suddenly grow to very high values. This phenomenon is termed a runaway and will be discussed in this paper using an adiabatic approximation. It is shown that for a runaway to occur the local energy density must amount to a common value independent of the rheology. In contrast to the constant strain rate case, shear heating is negligible until just before the instability occurs. When the melting point is reached shear stress will break down but the stored local energy will be set free and supply the latent heat of melting. The possibility of a runaway occurring is strongly dependent on the ambient temperature. In subduction shear zones neither shear stress nor strain rate are likely to be constant throughout, but if the former is constant or changes little on a 1–10 km scale a runaway is liable to occur at a depth of around 150 km thus possibly being the cause of calcalkaline volcanism.     

Vertical structure of the head of a cylindrical mantle plume from a model of two-phase flow with melting

Within the mushroom-shaped head of a cylindrical mantle plume melting occurs, the melt segregates from the matrix, and the matrix deforms and spreads laterally. These processes have been studied with a model of two-phase flow with melting. After characteristics of the solution near the axis of symmetry of the plume were found, a set of asymptotic relations for the variables along the symmetry axis was derived from McKenzie's equations for conservation of mass, momentum and energy of a two-phase system. The distribution of porosity along the plume axis and the vertical and radial segregation velocity of the melt in the vicinity of the axis of symmetry were obtained as functions of depth. Our analytic results show that within the head of a cylindrical mantle plume the contribution of the deformation of the matrix to the total non-hydrostatic pressure gradient cannot be neglected, and melt convergence or divergence is controlled by the radial scale of the upward velocity profile at the depth of the beginning of melting.     

Rheology of the Earth and a thermoconvective mechanism for sedimentary basin formation

A power-law non-Newtonian fluid is usually assumed to model slow flows in the mantle and, in particular, convective flows. However, the power-law fluid has no memory, in contrast to a real material. A new non-linear integral (having a memory) model is proposed to describe the rheology of rocks. The model is consistent with the theory of simple fluids with fading memory and with laboratory studies of rock creep. The proposed model reduces to the power-law fluid model for stationary flows and to the Andrade model for flows associated with small strains. Stationary convection beneath continents has been studied by Fleitout & Yuen (1984 ), who used the power-law fluid model and obtained the cold immobile boundary layer (continental lithosphere). In a stability analysis of this layer, the Andrade model must be used. The analysis shows that the lithosphere is overstable (the period of oscillation is about 200  Ma). In the present study, it is suggested that these thermoconvective oscillations of the lithosphere are a mechanism for sedimentary basin formation. The vertical crustal movement in sedimentary basins can be considered as a slow subsidence on which small-amplitude oscillations are superimposed. The longest period of oscillatory crustal movement is of the same order of magnitude as the period of convective oscillation of the lithosphere found in the stability analysis. Taking into account the difference between depositional and erosional transport rates we can explain the permanent subsidence as well as the oscillations.     

Effect of 3-D viscoelastic structure on post-seismic relaxation from the 2004 M= 9.2 Sumatra earthquake

The 2004 M = 9.2 Sumatra–Andaman earthquake profoundly altered the state of stress in a large volume surrounding the ∼1400 km long rupture. Induced mantle flow fields and coupled surface deformation are sensitive to the 3-D rheology structure. To predict the post-seismic motions from this earthquake, relaxation of a 3-D spherical viscoelastic earth model is simulated using the theory of coupled normal modes. The quasi-static deformation basis set and solution on the 3-D model is constructed using: a spherically stratified viscoelastic earth model with a linear stress–strain relation; an aspherical perturbation in viscoelastic structure; a 'static' mode basis set consisting of Earth's spheroidal and toroidal free oscillations; a "viscoelastic" mode basis set; and interaction kernels that describe the coupling among viscoelastic and static modes. Application to the 2004 Sumatra–Andaman earthquake illustrates the profound modification of the post-seismic flow field at depth by a slab structure and similarly large effects on the near-field post-seismic deformation field at Earth's surface. Comparison with post-seismic GPS observations illustrates the extent to which viscoelastic relaxation contributes to the regional post-seismic deformation.     

Numerical models of mantle convection with secular cooling

A 2-D time-dependent finite-difference numerical model is used to investigate the thermal character and evolution of a convecting layer which is cooling as it convects. Two basic cooling modes are considered: in the first, both upper and lower boundaries are cooled at the same rate, while maintaining the same temperature difference across the layer; in the second, the lower boundary temperature decreases with time while the upper boundary temperature is fixed at 0°C. The first cooling mode simulates the effects of internal heating while the second simulates planetary cooling as mantle convection extracts heat from, and thereby cools, the Earth's core. The mathematical analogue between the effects of cooling and internal heating is verified for finite-amplitude convection. It is found that after an initial transient period the central core of a steady but vigorous convection cell cools at a constant rate which is governed by the rate of cooling of the boundaries and the viscosity structure of the layer. For upper-mantle models the transient stage lasts for about 30 per cent of the age of the Earth, while for the whole mantle it lasts for longer than the age of the Earth. Consequently, in our models the bulk cooling of the mantle lags behind the cooling of the core-mantle boundary. Models with temperature-dependent viscosity are found to cool in the same manner as models with depth-dependent viscosity; the rate of cooling is controlled primarily by the horizontally averaged variation of viscosity with depth. If the Earth's mantle cools in a similar fashion, secular cooling of the planet may be insensitive to lateral variations of viscosity.     

A critical assessment of viscous models of trench topography and corner flow

Summary. We obtain stresses for Newtonian viscous flow in simple geometries (e.g. corner flow, bending flow) in order to study the effect of imposed velocity boundary conditions. Stress for a delta function velocity boundary condition decays as 1/ r ²; for a step function velocity, stress goes as 1/ r ; for a discontinuity in curvature, the stress singularity is logarithmic. For corner flow, which has a discontinuity of velocity at a certain point, the corresponding stress has a 1/ r singularity. However, for a more realistic circular-slab model, the stress singularity becomes logarithmic. Thus the stress distribution is very sensitive to the boundary conditions, and in evaluating the applicability of viscous models of trench topography it is essential to use realistic geometries.
Topography and seismicity data from northern Honshu, Japan, were used to construct a finite element model, with flow assumed constant speed and tangent to the top of the grid, for both Newtonian and non-Newtonian flow (power law 3 rheology). Normal stresses at the top of the grid are compared to the observed trench topography. There is poor agreement. Purely viscous models of subducting slabs with simple, geometrically consistent velocity boundary conditions do not predict normal stress patterns compatible with observed topography. Elasticity and plasticity appear to be important in determining trench topography.     

The deformation and compaction of partial molten zones

Summary. The segregation of melt from a partially molten source region requires a corresponding deformation of the unmelted residue ('matrix'). The role of matrix deformation during melt segregation is examined using simple one-dimensional models, for which the deformation consists only of bulk compression or 'compaction'. In model I, a volume fraction φ₀ of ascending mantle material undergoes pressure-release melting at a depth z = 0 (localized melting). Compaction of the matrix occurs in a boundary layer whose thickness (reduced compaction length δ_R) is proportional to the square root of the matrix viscosity. In the Earth's mantle, δ_R∼ 10–100 m, indicating that compaction cannot be important over large distances. Model II examines the case in which melting occurs over a depth range of order h (distributed melting). In the limit h ≪δ_R, the solution is the same as for the case of localized melting, except in a 'melting layer' of thickness ∼ h near z = 0. In the more realistic limit h ≫δ_R, compaction makes a negligible contribution to the balance of forces associated with melt segregation. This result is also valid for the more general case of two-dimensional flow. Compaction is therefore likely to be of negligible importance in the Earth's mantle, with the consequence that melt segregation can be accurately described by Darcy's law.     

Time-dependent thermal convection, mantle differentiation and continental-crust growth

The thermal evolution of the Earth is controlled by radioactive elements whose heat production rate decays with time and whose spatial distribution depends on chemical segregation processes.
We present a 2-D and finite-difference Boussinesq convection model with temperature-dependent viscosity and time- and space-dependent radioactive heat sources. We used Newtonian rheology, boxes of aspect ratio 3, and heating from within. Starting from the geochemical results of Hofmann (1988), it is assumed that the radioactive heat sources of the mantle were initially distributed homogeneously. In a number of calculations, however, higher starting abundances of radioactive sources were assumed in the upper mantle. For the present geological situation, this also results in a depleted upper mantle. It was assumed that, if the viscosity falls below a certain critical value, chemical segregation will take place. In this way, model continental crust develops, leaving behind areas of a depleted mantle. We obtained the heat source, flow line, temperature, viscosity and heat-flow distribution as a function of time with realistic values, especially for the present time. The present viscosity of the upper mantle is approximately at the standard value obtained for postglacial uplift modelling; the deeper-mantle viscosity is considerably higher. The time dependence of the computed mean of the kinetic energy of mantle convection bears a resemblance to that of the magmatic and orogenetic activity of the Earth. We assumed that the 670 km discontinuity cannot be penetrated by the flow.     

Impact of regional mantle flow on subducting plate geometry and interplate stress: insights from physical modelling

Physical models of subduction investigate the impact of regional mantle flow on the structure of the subducted slab and deformation of the downgoing and overriding plates. The initial mantle flow direction beneath the overriding plate can be horizontal or vertical, depending on its location with respect to the asthenospheric flow field. Imposed mantle flow produces either over or underpressure on the lower surface of the slab depending on the initial mantle flow pattern (horizontal or vertical, respectively). Overpressure promotes shallow dip subduction while underpressure tends to steepen the slab. Horizontal mantle flow with rates of 1–10 cm yr⁻¹ provides sufficient overpressure on a dense subducting lithosphere to obtain a subduction angle of  ∼60°  , while the same lithospheric slab sinks vertically when no flow is imposed. Vertical drag force (due to downward mantle flow) exerted on a slab can result in steep subduction if the slab is neutrally buoyant but fails to produce steep subduction of buoyant oceanic lithosphere. The strain regime in the overriding plate due to the asthenospheric drag force depends largely on slab geometry. When the slab dip is steeper than the interplate zone, the drag force produces negative additional normal stress on the interplate zone and tensile horizontal stress in the overriding plate. When the slab dip is shallower than the interplate zone, an additional positive normal stress is produced on the interplate zone and the overriding plate experiences additional horizontal compressive stress. However, the impact of the mantle drag force on interplate pressure is small compared to the influence of the slab pull force since these stress variations can only be observed when the slab is dense and interplate pressure is low.     

Material versus isobaric internal boundaries in the Earth and their influence on postglacial rebound

Most previous earth models used to calculate viscoelastic relaxation after the removal of the Late Pleistocene ice loads implicitly assume that there is no exchange of mass across the mantle density discontinuities on periods of tens of thousands of years (the material boundary formulation). In the present study, simple incompressible models are used to determine the Earth's behaviour in the case where the density discontinuity remains at a constant pressure rather than deforming with the material (the isobaric boundary formulation). The calculation of the movement of the boundary is more rigorous than in earlier studies and uses the local incremental pressure calculated at the depth of the boundary and allows for the vertical deformation caused by the change in volume as material changes phase. It is shown that the buoyancy modes associated with the density discontinuities decrease in strength and increase in relaxation time analogous to what results when the density contrast is reduced. Also, two viscoelastic modes arise from an isobaric boundary, which is also predicted when there is a contrast in rigidity or viscosity across a material boundary. The difference in predicted radial deformation between the isobaric boundary model and the material boundary model is largest for long-wavelength loads for which the material incremental pressure at depth is largest. If the isobaric boundary model is appropriate for the treatment of the mineral phase changes in the mantle on glacial rebound timescales, then previous inferences of the deep-mantle to shallow-mantle viscosity ratio based on large-scale deformation (spherical harmonic degree < 10) of the Earth and including data from the early part of the glacio-isostatic uplift are too small.     

Two-dimensional modelling of subduction zone anisotropy with application to southwestern Japan

We present a series of 2-D numerical models of viscous flow in the mantle wedge induced by a subducting lithospheric plate. We use a kinematically defined slab geometry approximating the subduction of the Philippine Sea plate beneath Eurasia. Through finite element modelling we explore the effects of different rheological and thermal constraints (e.g. a low-viscosity region in the wedge corner, power law versus Newtonian rheology, the inclusion of thermal buoyancy forces and a temperature-dependent viscosity law) on the velocity and finite strain field in the mantle wedge. From the numerical flow models we construct models of anisotropy in the wedge by calculating the evolution of the finite strain ellipse and combining its geometry with appropriate elastic constants for effective transversely isotropic mantle material. We then predict shear wave splitting for stations located above the model domain using expressions derived from anisotropic perturbation theory, and compare the predictions to ∼500 previously published shear wave splitting measurements from seventeen stations of the broad-band F-net array located in southwestern Japan. Although the use of different model parameters can have a substantial effect on the character of the finite strain field, the effect on the average predicted splitting parameters is small. However, the variations with backazimuth and ray parameter of individual splitting intensity measurements at a given station for different models are often different, and rigorous analysis of details in the splitting patterns allows us to discriminate among different rheological models for flow in the mantle wedge. The splitting observed in southwestern Japan agrees well with the predictions of trench-perpendicular flow in the mantle wedge along with B-type olivine fabric dominating in a region from the wedge corner to about 125 km from the trench.     

Inference of mantle viscosity from GRACE and relative sea level data

Gravity Recovery And Climate Experiment (GRACE) satellite observations of secular changes in gravity near Hudson Bay, and geological measurements of relative sea level (RSL) changes over the last 10 000 yr in the same region, are used in a Monte Carlo inversion to infer-mantle viscosity structure. The GRACE secular change in gravity shows a significant positive anomaly over a broad region (>3000 km) near Hudson Bay with a maximum of ∼2.5 μGal yr⁻¹ slightly west of Hudson Bay. The pattern of this anomaly is remarkably consistent with that predicted for postglacial rebound using the ICE-5G deglaciation history, strongly suggesting a postglacial rebound origin for the gravity change. We find that the GRACE and RSL data are insensitive to mantle viscosity below 1800 km depth, a conclusion similar to that from previous studies that used only RSL data. For a mantle with homogeneous viscosity, the GRACE and RSL data require a viscosity between  1.4 × 10²¹  and  2.3 × 10²¹  Pa s. An inversion for two mantle viscosity layers separated at a depth of 670 km, shows an ensemble of viscosity structures compatible with the data. While the lowest misfit occurs for upper- and lower-mantle viscosities of  5.3 × 10²⁰  and  2.3 × 10²¹  Pa s, respectively, a weaker upper mantle may be compensated by a stronger lower mantle, such that there exist other models that also provide a reasonable fit to the data. We find that the GRACE and RSL data used in this study cannot resolve more than two layers in the upper 1800 km of the mantle.     

Mantle convection under simulated plates: effects of heating modes and ridge and trench migration, and implications for the core—mantle boundary, bathymetry, the geoid and Benioff zones

Summary. Numerical convection models are presented in which plates are simulated by imposing piecewise constant horizontal velocities on the upper boundary. A 4 × 1 box of constant viscosity fluid and two-dimensional (2-D) flow is assumed. Four heating modes are compared: the four combinations of internal or bottom heating and prescribed bottom temperature or heat flux. The case with internal heating and an isothermal base is relevant to lower mantle or whole mantle convection, and it yields a lower thermal boundary layer which is laterally variable and can be locally reversed, corresponding to heat flowing back into the core locally. When scaled to the whole mantle, the surface deflections and gravity and geoid perturbations calculated from the models are comparable to those observed at the Earth's surface. For models with migrating ridges and trenches, the flow structure lags well behind the changing surface 'plate'configurations. This may help to explain the poor correlation between the main geoid features and plate boundaries. Trench migration substantially affects the dip of the cool descending fluid because of induced horizontal shear in the vicinity of the trench. Such shear is small for whole mantle convection, but is large for upper mantle convection, and would probably result in the Tonga Benioff zone dipping to the SE, opposite to the observed dip, for the case of upper mantle convection.     

Modelling of mantle postglacial relaxation in axisymmetric geometry with a composite rheology and a glacial load interpolated by adjusted spherical harmonics analysis

Although studies on glacial isostatic adjustment usually assume a purely linear rheology, we have previously shown that mantle relaxation after the melting of Laurentide ice sheet is better described by a composite rheology including a non-linear term. This modelling is, however, based on axially symmetric geometry and glacial forcing derived from ICE-3G and suffers from a certain amount of arbitrariness in the definition of the ice load. In this work we apply adjusted spherical harmonics analysis to interpolate the ice thicknesses of ICE-3G and ICE-1 glaciological models. This filters out the non-axisymmetric components of the ice load by considering only the zonal terms in the spherical harmonics expansion. The resulting load function is used in finite-element simulation of postglacial rebound to compare composite versus purely linear rheology. Our results confirm that composite rheology can explain relative sea level (RSL) data in North America significantly better than a purely linear rheology. The performance of composite rheology suggests that in future investigations, it may be better to use this more physically realistic creep law for modelling mantle deformation induced by glacial forcing.     

车辆碾压对沙质草原表土物理力学性质的影响

通过野外现场调查、载荷试验、轻型圆锥动力触探、车辆碾压原状草地观测试验及室内试验方法,对呼伦贝尔沙质草原不同碾压程度表层沙土物理力学性质及变形和剪切破坏特征进行研究。结果表明:碾压使上软下硬高压缩性的原状表层沙土因应力集中产生振动密实沉降、塑性变形,直接破坏表土层原状结构。碾压程度越大,沙土密实度越高、抗剪强度越大、承载力越高。碾压形成上硬下软土层,因强度不足发生整体剪切破坏,塑性变形区的沙土在重复荷载作用下产生振动蠕变及砂土液化,使土层强度、稳定性显著降低。车辆碾压可直接或间接破坏沙质草原表层沙土,加剧土层破口形成及扩大,加速草原沙漠化。     

南极罗斯岛及泰勒谷新生代火山岩微量元素特征及岩石成因

本文对采自南极罗斯岛及泰勒谷的新生代火山岩（包括鸟角碱玄岩、伊万思角歪长粗面响岩、罗德角碱玄响岩、克雷特山碱玄岩、碧玄岩博尼湖南岸碧玄岩）中的微量元素、稀土元素及同位素进行了系统的研究。查明研究区的火山岩未遭受地壳混染；证实它们可能来自两种不同的地幔源区。在岩浆演化方式上两套岩石也有所不同，碱玄岩和碧玄岩以地幔平衡部分熔融作用为主，而粗面响岩、碱玄响岩则以分离结晶作用为主。地幔部分熔融度为１．４６～３．５７％。最后对该区地幔的性质进行了初步讨论     

Model of the geoelectrical structure of the mid- and lower mantle in the Europe–Asia region

The conductivity structure of the Earth's mantle was estimated using the induction method down to 2100  km depth for the Europe–Asia region. For this purpose, the responses obtained at seven geomagnetic observatories (IRT, KIV, MOS, NVS, HLP, WIT and NGK) were analysed, together with reliable published results for 11  yr variations. 1-D spherical modelling has shown that, beneath the mid-mantle conductive layer (600–800  km), the conductivity increases slowly from about 1  S  m⁻¹ at 1000  km depth to 10  S  m⁻¹ at 1900  km, while further down (1900–2100  km) this increase is faster. Published models of the lower mantle conductivity obtained using the secular, 30–60  yr variations were also considered, in order to estimate the conductivity at depths down to the core. The new regional model of the lower mantle conductivity does not contradict most modern geoelectrical sounding results. This model supports the idea that the mantle base, situated below 2100  km depth, has a very high conductivity.     

P- and S-velocity images of the lithosphere–asthenosphere system in the Central Andes from local-source tomographic inversion

About 50 000 P and S arrival times and 25 000 values of t * recorded at seismic arrays operated in the Central Andes between 20°S and 25°S in the time period from 1994 to 1997 have been used for locating more than 1500 deep and crustal earthquakes and creating 3-D P , S velocity and Qp models. The study volume in the reference model is subdivided into three domains: slab, continental crust and mantle wedge. A starting velocity distribution in each domain is set from a priori information: in the crust it is based on the controlled sources seismic studies; in slab and mantle wedge it is defined using relations between P and S velocities, temperature and composition given by mineral physics. Each iteration of tomographic inversion consists of the following steps: (1) absolute location of sources in 3-D velocity model using P and S arrival times; (2) double-difference relocation of the sources and (3) simultaneous determination of P and S velocity anomalies, P and S station corrections and source parameters by inverting one matrix. Velocity parameters are computed in a mesh with the density of nodes proportional to the ray density with double-sided nodes at the domain boundaries. The next iteration is repeated with the updated velocity model and source parameters obtained at the previous step. Different tests aimed at checking the reliability of the obtained velocity models are presented. In addition, we present the results of inversion for Vp and Vp/Vs parameters, which appear to be practically equivalent to Vp and Vs inversion. A separate inversion for Qp has been performed using the ray paths and source locations in the final velocity model. The resulting Vp , Vs and Qp distributions show complicated, essentially 3-D structure in the lithosphere and asthenosphere. P and S velocities appear to be well correlated, suggesting the important role of variations of composition, temperature, water content and degree of partial melting.     

Ductile shear zones: some aspects of constant slip velocity and constant shear stress models

Summary The thermomechanical differential equations governing deformation in viscous shear zones have been solved for both constant velocity and constant stress boundary conditions. The solutions show that the inertial term in these equations can be neglected everywhere.
The starting condition of the constant velocity model has been shown to be a constant velocity gradient and not a Heaviside function. The temperature anomaly produced by shear heating at the centre of the shear zone is shown to increase gradually and continuously with time, not reaching an asymptotic value. Conclusions for the constant velocity boundary condition are otherwise generally similar to those presented by Yuen et al , and agree with Fleitout & Froidevaux. The temperatures reached by constant velocity shears are sufficient for partial melting.
Constant stress boundary condition shear zone models show an initially broad shear zone with uniform shear velocity gradient. Depending on the level of applied shear stress and ambient temperature, localized intense shear heating may develop followed by thermal runaway. At lower ambient temperatures relatively high stresses are required to produce thermal runaway.
The broadening of the constant velocity shear zone proceeds more rapidly with increased ambient temperature. This can be used to show that shear zones broaden with depth. The merging of parallel shear zone pairs has been investigated and shear zones separated by distances of less than 10km coalesce to form a single shear zone within 3 Myr. Only shear zones separated by 50km or more remain distinct over periods of tens of millions of years.