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1.
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.  相似文献   

2.
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.  相似文献   

3.
Summary. A thermal history model for the Earth is described in which the energetically important effects of convection are parameterized through the Nusselt number. The validity of the resulting quasi-steady-state thermal model is shown to depend upon the separation of two time-scales—a dynamic time-scale associated with the overturn time for an assumed mantle-wide convective circulation, and a thermal time-scale associated with the cooling of the planet. Provided the initial thermal state of the Earth was 'hot', the assumption of a time-scale separation can be shown under certain conditions, to be valid throughout the Earth's history. In this connection, the temperature-dependent mantle rheology plays a key role in regulating the thermal history. It is shown that the present-day, gross thermal structure of the Earth can be understood within the context of a quasi-steady-state model which is driven mainly by primordial heat. The notion of whole-mantle convection is shown to be consistent with several additional observational constraints, including the observed mean lithospheric thickness and the mean plate velocities. We briefly consider the extension of the parameterized thermal model to Venus.  相似文献   

4.
Speculations on the Thermal and Tectonic History of the Earth   总被引：3，自引：0，他引：3  
Summary. The connection between the Earth's thermal history and convection in the mantle is exploited to elucidate the early evolution of the Earth. It appears probable that convection extending over almost all of the mantle has dominated vertical heat transport throughout the whole of the Earth's history. Only in boundary layers at the surface and at a depth of 650–700 km is conduction likely to be important. The resulting evolution appears to be consistent with geological observations on early Precambrian rocks.
Various arguments are put forward in favour of two horizontal scales of convective flow in the mantle at depths less than 650 km. The large scale flow is related to the motion of major plates, and must be ordered over distances of more than 5000 km. Its evolution and energetics are discussed and there are no obvious problems in maintaining the proposed convective motions. Small scale flow with an extent of the order of 500 km appears necessary both to explain the heat flow through older parts of the Earth's surface and to reconcile the geophysical observations with the results of numerical experiments. Though the existence of the small scale flow is at present speculative, various tests of its presence are proposed.  相似文献   

5.
Summary Many accept thermal convection within the mantle of the Earth as the driving mechanism for continental drift. It is also of considerable interest to determine whether thermal convection is occurring within Venus, Mars, and the Moon. In this paper a systematic treatment of the stability of planetary interiors is given. The thermal stability problem for a layer of fluid heated from below is solved when the viscosity of the fluid increases exponentially with depth. For a semi-infinite fluid with exponentially increasing viscosity the critical Rayleigh number based on the surface viscosity and the scale length of the viscosity increase is found to be 30 for a fixed surface boundary condition and 23 for a free surface boundary condition. This stability analysis is also extended to include volume heat release. The thermal stability of the interiors of the Earth, Venus, Mars and the Moon is examined. Using temperature-depth profiles in the literature and a theoretical expression for the viscosity of a crystalline solid based on diffusion creep, viscosity depth profiles for planetary interiors are obtained. Because of the strong pressure effect the viscosity within the Earth and Venus increases greatly from a near surface minimum. For Mars the increase is less pronounced and within the interior of the Moon the viscosity is nearly constant. For all the cases considered the planetary interiors are found to be thermally unstable. Because of the dependence of viscosity on depth the interiors of the Moon and Mars are found to be considerably less stable than Venus and the Earth. It is concluded that thermal convection is occurring within the planetary bodies considered.  相似文献   

6.
Summary. A simple, analytical model for mantle convection with mobile surface plates is presented. Our aim is to determine under what conditions free convection can account for the observed plate motions, and to evaluate the thermal structure of the mantle existing under these conditions. Boundary layer methods are used to represent two-dimensional cellular convection at large Rayleigh and infinite Prandtl numbers. The steady-state structure consists of cells with isentropic interiors enclosed by thermal boundary layers. Lithospheric plates are represented as upper surfaces on each cell free to move at a uniform speed. Buoyancy forces are concentrated in narrow rising and decending thermal plumes; torques imparted by these plumes drive both the deformable mantle and overlying plate. Solutions are found for a comprehensive range of cell sizes. We derive an expression for the plate speed as a function of its length, the mantle viscosity and surface heat flux. Using mean values for these parameters, we find that thermal convection extending to 700 km depth can move plates at 1 cm yr-1, while convection through the whole mantle can move plates at 4–5 cm yr-1. Analysis of the steady-state temperature field, for the case of heating from below, shows that the upper thermal boundary layer develops a complex structure, including an 'asthenosphere' defined by a local maximum in the geotherm occurring at depths of 50–150 km.  相似文献   

7.
Summary. Phase boundaries are included in dynamical finite element models of mantle convection. They are represented by point chains which act as additional sources of buoyancy forces when distorted, and as additional source or sink of heat. The influence of the exothermic olivine-spinel transition is studied in both shallow and deep convection models. The flow is only slightly enhanced by the transition. The increase of temperature due to latent heat release is step-like in the deep model, in the case of shallow convection it is more diffuse. Other quantities like ocean-floor topography, gravity anomalies, and stress distribution are no more than moderately affected. In a further investigation the effect of spinel post-spinel transition, whether endothermic or exothermic, on deep convection is examined. The effect on the flow is negligibly small in both cases.  相似文献   

8.
For two decades leading to the late 1980s, the prevailing view from studies of glacial isostatic adjustment (GIA) data was that the viscosity of the Earth's mantle increased moderately, if at all, from the base of the lithosphere to the core–mantle boundary. This view was first questioned by Nakada & Lambeck , who argued that differential sea-level (DSL) highstands between pairs of sites in the Australian region preferred an increase of approximately two orders of magnitude from the mean viscosity of the upper to the lower mantle, in accord with independent inferences from observables related to mantle convection. We use non-linear Bayesian inference to provide the first formal resolving power analysis of the Australian DSL data set. We identify three radial regions, two within the upper mantle (110–270 km and 320–570 km depth) and one in the lower mantle (1225–2265 km depth), over which the average of viscosity is well constrained by the data. We conclude that: (1) the DSL data provide a resolution in the inference of upper mantle viscosity that is better than implied by forward analyses based on isoviscous regions above and below the 670 km depth discontinuity and (2) the data do not strongly constrain viscosity at either the base or top of the lower mantle. Finally, our inversions also quantify the significant bias that may be introduced in inversions of the DSL highstands that do not simultaneously estimate the thickness of the elastic lithosphere.  相似文献   

9.
A 3-D density model was created for the Central Balkans area down to a depth of 670  km on the basis of seismic (both artificial sources and earthquakes) and gravity data. This model is based on density columns constructed for the main geological units of the study region. The densities for these columns were obtained using the density variation method. This method makes it possible to extrapolate the density distribution from the well-studied uppermost layers to the deeper levels of the Earth. The constructed 3-D density model was interpreted in relation to the available data on the heat flow and the seismicity of the region. The subdivision of the region by the Maritza fault into two parts—the southern part including the Rhodope massif and the northern part including the structures of Alpine activation of Srednogorie and the Balkanides—was confirmed. The upraised position of the 400  km boundary within the upper mantle, which was established from the density modelling, is assumed to be a sign of development of recent geodynamical processes over the Srednogorie block. From the viewpoint of seismicity prediction, a finding of mantle inhomogeneities orthogonal to the Maritza suture is of great importance.  相似文献   

10.
Summary. Slow cooling of the whole Earth can be responsible for the convection in the core that is required to generate the magnetic field. Previous studies have assumed the cooling rate to be high enough for the whole core to convect. Here we study the effects of a low rate of cooling by assuming the temperature at the base of the mantle to remain constant with an initially entirely molten, adiabatic core. We argue that, in such a situation, convection would stop at the top of the core, and calculate the consequent thermal evolution. A stable, density stratified layer grows downwards from the core mantle boundary reaching a thickness of 100–1000 km in a few thousands of millions of years. There is some geomagnetic evidence to support belief in the existence of such a stable layer.  相似文献   

11.
Summary. A simplified model of convection in the mantle is used to investigate the transient effect of cooling a fluid layer from above, The model, representing the mantle overlain by the lithosphere, consists of a two-dimensional fluid layer overlain by a solid conducting lid. The initial temperature of both layers is the same, with the top surface of the lid kept at 0°C throughout. We observe the onset of small-scale flow in the model. In the absence of internal heating the behaviour of the system is controlled by the Rayleigh number, R , and the ratio of the thicknesses of the two layers, a . The onset time of convection as defined by reference to conduction temperature profiles is related simply to a boundary layer critical Rayleigh number. The mean temperature profiles for the convection model are also compared with the observed depth—age relation for oceanic lithosphere and the results are used to estimate the viscosity of the mantle.  相似文献   

12.
Summary. An approximate analytical solution for flow in a mantle plume of constant radius, viscosity, and density contrast is obtained in cylindrical coordinates. the differential equations for vertical velocity of the mantle surrounding the plume and for topography are homologous to the equation for flexure of an elastic plate. Although the model is too simple to be fully applicable to the Earth, one can conclude that the vertical velocity in the mantle changes significantly away from plumes, that the viscosity of the plume is important for controlling flow rate, and that the long-wavelength geoid anomalies are sensitive to the viscosity of the surrounding mantle. the first induced upwelling away from a plume is quite weak and unlikely to control the spacing of plumes.  相似文献   

13.
The short-period seismic phase Sn has been interpreted by Stephens & Isacks as a lid wave' in which the seismic energy is constrained to the uppermost few tens of kilometres of the mantle. We have extended their normal-mode interpretation for structures both with and without low-velocity zones (LVZ) in the upper mantle. We have used spherical, anelastic models of the Earth. For a model of an oceanic mantle with a LVZ, we agree that Sn is a lid wave for sources above 200–250 km, if only the onset of Sn is considered. The later portions of the Sn wave train sample the structure as deeply as the 420-km discontinuity. For deeper foci, the pseudo-lid wave does not appear to be generated; even the onset of Sn samples the deeper mantle structure. For a model of a continental mantle without a LVZ, in general, sources at all depths above the 420-km discontinuity appear to generate teleseismic Sn which samples the entire mantle as deeply as the discontinuity and which travels with a velocity significantly greater than the lid velocity. Thus the velocity of Sn may be an important diagnostic to determine whether or not a LVZ exists in the upper mantle.  相似文献   

14.
b
We investigate forward models of the gravitational potential spectrum generated by ensembles of discrete sources of anomalous mass, having radial distributions with different statistical properties. Models with a random distribution of point source locations throughout the volume of the mantle produce spectra similar to that of the Earth only when the (absolute) source magnitudes increase strongly with depth, at least as d 1.5. The effects of the geographic (latitude-longitude) distribution of source locations are generally unimportant in determining the general degree dependence of the potential spectrum. The dimensions of the sources are also of secondary importance, at least up to an angular diameter of about 40, i.e., continent-sized. Sources of this size confined to the upper mantle do not appear capable of producing the degree dependence of the observed geopotential spectrum; the low harmonics (2-4) in particular appear to require lower mantle sources of considerable strength. Further, at least some of these deep sources must be largely monopolar in nature, (i.e., uncompensated) due to the stronger depth attenuation of dipole (compensated) sources. Because topography on the core-mantle boundary must be either isostatically or dynamically compensated, it may contribute little strength to the observed potential spectrum.  相似文献   

15.
i
The effect of errors in the expression for dp/dr used in constructing the Earth Model A is examined. It is shown that, for a 10 per cent error in dp/dr arising from possible deviations from adiabatic gradients and uniform chemical composition in the regions B and D, the maximum error in the density ρ in the mantle of Model A would be only 0.07 g/cm3. This is less than one-quarter of the error that would be entailed if a 10 per cent correction to dp/dr were applied throughout the mantle. Thus temperature deviations to any likely extent cannot be considered as serious sources of error in the density distribution of Model A.  相似文献   

16.
Summary. The viscoelastic response of the Earth to the mass displacements caused by late Pleistocene deglaciation and concomitant sea level changes is shown to be capable of producing the secular motion of the Earth's rotation pole as deduced from astronomical observations. The calculations for a viscoelastic Earth yield a secular motion in the direction of 72° W meridian which is in excellent agreement with observed values. The average Newtonian viscosity and the relaxation time obtained from polar motion data are about (1.1 ± 0.6)1023 poise (P) and 104 (1 ± 0.5) yr. The non-tidal secular acceleration of the Earth can also be attributed to the viscoelastic response to deglaciation and results in an independent viscosity estimate of 1.6 × 1023 P with upper and lower limits of 1.1 × 1023 and 2.8 × 1023 P. These values are in agreement with those based on the polar drift analysis and indicate an average mantle viscosity of 1–2 × 1023 P.  相似文献   

17.
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 δR) is proportional to the square root of the matrix viscosity. In the Earth's mantle, δR∼ 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 ≪δR, 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 ≫δR, 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.  相似文献   

18.
A model of time-periodic mantle flow   总被引：1，自引：0，他引：1  
Summary. The instability of a layer consisting of a lighter viscous fluid on top of a heavier less viscous fluid is considered in the case when the heavy fluid is adiabatically stratified and the light fluid contains heat sources and possesses a lower heat conductivity. A perturbation in the thickness of the upper fluid layer causes horizontal temperature variations in the lower fluid. The motions induced by thermal buoyancy can interact with the distortion of the interface in such a way that the initial perturbation is reinforced in the form of an overstable oscillation. It is proposed that this mechanism is relevant to the problem of time-dependent flow in the Earth's mantle.  相似文献   

19.
Summary. It is known that flow in the mantle can produce preferred orientation in olivine crystals with seismic anisotropy as a consequence. Flow in the subcrustal lithosphere is unlikely because of the high viscosity. Lenses of high temperature and low-viscosity ( anomalous mantle ) are located under the crust in many tectonically active regions, and viscous flow can easily arise in such material resulting in seismic anisotropy. After cooling, such anomalous mantle acquires high viscosity and becomes incorporated into the lithospheric layer preserving the anisotropy produced by the flows which existed previously. The interaction of the stresses with cracks in the upper crust can be one of the causes of anisotropy in this layer.  相似文献   

20.
Observations of ice movements across the British Isles and of sea-level changes around the shorelines during Late Devensian time (after about 25 000 yr BP) have been used to establish a high spatial and temporal resolution model for the rebound of Great Britain and associated sea-level change. The sea-level observations include sites within the margins of the former ice sheet as well as observations outside the glaciated regions such that it has been possible to separate unknown earth model parameters from some ice-sheet model parameters in the inversion of the glacio-hydro-isostatic equations. The mantle viscosity profile is approximated by a number of radially symmetric layers representing the lithosphere, the upper mantle as two layers from the base of the lithosphere to the phase transition boundary at 400 km, the transition zone down to 670 km depth, and the lower mantle. No evidence is found to support a strong layering in viscosity above 670 km other than the high-viscosity lithospheric layer. Models with a low-viscosity zone in the upper mantle or models with a marked higher viscosity in the transition zone are less satisfactory than models in which the viscosity is constant from the base of the lithosphere to the 670 km boundary. In contrast, a marked increase in viscosity is required across this latter boundary. The optimum effective parameters for the mantle beneath Great Britain are: a lithospheric thickness of about 65 km, a mantle viscosity above 670 km of about (4-5) 1020 Pa s, and a viscosity below 670 km greater than 4 × 1021 Pa s.  相似文献   

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