A geophysical aspect of a disturbed fluid motion in the earth's core

Summary A magnetic dipole is supposed to be suddenly introduced in the earth's core (taken as an inviscid, incompressible fluid of finite electrical conductivity) to act as a source of disturbance. It is shown that although in the symmetric case of the problem the disturbed fluid is stagnant in any direction at the interface separating core from the solid insulating mantle; yet it should slip in any tangential direction at the interface, in each of the three unsymmetric cases considered here.     

Diapirism of depleted peridotite — a model for the origin of hot spots

A model is proposed for the origin of hot spots that depends on the existence of major-element heterogeneities in the mantle. Generation of basaltic crust at spreading centers produces a layer of residual peridotite ～20–25 km thick directly beneath the crust which is depleted in Fe/Mg, TiO₂, CaO, Al₂O₃, Na₂O and K₂O, and which has a slightly lower density than undepleted peridotite beneath it. Upon recycling of this depleted peridotite back into the deep mantle at subduction zones, it becomes gravitationally unstable, and tends to rise as diapirs through undepleted peridotite. For a density contrast of 0.05 g cm^?3, a diapir 60 km in diameter would rise at roughly 8 cm y^?1, and could transport enough heat to the base of the lithosphere to cause melting and volcanism at the surface. Hot spots are thus viewed as a passive consequence of mantle convection and fractionation at spreading centers rather than a plate-driving force.It is suggested that depleted diapirs exist with varying amounts of depletion, diameters, upward velocities and source volumes. Such variations could explain the occurrence of hot spots with widely varying lifetimes and rates of lava production. For highly depleted diapirs with very low Fe/Mg, the diapir would act as a heat source and the asthenosphere and lower lithosphere drifting across the diapir would serve as the source region of magmas erupted at the surface. For mildly depleted diapirs with Fe/Mg only slightly less than in normal undepleted mantle, the diapir could provide not only the source of heat but also most or all of the source material for the erupted magmas. The model is consistent with isotopic data that require two separate and ancient source regions for mid-ocean ridge and oceanic island basalts. The source for mid-ocean ridge basalts is considered to be material upwelling at spreading centers from the deep mantle. This material forms the oceanic lithosphere. Oceanic island basalts are considered to be derived from varying mixtures of sublithospheric and lower lithospheric material and the rising diapir itself.     

Transitions in thermal convection with strongly temperature-dependent viscosity in a wide box

Numerical models are systematically presented for time-dependent thermal convection of Newtonian fluid with strongly temperature-dependent viscosity in a two-dimensional rectangular box of aspect ratio 3 at various values of the Rayleigh number Ra_b defined with viscosity at the bottom boundary up to 1.6×10⁸ and the viscosity contrast across the box r_η up to 10⁸. We found that there are two different series of bifurcations that take place as r_η increases. One series of bifurcations causes changes in the behavior of the thermal boundary layer along the surface boundary from small-viscosity-contrast (SVC) mode, through transitional (TR) mode, to stagnant-lid (ST) mode, or from SVC mode directly to ST mode, depending on Ra_b. Another series of bifurcations causes changes in the aspect ratio of convection cells; convection with an elongated cell can take place at moderate r_η (10³–10^5.5 at Ra_b=6×10⁶), while only convection of aspect ratio close to 1 takes place at small r_η and large r_η. The parameter range of r_η and Ra_b for elongated-cell convection overlaps the parameter range for SVC and ST modes and include the entire parameter range for TR mode. In the elongated-ST regime, the lid of highly viscous fluid along the top boundary is not literally ‘stagnant’ but can horizontally move at a velocity high enough to induce a convection cell with aspect ratio much larger than 1.     

Three-dimensional modelling convection in the earth's mantle: Influence of the core-mantle boundary

Summary Mass heterogeneities in the Earth's mantle are derived from the spherical expansions of the core-mantle boundary topography, the surface topography and the external gravity field. The obtained density distribution provides the body forces driving the convection in the mantle. Assuming Newtonian rheology, the convection is modelled by solving the Stokes problem in the region extending from the top of the D"-layer to the base of the lithosphere. The derived model of mantle motions favours the concept of whole-mantle convection; its pattern connects the shape of the core-mantle boundary with surface tectonics.

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A quantitative kinematic theory of convection currents in the earth's mantle

Summary Based on a system of structurally simple postulations the kinematics of mantle convection is derived. With regard to the strain-stress relations valid in the mantle and the energy source of the convection the theory is without any presumptions. In compliance with recent hydrodynamic investigations the flow is introduced rather as roll currents than as a hexagonal cell pattern. From the feasible types of current a theoretical topography is derived which is in quantitative agreement with the observed one. Also the distribution of the seismic discontinuities substantiates the validity of the expression. Finally, some suggestions are given for a hydrodynamic theory of mantle convection. This paper contains that part of the theory which is necessary for testing the calculations, while the relationship of the theory to other geological and geophysical problems are dealt with by the author [26]²).     

Waves in a viscous fluid on a rotating sphere

Summary In this note the waves in a viscous fluid rotating on a sphere has been studied. The solution contains unknown constants which may be evaluated in particular cases applying the boundary conditions.     

The effect of the earth's rotation on ground water motion

The average pore velocity of ground water according to Darcy's law is a function of the fluid pressure gradient and the gravitational force (per unit volume of ground water) and of aquifer properties. There is also an acceleration exerted on ground water that arises from the Earth's rotation. The magnitude and direction of this rotation-induced force are determined in exact mathematical form in this article. It is calculated that the gravitational force is at least 300 times larger than the largest rotation-induced force anywhere on Earth, the latter force being maximal along the equator and approximately equal to 34 N/m(3) there. This compares with a gravitational force of approximately 10(4) N/m(3).     

A review of: “Geoelectromagnetic investigation of the earth's crust and mantle”

Abstract

By I. I. Rokityansky, 381 pages, Springer-Verlag, Berlin (1982). Price $65.80 ISBN 3 540 10630 8.     

Comparison between two methods of modelling the flow in a mantle with laterally variable viscosity

Summary Two different spectral methods have recently been used to model the flow driven by harmonic loads in a Newtonian mantle with laterally variable viscosity. The first method, by Zhang and Christensen (1993), transforms the problem with a general three-dimensional viscosity into a series of standard spherically symmetric problems. A different approach has been chosen by Martinec et al. (1993). Their method is based on integral formulation of the problem. The solution, which corresponds to a minimum of the dissipative energy, is found by means of the gradient search. We have tested the efficiency and numerical behaviour of both methods. The results of our tests favour the former method which is found more accurate and significantly faster than the gradient algorithm.     

Lateral variation in upper mantle viscosity: role of water

Differences in the viscosity of the earth's upper mantle beneath the western US (∼10¹⁸-10¹⁹ Pa s) and global average values based on glacial isostatic adjustment and other data (∼10²⁰-10²¹ Pa s) are generally ascribed to differences in temperature. We compile geochemical data on the water contents of western US lavas and mantle xenoliths, compare these data to water solubility in olivine, and calculate the corresponding effective viscosity of olivine, the major constituent of the upper mantle, using a power law creep rheological model. These data and calculations suggest that the low viscosities of the western US upper mantle reflect the combined effect of high water concentration and elevated temperature. The high water content of the western US upper mantle may reflect the long history of Farallon plate subduction, including flat slab subduction, which effectively advected water as far inland as the Colorado Plateau, hydrating and weakening the upper mantle.     

The effect of spatial variations in viscosity on the structure of mantle flows

According to an opinion widespread in the literature, high viscosity regions (HVRs) in the mantle always affect the structure of mantle flows, changing it in both the HVR itself and the entire mantle. Moreover, a simplified relation is often adopted according to which the flow velocity in the HVR decreases in inverse proportion to viscosity. Therefore, in order to treat a smoother value, some authors introduce a new variable equal to the product of the flow velocity and the viscosity value in a given place. On the basis of numerical modeling, this paper shows that HVRs of two types should be distinguished in the mantle. If an HVR is immobile, mantle flows actually do not penetrate it. If the viscosity increase is more than five orders, the HVR behaves as a solid and flow velocities within it almost vanish. However, if an HVR is free, it moves together with the mantle flow. Then, the general structure of flows changes weakly and flow velocities within the HVR become approximately equal to the average velocity of flows in the absence of the HVR. Horizontal layers and vertical columns differing in viscosity from the mantle behave as regions of the first type, whose flow velocities can differ by a few orders. However, even such large-scale regions as the continental lithosphere, whose viscosity is four to five orders higher than in the surrounding mantle, float together with continents at velocities comparable to mantle flows, i.e., behave as regions of the second type.     

Convection of a fluid with strongly temperature and pressure dependent viscosity

Plate tectonics on the Earth is a surface manifestation of convection within the Earth’s mantle, a subject which is as yet improperly understood, and it has motivated the study of various forms of buoyancy-driven thermal convection. The early success of the high Rayleigh number constant viscosity theory was later tempered by the absence of plate motion when the viscosity is more realistically strongly temperature dependent, and the process of subduction represents a continuing principal conundrum in the application of convection theory to the Earth. A similar problem appears to arise if the equally strong pressure dependence of viscosity is considered, since the classical isothermal core convection theory would then imply a strongly variable viscosity in the convective core, which is inconsistent with results from post-glacial rebound studies. In this paper we address the problem of determining the asymptotic structure of high Rayleigh number convection when the viscosity is strongly temperature and pressure dependent, i.e. thermobaroviscous. By a method akin to lid-stripping, we are able to extend numerical computations to extremely high viscosity contrasts, and we show that the convective cells take the form of narrow, vertically-oriented fingers. We are then able to determine the asymptotic structure of the solution, and it agrees well with the numerical results. Beneath a stagnant lid, there is a vigorous convection in the upper part of the cell, and a more sluggish, higher viscosity flow in the lower part of the cell. We then offer some comments on the possible meaning and interpretation of these results for planetary mantle convection.     

Exact analytical solutions of the stokes equation for testing the equations of mantle convection with a variable viscosity

Presently, the study of the mantle flow structure is mainly based on numerical modeling. The most important stage of the development of a computer program is its testing. For this purpose, results of various test models of convection flows with a given set of parameters are compared. The solution of the Stokes equation, involving the derivative of viscous stresses, is most difficult. Exact analytical solutions of the Stokes equation are obtained in this work for various cases of special loads. These solutions can be used as benchmarks for testing programs of numerical calculation of viscous flows in both geophysics and engineering. The advantage of this testing technique is the exceptional simplicity of the solution form, the admissibility of any spatial viscosity variations, and the fact that solutions can be compared not for a narrow set of the solution parameters but for any distributions of velocities, viscous stresses, and pressures at all points of the space.     

On heterogeneities with reduced viscosity in the mantle under the Kamchatka volcanoes according to seismological data

A seismological study of the upper mantle under the Kamchatka volcanoes using body waves from nearby earthquakes has shown local heterogencities consisting of materials with reduced elastic properties at depths from 30 to 90 km. The estimated value of the upper limit of viscosity,η, is about 6 × 10²⁰ pois for the material of the mantle aseismic zone under the Kamchatka volcanoes at depths of ～ 70–150 km. It is suggested that the magmatic chambers are rooted in the mantle heterogeneities filled with substance of reduced elasticity and viscosity.     

Horizontal stresses in the mantle and in the moving continent for the model of two-dimensional convection with varying viscosity

Numerical experiments on studying the spatial fields and evolution of viscous overlithostatic horizontal stresses and pressure in the mantle and in the moving continent are carried out. The continent moves consistently with time-dependent forces, which act from the viscous mantle. By introducing the varying viscosity, we gain the possibility for taking into account the oceanic lithosphere and the difference between the viscosity of the upper and the lower mantle in the context of a purely viscous model. The typical overlithostatic horizontal stresses in the main part of the mantle are ±(7–9) MPa (70–90 bar); in the highly viscous regions and, particularly, in the subduction zones they are at least three times larger. The descending mantle flows in the depth interval from approximately 50 km to about 300 km are more sharply pronounced in the pressure field than in the field of horizontal stresses. At the considered stages of motion and in different parts, the continent is characterized by the following typical values of stresses: the overlithostatic pressure ranges from ?5 to +15 MPa; the horizontal overlithostatic tensile stress amounts up to ?4MPa (?40 bar); and the compressive stress in case of the overriding of the subduction zone attains +35 MPa (350 bar).     

Carbonatitic volcanism in the Kaiserstuhl alkaline complex: Evidence for highly fluid carbonatitic melts at the earth's surface

Extrusive carbonatites are described from the Miocene alkaline complex of the Kaiserstuhl, Rhinegraben, Western Germany. Agglutinated carbonatitic lapilli form pyroclastic rocks in which all components show forms acquired when a highly fluid melt was sprayed into the air by an explosive eruption: droplets, spherical and elliptical lapilli, rods, dumbbell and pear-shaped forms.Complete morphological analogies suggest a mechanism similar to the formation of “Pele's tears”, basaltic droplets formed by the eruption of the most fluid Hawaiian basaltic magmas. Evidence is provided by this example that CaCO₃-carbonatitic magmas can exist in nature under surface conditions displaying extremely low viscosity.     

横向黏度变化的全地幔对流应力场初步研究

将地幔地震波速度异常转换为地幔横向黏度变化(达到3个数量级),在球坐标系下计算了瑞雷数为106、上边界为刚性、下边界为应力自由等温边界条件下的岩石层底部的地幔对流极型和环型应力场.结果表明,地幔对流极型应力场与地表大尺度构造具有良好的对应关系:俯冲带和碰撞带的应力呈现挤压状态,而洋中脊处的应力则呈现拉张状态.地幔对流环...     

Peridotites from the southern Mariana forearc: Heterogeneous fluid supply in mantle wedge

Detailed petrological work was carried out on serpentinized peridotite dredged and sampled by submersible from the southern part of the Mariana Trench to reveal the nature of the mantle wedge in the southern Mariana forearc. The southern part of the Mariana Trench is important in that we should expect to find a transect of a typical island arc structure; that is, from east to west, the Mariana forearc, the Mariana arc proper, the Mariana Trough (active back-arc spreading center), and the West Mariana Ridge (remnant arc). The most striking feature of peridotites from the southern part of the trench is that primary hornblende is a major constituent mineral in many specimens. Thus, the peridotite samples are divided into anhydrous (A-type), hydrous (H-type) and intermediate (I-type) groups. Petrological data suggest that each type of peridotite is a residue of extensive partial melting in the upper mantle. It is argued here that the I- and H-type peridotites were modified from `proto-A-type peridotite' by fluid infiltration. The fluid was enriched in Al, Ti, Fe, and alkalis, and may have caused changes in mineral and bulk chemical compositions of the peridotites. A-type peridotite derives from the `proto-A-type peridotite' directly, without any fluid contamination. After the formation of the `proto-A-, I-, and H-type peridotites', lower-temperature fluids, probably of seawater origin, produced retrograde metamorphism and alteration including serpentinization. The mantle wedge in the southern Mariana forearc was heterogeneous in fluid supply.