Plateness of the Oceanic Lithosphere and the Thermal Evolution of the Earth’s Mantle (original) (raw)
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Generation of plate-tectonic behavior and a new viscosity profile of the Earth's mantle
U. Walzer, R. Hendel, and J. Baumgardner. Generation of plate-tectonic behavior and a new viscosity profile of the Earth's mantle. In D. Wolf, G. Münster, and M. Kremer, editors, NIC Symposium, volume 20 in NIC Series, pages 419-428, Jülich, 2003b. Generation of Plate-Tectonic Behavior and a New Viscosity Profile of the Earth's Mantle Uwe Walzer1, Roland Hendel1, John Baumgardner2 1 Institut für Geowissenschaften, Friedrich-Schiller-Universität, Burgweg 11, 07749 Jena, Germany 2 Los Alamos National Laboratory, MS B216 T-3, Los Alamos, NM 87545, USA Abstract. This paper reports a series of compressible spherical-shell convection calculations with a new viscosity profile, called eta3 , that is derived from PREM and mineral physics. The viscosity profile displays not only a high-viscosity lithosphere and a viscosity hill in the central region of the lower mantle of the Earth but also a prominent high-viscosity transition layer inferred to arise from a high garnet content. Moreo...
Continental Growth and Thermal Convection in the Earth’s Mantle
High Performance Computing in Science and Engineering ’06, 2007
The main subject of this paper is the numerical simulation of the chemical differentiation of the Earth's mantle. This differentiation induces the generation and growth of the continents and, as a complement, the formation and augmentation of the depleted MORB mantle. Here, we present for the first time a solution of this problem by an integrated theory in common with the problem of thermal convection in a 3-D compressible spherical-shell mantle. The whole coupled thermal and chemical evolution of mantle plus crust was calculated starting with the formation of the solid-state primordial silicate mantle. No restricting assumptions have been made regarding number, size and form of the continents. It was, however, implemented that moving oceanic plateaus touching a continent are to be accreted to this continent at the corresponding place. The model contains a mantle-viscosity profile with a usual asthenosphere beneath a lithosphere, a highly viscous transition zone and a second low-viscosity layer below the 660-km mineral phase boundary. The central part of the lower mantle is highly viscous. This explains the fact that there are, regarding the incompatible elements, chemically different mantle reservoirs in spite of perpetual stirring during more than 4.49 × 10 9 a. The highly viscous central part of the lower mantle also explains the relatively slow lateral movements of CMB-based plumes, slow in comparison with the lateral movements of the lithospheric plates. The temperature-and pressure-dependent viscosity of the model is complemented by a viscoplastic yield stress, σy. The paper includes a comprehensive variation of parameters, especially the variation of the viscosity-level parameter, rn, the yield stress, σy, and the temporal average of the Rayleigh number. In the rn-σy plot, a central area shows runs with realistic distributions and sizes of continents. This area is partly overlapping with the rn-σy areas of piecewise plate-like movements of the lithosphere and of realistic values of the surface heat flow and Urey number. Numerical problems are discussed in Section 3.
The effects of a variation of the radial viscosity profile on mantle evolution
Tectonophysics, 2004
The present paper describes a set of numerical experiments on the mantle's thermal evolution with an infinite Prandtl number fluid in a compressible spherical shell heated mainly from within. We used the anelastic liquid approximation with Earth-like material parameters. The usual variable-viscosity approach in mantle-convection models is the assumption of a temperature dependence only. The resulting thermal boundary layers are included in our model also, but an additional viscosity profile of the interior mantle was derived: The Birch -Murnaghan equation was employed to derive the Grüneisen parameter and other physical quantities as a function of depth from observational values provided by PREM. We computed the melting temperature and a new mantle viscosity profile, called eta3, using the Grüneisen parameter, Lindemann's law and some solid-state physics considerations. The new features of eta3 are a high-viscosity transition layer with rather high viscosity gradients at its boundaries, a second lowviscosity layer beginning under the 660-km discontinuity, and a strong viscosity increase in the central parts of the lower mantle. The rheology is Newtonian but it is supplemented by a viscoplastic yield stress, r y . A viscosity-level parameter, r n , and r y have been varied. For a medium-sized Rayleigh-number -yield-stress area, eta3 generates a stable, plate-tectonic behavior near the surface and simultaneously thin sheet-like downwellings in the depth. Outside this area, three other types of solution were found. Not only the planforms but also the evolution of the Rayleigh number, the reciprocal Urey number, the Nusselt number, the surface heat flow, etc., have been studied. We repeated this investigation with two very different basic viscosity profiles, etaKL5a and etaKM, of other authors. A comparison reveals that eta3 facilitates the generation of surface plates and thin sheet-like downwellings in the depth considerably more than etaKL5a or even etaKM. The presence of two internal low-viscosity layers is obviously conducive for plateness and thin sheet-like downwellings. For an infinite yield stress, the thin cold sheet-like downwellings are reticularly connected. However, the distribution of the downwellings is more Earth-like if a realistic yield stress is added. D
Toward a Thermochemical Model of the Evolution of the Earth’s Mantle
High Performance Computing in Science and Engineering’ 04, 2005
ive to variations of the Rayleigh number and of the thermal boundary condition at CMB. The different parts of this paper are closely connected by the algorithm. The continuation of the first finding leads to a 3-D, up to now purely thermal model of mantle evolution and plate generation. This second model was used to carry out a series of three-dimensional compressible spherical-shell convection calculations with another new, but related viscosity profile, called eta3, that is derived from PREM and mineral physics, only. Here, the Birch-Murnaghan equation was used to derive the Grüneisen parameter as a function of depth. Adding the pressure dependence of the thermal expansion coefficient of mantle minerals, we derived the specific heats, cp and cv, too. Using the Gilvarry formulation, we found a new melting temperature of the mantle and the new viscosity profile, eta3. The features of eta3 are a highviscosity transition layer, a second low-viscosity layer beginning under the 660-km discontinuity, and a strong viscosity maximum in the central parts of the lower mantle. The rheology is Newtonian but it is supplemented by a viscoplastic yield stress, σy. A viscosity-level parameter, rn, and σy have been varied. For a medium-sized Rayleigh-number-yield-stress area, eta3 generates a stable, plate-tectonic behavior near the surface and simultaneously thin sheet-like downwellings in the depth. Outside this area three other types of solution were found. The presence of two internal low-viscosity layers and of σy is obviously conducive for plateness and thin sheet-like downwellings. The distribution of the downwellings is more Earth-like if the yield stress is added. The outlines of a combination of the two models have been discussed.
Variation of Non-Dimensional Numbers and a Thermal Evolution Model of the Earth’s Mantle
High Performance Computing in Science and Engineering ’02, 2003
A 3-D compressible spherical-shell model of the thermal convection in the Earth's mantle has been investigated with respect to its long-range behavior. In this way, it is possible to describe the thermal evolution of the Earth more realistically than by parameterized convection models. The model is heated mainly from within by a temporally declining heat generation rate per volume and, to a minor degree, from below. The volumetrically averaged temperature, Ta, diminishes as a function of time, as in the real Earth. Therefore, the temperature at the core-mantle boundary, TCMB,av, has not been kept constant but the heat flow, in accord with Stacey (1992). Therefore, TCMB,av decreases like Ta. This procedure seems to be reasonable since evidently nobody is able to propose a comprehensible thermostatic mechanism for CMB. First of all, a radial distribution of the starting viscosity has been derived using PREM and solid-state physics. The time dependence of the viscosity is essential for the evolution of the Earth since the viscosity rises with declining temperature. For numerical reasons, the temperature-dependent factor of the model viscosity is limited to four orders of magnitude.
Journal of Geophysical Research, 1998
A more general expression for the mantle vorticity equation is proposed for convection using axisymmetrical spherical geometry. Both the main mantle phase changes and radial and lateral variations of viscosity due to temperature and pressure. Four series of computations have been performed with (1) both the latent heat releases of the 400 km exothermic and the 670 km endothermic ph .ase change and uniform and constant mantle viscosity; (2) the 670 km phase change alone and viscosity jumps of 10 or 30 between upper and lower mantle phases; (3) the 670 km endothermic phase change, a viscosity contrast of 30, and temperature and pressure dependent viscosity law; and (4) both 400 km and 670 km phase changes, a viscosity jump of 30, and a temperature and pressure dependent viscosity. The 400 km exothermic phase change modifies the global structure from partly layered to whole mantle convection. This effect is opposite to the effect obtained by increasing the viscosity jump at 670 km. However, both effects induce unrealistic thermal behavior which will not appear with temperature dependent laws for viscosity. The mantle avalanches which suddenly inject huge quantities of cold material into the lower mantle have effects at the surface and at the coremantle boundary (CMB). They induced heat flow crises which explain the huge volcanic events, high rates of mid-oceanic ridge accretion, and periods of low-frequency magnetic reversal. The surface heat flow proceeds directly from the upper mantle return flow along with the avalanches. The temperature dependent viscosity tends to decrease the strength of the avalanches. The bottom heat flow and the birth of CMB plumes may be considered as the consequences of cold upper mantle material arrival at the CMB. The lower mantle and the upper mantle transit times depend on the thickness of upper and lower mantles but also on the phase changes and on the viscosity. The CMB and surface perturbations may be simultaneous (to a few tens of million years).The temporal evolution of the convection pattern during an avalanche allows us to propose self-consistent mechanisms for slab migration above the 670 km discontinuity for the birth and disappearance of ridges, the rising of powerful plumes from the CMB, and the creation of low-viscosity zones which may act as a lubricant under continents for fast migration. These results show that the main mantle phase changes, combined with temperature and pressure dependent viscosity, induce convective behavior which provides an explanation for most of the past and present large-scale dynamic behavior of the Earth's global tectonics. equations (including the thermal equation). In the first approach, the density anomalies of kinematic models are computed from lateral seismic velocity anomalies which may be considered as a rough map of the lateral thermal variations within the mantle. From the first generation of these dynamic models [see, e.g., Richards and Hager, 1984; Ricard et al., 1984] to the most recent models, several improvements have been taken into account such as the compressibility of mantle [Thoraval et al., 1994], the motion of surface plates [e.g., Ricard and Vigny, 1989], and the effects of the main mantle discontinuities [Thoraval et al., 1995]. In spite of a still present debate about the amplitude of the dynamic surface topography, these kinematic models mainly agree that an abrupt mantle viscosity jump of about 30 between the upper and the lower mantles is required to retrieve the main pattern of the geoid. The second approach consists of solving the full set of convection equations. This allows us to gain information about the temporal behavior of the mantle and therefore about the thermal evolution of the Earth. Recently, these models have proved the chaotic behavior of mantle convection which prevents geophysicists from retrieving the exact pattern of temperature within the mantle [Machetel and Yuen, 1986, 1989]. However, this approach is able to check the geophysical relevance of the main model assumptions. 4929 4930 BRUNET AND MACHETEL: MANTLE CONVECFION AND LARGE-SCALE 2F_,C-TONIC Christensen and Yuen [1984, 1985] were the first to compute the embedding behavior of the endothermic phase change. New interest has been stimulated with the work by Machetel and Weber [1991], which showed that an intermittent layering, punctuated by sudden avalanches of upper mantle material sinking deeply and rapidly into the lower mantle, may be the prevailing regime within the mantle. This behavior, which allows us to reconcile most of the geophysical arguments in favor of either a whole mantle or a layered convection, is closely related to the negative Clapeyron slope of the 670 km depth phase change. Since then a number of studies have been devoted to this question. The effects of the 670 km endothermic phase change on the structure of mantle convection have been widely documented by numerical models. They have been run in twoand three-dimensional (2-D and 3-D) Cartesian geometry [i.e., Steinbach and Yuen, 1992; Honda et al., 1993; Steinbach and Yuen, 1994; Yuen et al., 1995] and in spherical geometry with the axisymmetrical assumption [Machetel and Weber, 1991; Peltier and Solheim, 1992; Bercovici et al., 1993; Machetel, 1993; Solheim and Peltier, 1994a,b] and with full 3-D 15917, 1994.
Journal of Geophysical Research, 1997
We present new inferences of the radial profile of mantle viscosity that simultaneously fit long-wavelength free-air gravity harmonics associated with mantle convection and a large set of decay times estimated from the postglacial uplift of sites within previously glaciated regions (Hudson Bay, Arctic Canada, and Fennoscandia). The relative sea level variation at these latter sites is constrained by age-height pairs obtained by geological survey, rather than the subjective trends which are commonly used in glacial isostatic adjustment (GIA) studies.
A simple global model of plate dynamics and mantle convection
Journal of Geophysical Research, 1981
Cooling and thickening of lithospheric plates with age and subduction result in large-scale horizontal density contrasts tending to drive plate motions and mantle flow. We quantify the driving forces associated with these density contrasts to determine if they can drive the observed plate motions. First, twodimensional models are computed to evaluate the effects of assumed rheologies and boundary conditions. We are unable to obtain platelike behavior in viscous models with traction-free boundary conditions. The piecewise uniform velocities distinctive of plate motion can be imposed as boundary conditions and the dynamic consistency of the models evaluated by determining if the net force on each vanishes. If the lithosphere has a Newtonian viscous rheology, the net force on any plate is a strong/•/•,,ction of the effective grid spacing used, leading to ambiguities in interpretation. Incorporating a rigid-plastic lithosphere, which fails at a critical yield stress, into the otherwise viscous model removes these ambiguities. The model is extended to the actual three-dimensional (spherical) plate geometry. The observed velocities of rigid-plastic plates are matched to the solution of the viscous Stokes equation at the lithosphere-asthenosphere boundary. Body forces from the seismically observed slabs, from the thickening of the lithosphere obtained from the actual lithospheric ages, and from the differences in structure between continents and oceans are included. Interior density contrasts such as those resulting from upwellings from a hot bottom boundary layer are assumed to occur on a scale small compared to plate dimensions and are not included. The driving forces from the density contrasts within the plates are calculated and compared to resisting forces resulting from viscous drag computed from the three-dimensional global return flow and resistance to deformation at converging boundaries; the rms residual torque is -•30% of the driving torque. The density contrasts within the plates themselves can reasonably account for plate mo-
The thermal evolution of an Earth with strong subduction zones
Geophysical Research Letters, 1999
It is commonly supposed that plate tectonic rates are controlled by the temperature-dependent viscosity of Earth's deep interior. If this were so, a small decrease in mantle temperature would lead to a large decrease in global heat transport. This negative feedback mechanism would prevent mantle temperatures from changing rapidly with time. We propose alternatively that convection is primarily resisted by the bending of oceanic lithosphere at subduction zones. Because lithospheric strength should not depend strongly on interior mantle temperature, this relationship decreases the sensitivity of heat flow to changes in interior mantle viscosity, and thus permits more rapid temperature changes there. The bending resistance is large enough to limit heat flow rates for effective viscosities of the lithosphere greater than about 1023 Pa s, and increases with the cube of plate thickness. As a result, processes that affect plate thickness, such as small-scale convection or subduction initiation, could profoundly influence Earth's thermal history.
Using thermo-mechanical models of subduction to constrain effective mantle viscosity
Earth and Planetary Science Letters, 2020
Mantle convection and plate dynamics transfer and deform solid material on scales of hundreds to thousands of km. However, viscoplastic deformation of rocks arises from motions of defects at subcrystal scale, such as vacancies or dislocations. In this study, results from numerical experiments of dislocation dynamics in olivine for temperatures and stresses relevant for both lithospheric and asthenospheric mantle (800-1700 K and 50-500 MPa; Gouriet et al., 2019) are used to derive three sigmoid parameterizations (erf, tanh, algebraic), which express stress evolution as a function of temperature and strain rate. The three parameterizations fit well the results of dislocation dynamics models and may be easily incorporated into geodynamical models. Here, they are used in an upper mantle thermo-mechanical model of subduction, in association with diffusion creep and pseudo-brittle flow laws. Simulations using different dislocation creep parameterizations exhibit distinct dynamics, from unrealistically fast-sinking slabs in the erf case to very slowly-sinking slabs in the algebraic case. These differences could not have been predicted a priori from comparison with experimentally determined mechanical data, since they principally arise from feedbacks between slab sinking velocity, temperature, drag, and buoyancy, which are controlled by the strain rate dependence of the effective asthenosphere viscosity. Comparison of model predictions to geophysical observations and to uppermantle viscosity inferred from glacial isostatic adjustment shows that the tanh parameterization best fits both crystal-scale and Earth-scale constraints. However, the parameterization of diffusion creep is also important for subduction bulk dynamics since it sets the viscosity of slowly deforming domains in the convecting mantle. Within the range of uncertainties of experimental data and, most importantly, of the actual rheological parameters prevailing in the upper mantle (e.g. grain size, chemistry), viscosity enabling realistic mantle properties and plate dynamics may be reproduced by several combinations of parameterizations for different deformation mechanisms. Deriving mantle rheology cannot therefore rely solely on the extrapolation of semi-empirical flow laws. The present study shows that thermo-mechanical models of plate and mantle dynamics can be used to constrain the effective rheology of Earth's mantle in the presence of multiple deformation mechanisms.