Kinematic models of large-scale flow in the Earth's mantle (original) (raw)
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Mantle flow and the evolution of the lithosphere
Physics of the Earth and Planetary Interiors, 1993
The evolution of the lithosphere is mainly controlled by time-dependent forces due to (1) plate tectonic processes and (2) sublithospheric mantle flow. Plate tectonic processes like continental collision may provide strong thermal disturbances and, after completion, may trigger secondary convection beneath the lithosphere. Without such mantle flows lateral variations of temperature (and associated variations of lithospheric thickness hL or seismic velocities) will equilibrate after time scales which are considerably shorter than the geologic ages of several provinces in Europe.
Geophysical Journal International, 2006
Modelling the geoid has been a widely used and successful approach in constraining flow and viscosity in the Earth's mantle. However, details of the viscosity structure cannot be tightly constrained with this approach. Here, radial viscosity variations in four to five mantle layers (lithosphere, upper mantle, one to two transition zone layers, lower mantle) are computed with the aid of independent mineral physics results. A density model is obtained by converting s-wave anomalies from seismic tomography to density anomalies. Assuming both are of thermal origin, conversion factors are computed based on mineral physics results. From the density and viscosity model, a model of mantle flow, and the resulting geoid and radial heat flux profile are computed. Absolute viscosity values in the mantle layers are treated as free parameters and determined by minimizing a misfit function, which considers fit to geoid, 'Haskell average' determined from post-glacial rebound and the radial heat flux profile and penalizes if at some depth computed heat flux exceeds the estimated mantle heat flux 33 TW. Typically, optimized models do not exceed this value by more than about 20 per cent and fit the Haskell average well. Viscosity profiles obtained show a characteristic hump in the lower mantle, with maximum viscosities of about 10 23 Pa s just above the D layer-several hundred to about 1000 times the lowest viscosities in the upper mantle. This viscosity contrast is several times higher than what is inferred when a constant lower mantle viscosity is assumed. The geoid variance reduction obtained is up to about 80 per cent-similar to previous results. However, because of the use of mineral physics constraints, a rather small number of free model parameters is required, and at the same time, a reasonable heat flux profile is obtained. Results are best when the lowest viscosities occur in the transition zone. When viscosity is lowest in the asthenosphere, variance reduction is about 70-75 per cent. Best results were obtained with a viscous lithosphere with a few times 10 22 Pa s. The optimized models yield a core-mantle boundary excess ellipticity several times higher than observed, possibly indicating that radial stresses are partly compensated due to non-thermal lateral variations within the lowermost mantle.
1992
The impact of lateral variations in the thickness of the lithosphere on surface topography, horizontal intraplate deformation and stress accumulation is studied for plates that drift with respect to the highly viscous lower mantle and the transition zone. The lithosphere and upper mantle are described by a viscoelastic Maxwell rheology within the framework of a finite element scheme which allows the modeling of heterogeneous lithospheric structures in 2D vertical cross sections. The geophysical signatures are found to be extremely sensitive to lateral viscosity contrasts which interact with the upper mantle flow. This mechanism can contribute to a certain extent and in concert with the other driving forces of plate tectonics to the evolution of back-arc basins, to the explanation of the largest angle of subduction in west-dipping slabs and to the initiation of subduction of an oceanic lithosphere underneath a stable continental one.
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-
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.
The effect of spatial variations in viscosity on the structure of mantle flows
Izvestiya, Physics of the Solid Earth, 2006
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.
The viscosity of Earth’s lower mantle inferred from sinking speed of subducted lithosphere
Physics of the Earth and Planetary Interiors, 2012
The viscosity of the mantle is indispensable for predicting Earth's mechanical behavior at scales ranging from deep mantle material flow to local stress accumulation in earthquakes zones. But, mantle viscosity is not well determined. For the lower mantle, particularly, only few constraints result from elaborate high-pressure experiments (Karato, 2008) and a variety of viscosity depth profiles result from joint inversion of the geoid and postglacial rebound data . Here, we use inferred lower-mantle sinking speed of lithosphere subduction remnants as a unique internal constraint on modeling the viscosity profile. This entails a series of elaborate dynamic subduction calculations spanning a range of viscosity profiles from which we select profiles that predict the inferred sinking speed of 12 ± 3 mm/yr . Our modeling shows that sinking speed is very sensitive to lower mantle viscosity. Good predictions of sinking speed are obtained for nearly constant lower mantle viscosity of about 3-4 Â 10 22 Pa s. Viscosity profiles incorporating a viscosity maximum in the deep lower mantle, as proposed in numerous studies, only lead to a good prediction in combination with a weak postperovskite layer at the bottom of the lower mantle, and only for a depth average viscosity of 5 Â 10 22 Pa s.
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...
Tectonophysics, 2017
Earth's continents drift in response to the force balance between mantle flow and plate tectonics and actively change the plate-mantle coupling. Thus, the patterns of continental drift provide relevant information on the coupled evolution of surface tectonics, mantle structure and dynamics. Here, we investigate rheological controls on such evolutions and use surface tectonic patterns to derive inferences on mantle viscosity structure on Earth. We employ global spherical models of mantle convection featuring self-consistently generated plate tectonics, which are used to compute time-evolving continental configurations for different mantle and lithosphere structures. Our results highlight the importance of the wavelength of mantle flow for continental configuration evolution. Too strong short-wavelength components complicate the aggregation of large continental clusters, while too stable very long wavelength flow tends to enforce compact supercontinent clustering without reasonable dispersal frequencies. Earth-like continental drift with episodic collisions and dispersals thus requires a viscosity structure that supports long-wavelength flow, but also allows for shorter-wavelength contributions. Such a criterion alone is a rather permissive constraint on internal structure, but it can be improved by considering continental-oceanic plate speed ratios and the toroidal-poloidal partitioning of plate motions. The best approximation of Earth's recent tectonic evolution is then achieved with an intermediate lithospheric yield stress and a viscosity structure in which oceanic plates are ∼10 3 × more viscous than the characteristic upper mantle, which itself is ∼100-200× less viscous than the lowermost mantle. Such a structure causes continents to move on average ∼(2.2 ± 1.0)× slower than oceanic plates, consistent with estimates from present-day and from plate reconstructions. This does not require a low viscosity asthenosphere globally extending below continental roots. However, this plate speed ratio may undergo strong fluctuations on timescales of several 100 Myr that may be linked to periods of enhanced continental collisions and are not yet captured by current tectonic reconstructions.
Journal of Geophysical Research, 1978
Fully two-dimensional analytic boundary layer solutions are used to model the thermomechanicai structure of the oceanic upper mantle when a shallow horizontal return flow helps balance the lithospheric transport of mass from ridge to trench. The following are all incorporated in the solutions: horizontal and vertical advection of heat, vertical heat conduction, viscous dissipation, adiabatic heating and cooling, buoyancy, and the pressure-and temperature-dependent nonlinear rheology of olivine. Depth profiles of horizontal and vertical velocities, temperature, and shear stress are calculated for several ages of the ocean floor. Such solutions are used to construct accurate isotherm and streamline patterns within the rigid lithosphere and high-shear, return flow asthenosphere of the oceanic upper mantle boundary layer. Ocean floor topography is inferred from the thermal contraction of the cooling lithosphere and asthenosphere and from the adverse horizontal pressure gradient required by the dynamics to drive the shallow return flow. The flattening of the topography of the old ocean floor can be attributed to the retardation of boundary layer cooling by shear heating and/or to the adverse pressure gradient of a shallow return flow. The latter effect would be dominant if a shallow return flow did occur in the earth's upper mantle. Solutions which provide adequate fits to the ocean floor bathymetry data for the Pacific Plate can be found if the activation yolume for the creep of olivine is small, i.e., about 11 cma/mol, and if the deep mantle temperature T is high, i.e., if T is about 1500øC at depths of 100-200 km (depending on age) for dry olivine or about 1400øC at similar depths for wet olivine. The upper mantle temperatures required for a shallow return flow to be compatible with bathymetry data imply partial melting in the lower lithosphere and upper asthenosphere from the ridge axis to ages of about 10 m.y. Shear stresses at the base of the rigid lithosphere generally range from about 1 to several tens of bars, and horizontal adverse pressure gradients at great depth vary from about 10 to 100 mbar/km for wide variations in the extent of return flow and d•ep mantle temperature. For a relatively cold deep mantle, shear stresses in the lower lithosphere and asthenosphere decrease almost linearly with depth, implying horizontal pressure gradients essentially constant with depth. For a hot deep mantle, shear stress versus depth profiles show curvature in the lower lithosphere and upper asthenosphere and a linearly decreasing pattern at greater depths. Under such circumstances, horizontal pressure gradients exhibit considerable depth variation including the possibility of a reversal in sign between the top and the bottom of the asthenosphere.