Mantle plumes control magnetic reversal frequency

Magnetic reversal frequency correlates inversely with mantle plume activity for the past 150 Ma, as measured by the volume production rate of oceanic plateaus, seamount chains, and continental flood basalts. This inverse correlation is especially striking during the long Cretaceous magnetic normal “superchron”, when mantle plume activity was at a maximum. We suggest that mantle plumes control magnetic reversal frequency by the following sequence of events. Mantle plumes rise from theD″ seismic layer just above the core/mantle boundary, thinningD″ to fuel the plumes. This increases core cooling by allowing heat to be conducted more rapidly across the core/mantle boundary. Outer core convective activity then increases to restore the abnormal heat loss, causing a decrease in magnetic reversal frequency in accord with model predictions for bothα² andαω dynamos. When core convective activity increases above a critical level, a magnetic superchron results. The pulse of plume activity that caused the Cretaceous superchron resulted in a minimum increase in core heat loss of about 1200 GW over the present-day level, which corresponds to an increase in Joule heat production of about 120 GW within the core.     

Homogenization of the mantle by convective mixing and diffusion

Mantle convection stirs and homogenizes the subducted oceanic lithosphere with the convecting mantle. Convective mixing stretches and thins the subducted oceanic crust from an original thickness of 6 km to a thickness of 2 cm or less. The thinned, subducted oceanic crust can be observed as pyroxenite bands in high-temperature peridotite massifs. On the scale of centimeters, the bands are destroyed by diffusive processes. In this paper, the homogenization of the subducted oceanic crust with the depleted mantle is modeled by considering the combined problem of thinning and diffusion at a stagnation point. A layer of different composition from the surrounding material is thinned by normal strain until its identity is destroyed by diffusive processes. Thinning dominates the destruction of a layer if a²/D< 1, where is the strain rate, 2a is the initial layer thickness, and D is the diffusivity. Diffusion dominates if a²/D< 1. Our results indicate that the mantle is homogeneous at the centimeter scale. This conclusion is insensitive to variations in the strain rate and the diffusivity, and it is supported by isotopic studies of high-temperature peridotite massifs. Variations in isotope ratios in MORB can be attributed to the imperfect homogenization of the MORB source region.     

Topography on the D′′ region from analysis of a thin dense layer beneath a convecting cell

In this study, we examine the development of topography on a thin dense layer at the base of the lower mantle. The effect of the convecting mantle above is represented as a traction acting on the upper surface of the layer. Topography on the layer boundaries is predicted by a balance of dynamic flow stress and external traction. The nature of boundary topography depends on the magnitude of the driving tractions and the density variation within the layer. If we assume that the layer density is greatest beneath areas of mantle downwelling and decreases to a minimum beneath areas of mantle upwelling (the layer is thermally coupled to the convection in the overlying mantle) then its upper boundary develops a cusp-like peak beneath the upwelling mantle. The height of this peak is potentially much greater than the layer thickness. If, however, the layers are effectively coupled by viscous shear then internal density gradients of the opposite sign may be established. In this case, we observe solutions where the layer is completely swept away beneath areas of mantle downwelling leaving steep-sided ‘islands’ of dense material. This mechanism therefore provides a possible explanation for steep-sided anomalously slow regions at the base of the mantle observed by seismic methods (e.g. beneath south Africa) or for discrete ultralow velocity zones detected at the core-mantle boundary beneath locations of surface hotspots. The magnitude of the upper boundary driving tractions compared to the density gradient within the layer is the key parameter that determines the nature of flow in, and consequently boundary topography of, the layer. The deflection of the core-mantle boundary is small compared with that of the top of the dense layer, but a change in sign of the ratio of these deflections is observed as the magnitude of the driving tractions changes relative to the magnitude of the internal density gradient. We compare seismic measurements of core-mantle boundary topography and D′′ topography with the predictions of this model in an attempt to constrain model parameters, but no clear correlation seems to exist between D′′ thickness and CMB topography.     

On the rise of strongly tilted mantle plume tails

The rise of an initially horizontal, buoyant cylinder of fluid through a denser fluid at low Reynolds number is used to look at the ascent of strongly tilted mantle plumes through the mantle. Such ascents are characterized by (1) the growth of instabilities and (2) the development of a thermal wake downstream. Three-dimensional numerical experiments were carried out to examine these features. An hybrid particle-in-cell finite element method was used to look at the rise of non-diffusing cylinders and, a standard finite element method was used to look at the diffusing case. First the experiments show that the timescale of the fastest growing instability vary with the Rayleigh number and the viscosity ratio. In particular the growth rate decreases as the Rayleigh number decreases, in agreement with our analysis of the laboratory experiments of Kerr et al. (2008). Second the experiments show that the length of the thermal wake increases with the Rayleigh number but the change in viscosity has almost no influence on the wake length. Applied to strongly tilted mantle plumes we conclude that such plumes cannot be unstable given the plume timescales. We also discuss the application of this conclusion to weakly tilted plumes. Besides, this study allows to predict that mantle plumes are unlikely to have developed a significant thermal wake by the time they reach the surface. Finally, the resolution that is required to allow for the growth of mantle plume tails by combined diffusion and thermal entrainment is shown to represent a challenge for the large scale mantle convection simulations.     

Heat transport by variable viscosity convection and implications for the Earth's thermal evolution

The case is presented that the efficiency of variable viscosity convection in the Earth's mantle to remove heat may depend only very weakly on the internal viscosity or temperature. An extensive numerical study of the heat transport by 2-D steady state convection with free boundaries and temperature dependent viscosity was carried out. The range of Rayleigh numbers (Ra) is 10⁴?10⁷ and the viscosity contrast goes up to 250000. Although an absolute or relative maximum of the Nusselt number (Nu) is obtained at long wavelength in a certain parameter range, at sufficiently high Rayleigh number optimal heat transport is achieved by an aspect ratio close to or below one. The results for convection in a square box are presented in several ways. With the viscosity ratio fixed and the Rayleigh number defined with the viscosity at the mean of top and bottom temperature the increase of Nu with Ra is characterized by a logarithmic gradient β = ?ln(Nu)/? ln(Ra) in the range of 0.23–0.36, similar to constant viscosity convection. More appropriate for a cooling planetary body is a parameterization where the Rayleigh number is defined with the viscosity at the actual average temperature and the surface viscosity is fixed rather than the viscosity ratio. Now the logarithmic gradient β falls below 0.10 when the viscosity ratio exceeds 250, and the velocity of the surface layer becomes almost independent of Ra. In an end-member model for the Earth's thermal evolution it is assumed that the Nusselt number becomes virtually constant at high Rayleigh number. In the context of whole mantle convection this would imply that the present thermal state is still affected by the initial temperature, that only 25–50% of the present-day heat loss is balanced by radiogenic heat production, and the plate velocities were about the same during most of the Earth's history.     

Deconvolution of overcritical P-wave reflections from the top of D″

We have developed a method to retrieve overcritical PdP reflections from the top of D″ from the data. The differential travel-time, amplitude ratio and phase advance of the reflected PdP waveform relative to the direct P waveform are accurately obtained. Kirchhoff synthetics have been used to model the reflected waveforms for a set of different incidence angles i and velocity contrasts δα at the reflector which were then used as reference wavelets for the deconvolution.The results from a Gräfenberg data set differ markedly from the values predicted by the one-dimensional PWDK model derived from the same data. However, there are large uncertainties in i and δα. This could be caused by the presence of significant lateral heterogeneity in D″ or the need to model other phases which may exist such as the diving waves PDP and PDDP. The method is also applied to two other data examples. The trade-offs between different model parameters are examined.     

Viscous entrainment by sinking plumes

Geochemical models invoking several distinct reservoirs in the mantle, with different time histories, raise important questions about the exchange of mass between them. If two of these reservoirs are the upper and lower mantle, above and below about 700 km, then sinking of cold slabs through this level is one of a number of possible ways in which mixing can occur. In addition, if slabs do penetrate the transition zone, surrounding upper layer material will be dragged downwards. We have examined the interaction of very viscous plumes, or slabs, with density and viscosity interfaces in a series of laboratory experiments using fluids of different viscosities and densities and have documented several mechanisms which can lead to significant entrainment and mixing. If a slab remains planar as it passes through a density interface, a boundary layer of lighter fluid is pulled into the lower layer and we predict the consequent mass flux. When a near-vertical slab becomes unstable to folding (as it does if it has a sufficient viscosity contrast with its surroundings and its length is greater than about five times its thickness), there is another more efficient entrainment mechanism: upper layer fluid is trapped between the folds in the slab. The effective entrainment increases as the density difference between the upper and lower layers decreases. An increase in viscosity with depth also leads to buckling instability and folding of the surrounding material into the slab material. On the other hand, when there is substantial density difference between the layers a dense slab can cease to sink through the interface but spread out along the interface because it is unstable and incorporates enough upper layer fluid between its folds to become neutrally buoyant. The range of slab behaviour occurring in the mantle is not known but we draw attention to the various possibilities and to the implications for mass flux between layers.     

A benchmark comparison of numerical methods for infinite Prandtl number thermal convection in two-dimensional Cartesian geometry

Abstract

A comparison is made between seven different numerical methods for calculating two-dimensional thermal convection in an infinite Prandtl number fluid. Among the seven methods are finite difference and finite element techniques that have been used to model thermal convection in the Earth's mantle. We evaluate the performance of each method using a suite of four benchmark problems, ranging from steady-state convection to intrinsically time-dependent convection with recurring thermal boundary layer instabilities. These results can be used to determine the accuracy of other computational methods, and to assist in the development of new ones.     

Mantle plumes in the models of quasi-turbulent thermal convection

The process of multiple self-nucleation and ascent of mantle plumes is studied in the numerical models of thermal convection. The plumes are observed even in the simplest isoviscous models of thermal convection that leave aside the more complex rheology of the material, thermochemical effects, phase transformations, etc., which, although controlling the features of plumes, are not necessary for their formation. The origin of plumes is mainly due to the instability of the mantle flows at highly intense (low-viscous) thermal convection. At high viscosity, convective flows form regular cells. As viscosity decreases, the ascending and descending flows become narrower and unsteady. At a further decrease in viscosity, the ascending plumes assume a mushroom-like shape and occasionally change their position in the mantle. The lifetime of each flow can attain 100 Ma. Using markers allows visualizing the evolution of the shape of the mantle plumes.     

Rheology of the mantle and tectonics of the oceanic lithospheric plates

The modern concepts of the rheology of viscous mantle and brittle lithosphere, as well as the results of the numerical experiments on the processes in a heated layer with a viscosity dependent on pressure, temperature, and shear stress, are reviewed. These dependences are inferred from the laboratory studies of olivine and measurements of postglacial rebound (glacial isostatic adjustment) and geoid anomalies. The numerical solution of classical conservation equations for mass, heat, and momentum shows that thermal convection with a highly viscous rigid lithosphere develops in the layer with the parameters of the mantle with the considered rheology under a temperature difference of 3500 K, without any special additional conditions due to the self-organization of the material. If the viscosity parameters of the lithosphere correspond to dry olivine, the lithosphere remains monolithic (unbroken). At a lower strength (probably due to the effects of water), the lithosphere splits into a set of separate rigid plates divided by the ridges and subduction zones. The plates submerge into the mantle, and their material is involved in the convective circulation. The results of the numerical experiment may serve as direct empirical evidence to validate the basic concepts of the theory of plate tectonics; these experiments also reveal some new features of the mantle convection. The probable structure of the flows in the upper and lower mantle (including the asthenosphere), which shows the primary role of the lithospheric plates, is demonstrated for the first time.     

Coupled Process Models of Fluid Flow and Heat Transfer in Hydrothermal Systems in Three Dimensions

Geothermal fields and hydrothermal mineral deposits are manifestations of the interaction between heat transfer and fluid flow in the Earth’s crust. Understanding the factors that drive fluid flow is essential for managing geothermal energy production and for understanding the genesis of hydrothermal mineral systems. We provide an overview of fluid flow drivers with a focus on flow driven by heat and hydraulic head. We show how numerical simulations can be used to compare the effect of different flow drivers on hydrothermal mineralisation. We explore the concepts of laminar flow in porous media (Darcy’s law) and the non-dimensional Rayleigh number (Ra) for free thermal convection in the context of fluid flow in hydrothermal systems in three dimensions. We compare models of free thermal convection to hydraulic head driven flow in relation to hydrothermal copper mineralisation at Mount Isa, Australia. Free thermal convection occurs if the permeability of the fault system results in Ra above the critical threshold, whereas a vertical head gradient results in an upward flow field.     

Plume Mode of Thermal Convection in the Earth’s Mantle

In our previous works, based on numerical models, it was shown that under certain conditions a hot material can rise in portions in the tails of thermal mantle plumes. The spectrum of these pulsations can correspond to the observed spectra of catastrophic hotspot eruptions. Since most of the existing numerical models of thermal convection for the mantle of the present Earth do not reveal these pulsations, in this work, we analyze the physical cause and initiation conditions of pulsations of thermal plumes. The results of a numerical solution of the thermal convection equations for a material with varying parameters in the extended Boussinesq approximation are presented. It is shown how the structure of the convection is transformed with the increase of convection intensity. At the Rayleigh numbers Ra > 10⁶, convection becomes unsteady, and the configuration of the ascending and descending flows changes. The new flow emerging at the mantle bottom acquires a mushroom shape with a head and a tail. After the rise of the plume’s head to the surface, the tail remains in the mantle in the form of a quasi-stationary hot steam. It turns out that at Ra ~ 5 × 10⁷, the thermal mantle plume becomes pulsating and its tail is in fact a heated channel through which the hot material rises in successive portions. At the Rayleigh numbers Ra > 5 × 10⁸, the tail of the thermal plume breaks and the plume becomes a regular conveyor of separate ascending portions of the hot material, which are referred to as thermals. Thus, thermal convection with pulsating plumes takes place at the transitional stage from the regime of quasi-stationary plumes to the regime of thermals.     

利用地震层析成像数据计算地幔对流新模型的探讨

假设地幔地震层析成像数据对应的地幔横向不均匀结构是地幔热对流的结果. 将地震层析成像数据转化为地幔温度(或密度)不均匀分布，考虑热流体动力学的三个基本方程，顾及热输运方程中的非线性项，直接将地震层析成像转化的地幔温度不均匀分布作为内部荷载引入基本方程, 反演计算地幔对流. 本文在利用地震层析成像数据计算地幔对流模型的新理论和方法的基础上，用SH12WM13地震层析成像模型数据，计算了全球地幔对流格局. 结果表明，对流格局不仅依赖地震层析成像数据，而且在很大程度上受地幔动力学框架、热动力参数和边界条件的所确定的系统响应函数的影响. 显示了地幔中复杂的对流格局，特别是区域性层状对流以及多层对流环可能在地幔中存在的现象.     

Analysis of tracer tomography using temporal moments of tracer breakthrough curves

Hydraulic/partitioning tracer tomography (HPTT) was recently developed by Yeh and Zhu [Yeh T-CJ, Zhu J. Hydraulic/partitioning tracer tomography for characterization of dense nonaqueous phase liquid source zones, Water Resour Res 2007;43:W06435. doi:10.1029/2006WR004877.] for estimating spatial distribution of dense nonaqueous phase liquids (DNAPLs) in the subsurface. Since discrete tracer concentration data are directly utilized for the estimation of DNAPLs, this approach solves the hyperbolic convection–dispersion equation. Solution to the convection–dispersion equation however demands fine temporal and spatial discretization, resulting in high computational cost for an HPTT analysis. In this work, we use temporal moments of tracer breakthrough curves instead of discrete concentration data to estimate DNAPL distribution. This approach solves time independent partial differential equations of the temporal moments, and therefore avoids solving the convection–dispersion equation using a time marching scheme, resulting in a dramatic reduction of computational cost. To reduce numerical oscillations associated with convection dominated transport problems such as in inter-well tracer tests, the approach uses a finite element solver adopting the streamline upwind Petrov–Galerkin method to calculate moments and sensitivities. We test the temporal moment approach through numerical simulations. Comparing the computational costs between utilizing moments and discrete concentrations, we find that temporal moments significantly reduce the computation time. We also find that tracer moment data collected through a tomographic survey alone are able to yield reasonable estimates of hydraulic conductivity, as indicated by a correlation of 0.588 between estimated and true hydraulic conductivity fields in the synthetic case study.     

A new conceptual model for whole mantle convection and the origin of hotspot plumes

A new conceptual model of mantle convection is constructed for consideration of the origin of hotspot plumes, using recent evidence from seismology, high-pressure experiments, geodynamic modeling, geoid inversion studies, and post-glacial rebound analyses. This conceptual model delivers several key points. Firstly, some of the small-scale mantle upwellings observed as hotspots on the Earth's surface originate at the base of the mantle transition zone (MTZ), in which the Archean granitic continental material crust (TTG; tonalite-trondhjemite-granodiorite) with abundant radiogenic elements is accumulated. Secondly, the TTG crust and the subducted oceanic crust that have accumulated at the base of MTZ could act as thermal or mechanical insulators, leading to the formation of a hot and less viscous layer just beneath the MTZ; which may enhance the instability of plume generation at the base of the MTZ. Thirdly, the origin of some hotspot plumes is isolated from the large low shear-wave velocity provinces (LLSVPs) under Africa and the South Pacific. I consider that the conceptual model explains why almost all the hotspots around Africa are located above the margins of the African LLSVP. Because a planetary-scale trench system surrounding a “Pangean cell” has been spatially stable throughout the Phanerozoic, a large amount of the oceanic crustal layer is likely to be trapped in the MTZ under the Pangean cell. Therefore, under Africa, almost all of the hotspot plumes originate from the base of the MTZ, where a large amount of TTG and/or oceanic crusts has accumulated. This conceptual model may explain the fact that almost all the hotspots around Africa are located on margins above the African LLSVP. It is also considered that some of the hotspot plumes under the South Pacific thread through the TTG/oceanic crusts accumulated around the bottom of the MTZ, and some have their roots in the South Pacific LLSVP while others originate from the MTZ. The numerical simulations of mantle convection also speculate that the Earth's mantle convection is not thermally double-layered at the ringwoodite to perovskite + magnesiowüstite (Rw → Pv + Mw) phase boundary, because of its gentle negative Clapeyron slope. This is in contrast with some traditional images of mantle convection that have independent convection cells between the upper and lower mantle. These numerical studies speculate that the generation of stagnant slab at the base of the MTZ (as seismically observed globally) may not be due to the negative Clapeyron slope, and may instead be related to a viscosity increase (i.e., a viscosity jump) at the Rw → Pv + Mw phase boundary, or to a chemically stratified boundary between the upper and the lower mantle, as suggested by a recent high-pressure experiment.     

From stable dipolar towards reversing numerical dynamos

We are using a three-dimensional convection-driven numerical dynamo model without hyperdiffusivity to study the characteristic structure and time variability of the magnetic field in dependence of the Rayleigh number (Ra) for values up to 40 times supercritical. We also compare a variety of ways to drive the convection and basically find two dynamo regimes. At low Ra, the magnetic field at the surface of the model is dominated by the non-reversing axial dipole component. At high Ra, the dipole part becomes small in comparison to higher multipole components. At transitional values of Ra, the dynamo vacillates between the dipole-dominated and the multipolar regime, which includes excursions and reversals of the dipole axis. We discuss, in particular, one model of chemically driven convection, where for a suitable value of Ra, the mean dipole moment and the temporal evolution of the magnetic field resemble the known properties of the Earth’s field from paleomagnetic data.     

Core–mantle boundary topography as a possible constraint on lower mantle chemistry and dynamics

The origin of large low shear-wave velocity provinces (LLSVPs) in the lowermost mantle beneath the central Pacific and Africa is not well constrained. We explore numerical convection calculations for two proposed hypotheses for these anomalies, namely, thermal upwellings (e.g., plume clusters) and large intrinsically dense piles of mantle material (e.g., thermochemical piles), each of which uniquely affects the topography on Earth's core–mantle boundary (CMB). The thermochemical pile models predict a relatively flat but elevated CMB beneath piles (presumed LLSVPs), with strong upwarping along LLSVP margins. The plume cluster models predict CMB upwarping beneath upwellings that are less geographically organized. Both models display CMB depressions beneath subduction related downwelling. While each of the two models produces a unique, characteristic style of CMB topography, we find that seismic models will require shorter length scales than are currently being employed in order to distinguish between the end-member dynamic models presented here.     

Chaotic axisymmetrical spherical convection and large-scale mantle circulation

This paper presents a study of high Rayleigh number (up to 200 times supercritical) axisymmetrical convection in a spherical shell with an aspect ratio relevant for the Earth's lower mantle. Both bottom-heated and internal heated cases have been considered. Computations have been carried out for an infinite Prandtl number isoviscous fluid with free slip isothermal boundary conditions. The first part of the paper is devoted to the influence of the resolution on the accuracy of the numerical results. It is shown that the resolution strongly influences the onset of time dependence. Recent methods of non-linear physics have been used to prove that the time dependence and the chaotic behaviors of the solutions are real ones. From these results we can confirm that convection is chaotic, in this particular geometry, even for Rayleigh numbers 200 times critical. Aperiodic boundary layer instabilities are found to be incapable of breaking up the large-scale flow, owing to the shear of the global circulation. Spectral analysis of the power associated with the thermal anomalies shows that there is an upward cascade of energy, due to small-scale chaotic instabilities, from l = 2 to l = 4–6 at the bottom boundary, in agreement with new seismic observations at the core-mantle boundary [1–3].     

A matrix-dependent transfer multigrid method for strongly variable viscosity infinite Prandtl number thermal convection

Abstract

We apply a two-dimensional Cartesian finite element treatment to investigate infinite Prandtl number thermal convection with temperature, strain rate and yield stress dependent rheology using parameters in the range estimated for the mantles of the terrestrial planets. To handle the strong viscosity variations that arise from such nonlinear rheology in solving the momentum equation, we exploit a multigrid method based on matrix-dependent intergrid transfer and the Galerkin coarse grid approximation. We observe that the matrix-dependent transfer algorithm provides an exceptionally robust and efficient means for solving convection problems with extreme viscosity gradients. Our algorithm displays a convergence rate per multigrid cycle about five times better than what other published methods (e.g., CITCOM of Moresi and Solomatov, 1995) offer for cases with similar extreme viscosity variation. The algorithm is explained in detail in this paper.

When this method is applied to problems with temperature and strain rate dependent rheologies, we obtain strongly time dependent solutions characterized by episodic avalanching of cold material from the upper boundary layer to the bottom of the convecting domain for a significantly broad range of parameter values. In particular, we observe this behavior for the relatively simple case of temperature dependent Newtonian rheology with a plastic yield stress. The intensity and temporal character of the episodic behavior depends sensitively on the yield stress value. The regions most strongly affected by the yield stress are thickened portions of the cold upper boundary layer which can suddenly become unstable and form downgoing diapirs. These computational results suggest that the finite yield properties of silicate rocks must play a vitally important role in planetary mantle dynamics. Although our example calculations were selected mainly to illustrate the power of our multigrid method, they suggest that many possible exotic behaviors in planetary mantles have yet to be discovered.     

Long wavelength thermal convection between non-conducting boundaries

Non-linear Rayleigh-Bénard convection in a fluid layer is considered as a model of convection in the Earth's upper mantle. Previous studies have shown that when the temperature is held fixed at one of the boundaries of the layer, convection takes place in cells of width of the order of the layer depth or less. We investigate the effects of a different thermal boundary condition, in which the flux of heat is held fixed on both layer boundaries; then if this flux is just greater than that required for the onset of convection, motion takes place on horizontal scales much greater than the layer depth. An analytical treatment of the equations, based on an expansion in the depth-to-width ratio of the cells, shows that cells of a definite horizontal scale are the fastest growing according to linearised theory, but that these cells are unstable to ones of larger wavelength than themselves. Thus the dominant wavelength lengthens with time. The results hold whether the heat flux is generated internally of comes from beneath the layer. These results produce flow patterns similar to those found when the heat flux is much greater than the critical value. The results have important consequences for the understanding of mantle convection.