Paul J. Tackley

A doubling of the post-perovskite phase boundary and structure of the Earth's lowermost mantle.

The thermal structure of the Earths lowermost mantle—the D″ layer spanning depths of ∼2,600–2,900 kilometres—is key to understanding the dynamical state and history of our planet. Earths temperature profile (the geotherm) is mostly constrained by phase transitions, such as freezing at the inner-core boundary or changes in crystal structure within the solid mantle, that are detected as discontinuities in seismic wave speed and for which the pressure and temperature conditions can be constrained by experiment and theory. A recently discovered phase transition at pressures of the D″ layer is ideally situated to reveal the thermal structure of the lowermost mantle, where no phase transitions were previously known to exist. Here we show that a pair of seismic discontinuities observed in some regions of D″ can be explained by the same phase transition as the result of a double-crossing of the phase boundary by the geotherm at two different depths. This simple model can also explain why a seismic discontinuity is not observed in some other regions, and provides new constraints for the magnitude of temperature variations within D″.

Effects of strongly variable viscosity on three‐dimensional compressible convection in planetary mantles

A systematic investigation into the effects of temperature dependent viscosity on three-dimensional compressible mantle convection has been performed by means of numerical simulations in Cartesian geometry using a finite volume multigrid code, with a factor of 1000–2500 viscosity variation, Rayleigh numbers ranging from 105–107, and stress-free upper and lower boundaries. Considerable differences in model behavior are found depending on the details of rheology, heating mode, compressibility, and boundary conditions. Parameter choices were guided by realistic Earth models. In Boussinesq, basally heated cases with viscosity solely dependent on temperature and stress-free, isothermal boundaries, very long wavelength flows (∼25,000 km, assuming the depth corresponds to mantle thickness) with cold plumes and hot upwelling sheets result, in contrast to the upwelling plumes and downwelling sheets found in small domains, illustrating the importance of simulating wide domains. The addition of depth dependence results in small cells and reverses the planform, causing hot plumes and cold sheets. The planform of temperature-dependent viscosity convection is due predominantly to vertical variations in viscosity resulting from the temperature dependence. Compressibility, with associated depth-dependent properties, results in a tendency for broad upwelling plumes and narrow downwelling sheets, with large aspect ratio cells. Perhaps the greatest modulation effect occurs in internally heated compressible cases, in which the short-wavelength pattern of time-dependent cold plumes commonly observed in constant-viscosity calculations completely changes into a very long wavelength pattern of downwelling sheets (spaced up to 24,000 km apart) with time-dependent plumelike instabilities. These results are particularly interesting, since the basal heat flow in the Earths mantle is usually thought to be very low, e.g., 5–20% of total. The effects of viscous dissipation and adiabatic heating play only a minor role in the overall heat budget for constant-viscosity cases, an observation which is not much affected by the Rayleigh number. However, viscous dissipation becomes important in the stiff upper boundary layer when viscosity is temperature dependent. This effect is caused by the very high stresses occurring in this stiff lid, typically 2 orders of magnitude higher than the stresses in the interior of the domain for the viscosity contrast modeled here. The temperature in the interior of convective cells is highly sensitive to the material properties, with temperature-dependent viscosity and depth-dependent thermal conductivity strongly increasing the internal temperature, and depth-dependent viscosity strongly decreasing it. The sensitivity of the observed flow pattern to these various complexities clearly illustrates the importance of performing compressible, variable-viscosity mantle convection calculations with rheological and thermodynamic properties matching as closely as possible those of the Earth.

Effects of multiple phase transitions in a three‐dimensional spherical model of convection in Earth's mantle

Numerical models of mantle convection that incorporate the major mantle phase changes of the transition zone reveal an inherently three-dimensional flow pattern, with cylindrical features and linear features that behave differently in their ability to penetrate the 670-km discontinuity. The dynamics are dominated by accumulation of cold linear downwellings into rounded pools above the endothermic phase change at 670 km depth, resulting in frequent “avalanches” of upper mantle material into the lower mantle. The effect of the exothermic phase transition at 400 km depth is to reduce the overall degree of layering by pushing material through the 670-km phase change, resulting in smaller and more frequent avalanches, and a wider range of morphologies. Large quantities of avalanched cold material accumulate above the coremantle boundary (CMB), resulting in a region of strongly depressed mean temperature at the base of the mantle. The 670-km phase change has a strong effect on the temperature field, with three-distinct regions being visible: (1) the upper mantle, containing linear downwellings and pools of cold material in the transition zone and characterized by a high amplitude long wavelength spectrum; (2) the midmantle, containing quasi-cylindrical avalanche conduits and characterized by a low amplitude, broad spectrum; and (3) the deep mantle, containing large pools of cold, avalanched material and characterized by a high amplitude, ultra-red (i.e., long wavelength) spectrum. The effect on the velocity field is very different. Flow penetration across the 670-km phase change is strongly wavelength-dependent, with easy penetration at long wavelengths but strong inhibition at short wavelengths. Thus, when comparing numerical models with long wavelength seismic tomography, diagnostics based on the density field, such as the radial correlation function, are much more sensitive to the effects of phase transitions than those based on the velocity field. The amplitude of the geoid is not significantly affected by the partial layering, because the contribution from the strong heterogeneity in the transition zone is almost perfectly balanced by the contribution from deflection of the 670-km discontinuity. Avalanches are associated with geoid lows. However, a more complex viscosity structure is required to correctly match the sign of the geoid over slabs in Earth.

Self-consistent generation of tectonic plates in three-dimensional mantle convection

Abstract Despite the fundamental importance of plates in the Earths mantle convection, plates have not generally been included in numerical convection models or analog laboratory experiments, mainly because the physical properties which lead to plate tectonic behavior are not well understood. Strongly temperature-dependent viscosity results in an immobile rigid lid, so that plates, where included at all in 3-D models, have always been imposed by hand. An important challenge is thus to develop a physically reasonable material description which allows plates to develop self-consistently; this paper focuses on the role of ductile shear localization. In two-dimensional geometry, it is well-established that strain-rate softening, non-Newtonian rheologies (e.g. power-law, visco-plastic) cause weak zones and strain-rate localization above up- and down-wellings, resulting in a rudimentary approximation of plates. Three-dimensional geometry, however, is fundamentally different due to the presence of transform plate boundaries with associated toroidal motion. Since power-law and visco-plastic rheologies do not have the property of producing shear localization, it is not surprising that they do not produce good plate-like behavior in three-dimensional calculations. Here, it is argued that a strain-rate-weakening rheology, previously shown to produce plate-like behavior in a two-dimensional sheet representing the lithosphere, is a reasonable generic description of various weakening processes observed in nature. One- and two-dimensional models are used to show how this leads to shear localization and the formation of ‘faults’. This rheology is then applied to the high-viscosity lithosphere of 3-D mantle convection calculations, and the velocity-pressure/viscosity solution for the entire 3-D domain (lid and underlying mantle) is solved self-consistently. It is found that the lithosphere divides into a number of very high-viscosity plates, separated by narrow, sharply defined weak zones with a viscosity many orders of magnitude less than the plate interiors. Broad weak zones with dominant convergent/divergent motion above up- and down-wellings are interconnected by a network of narrow weak zones with dominant strike-slip motion. Passive spreading centers are formed in internally heated cases. While the resulting plates are not fully realistic, these results show that self-consistent plate generation is a realizable goal in three-dimensional mantle convection, and provide a promising avenue for future research.

Effects of strongly temperature‐dependent viscosity on time‐dependent, three‐dimensional models of mantle convection

Numerical simulations of thermal convection in a wide (8×8×1) Cartesian box heated from below with temperature-dependent viscosity contrasts of 1000, and Rayleigh number 105 show that boundary conditions and aspect ratio have an enormous effect on the preferred flow pattern. With rigid upper and lower boundaries, spoke-pattern flow with small (diameter ∼ 1.5) cells is obtained, consistent with laboratory experiments and previous numerical results. However, with the arguably more realistic stress-free boundaries, the flow chooses the largest possible wavelength, forming a single square cell of aspect ratio 8, with one huge cylindrical downwelling surrounded by upwelling sheets. The addition of stress-dependence to the rheology weakens the stiff upper boundary layer, resulting in smaller cells, though still with upwelling sheets and downwelling plumes.

Mixing and deformations in mantle plumes

The long standing idea that the source of oceanic island basalts includes ancient subducted material is strengthened by recent geochemical observations for Hawaii [Lassiter and Hauri, Earth Planet. Sci. Lett. 164 (1998) 4833496] and Iceland [Kempton et al., Earth Planet. Sci. Lett. 177 (2000) 2553271]. In particular, the isotopic variations in Hawaiian shield lavas indicate the presence of two distinct recycled components: ancient oceanic crust+sediments, and altered ultramafic lower crust or lithospheric mantle. Lassiter and Hauri [Earth Planet. Sci. Lett. 164 (1998) 4833496] suggest that both components are from the same packet of recycled oceanic lithosphere, thus implying that chemical heterogeneities a few km thick can be preserved in the convecting mantle. In this paper we investigate the role of mantle plumes in stirring mantle heterogeneities and we address the following questions: (1) Is the heterogeneous nature of plumes inherited at the source or does it develop through entrainment? (2) Is stirring more efficient in the plume head or in the long-lived plume tail? (3) Are the geochemical implications consistent with fluid dynamical models? We use a three-dimensional numerical model in Cartesian geometry to simulate the dynamics of an isolated plume. Transport calculations, conducted on a vertical plane of symmetry, allow us to advect passive tracers forward or backward in time to investigate mixing. We also calculate the finite-time Lyapunov exponents in order to quantify the deformations associated to the plume rise. Our results show that: (1) the thermal boundary layer, where the plume forms, is the region most efficiently sampled by a mantle plume. Since the overlying mantle is not entrained in the plume head, we speculate that the geochemically heterogeneous nature of plumes is inherited from the source. Our results also predict the absence of present-day upper mantle, source of MORB, in plume lavas. (2) Heterogeneities initially located in the source region undergo a series of stretching and folding events while rising in the plume head and may be reduced to narrow filaments. We find that stirring is more important in the plume head than in the long-lived plume tail. Therefore, our results predict that distinct geochemical heterogeneities are more likely to be found in hotspot lavas rather than in flood basalt lavas, associated to partial melting of a plume tail and a plume head [Richards et al., Science 246 (1989) 103^107], respectively. (3) High Lyapunov exponents, indicating high deformations, are found at the frontier between the plume head and the sublithospheric mantle surrounding the plume head. We speculate that the arrival of a large plume head could induce seismic anisotropy in the shallow upper mantle. fl 2002 Elsevier Science B.V. All rights reserved.

Transitions in thermal convection with strongly variable viscosity

One of the most important material properties influencing the style of convection in the mantles of terrestrial planets is the extreme temperature-dependence of viscosity. Three-dimensional numerical convection calculations in a wide (8 × 8 × 1) cartesian box and in a spherical shell (ratio of inner to outer radius of 0.55, characteristic of terrestrial planets) both display two fundamental transitions as the viscosity contrast is progressively increased from unity to a factor of 105. These transitions not only mark changes in the style of deformation in the upper boundary layer from mobile-lid to sluggish-lid to stagnant-lid but also have dramatic effects on the style, planform, and horizontal length scales of convection in the entire domain. Vertical variations of viscosity are the most important for determining the horizontal length scales of the convective patterns while lateral viscosity variations play a role in shaping the relative structures of the upwelling and downwelling flows. Convection in Venus appears to be represented most closely by the sluggish-lid regime of convection, whereas the Earth, with plate tectonics, more closely resembles the mobile-lid style of convection. Forcing plate-like characteristics onto the convective flows in the form of imposed weak zones and prescribed surface velocities results in flow patterns dominated entirely by the form used to enforce the plate-like behavior and tells us little about why the mantle exhibits long-wavelength heterogeneity.

Evolution of U‐Pb and Sm‐Nd systems in numerical models of mantle convection and plate tectonics

hypotheses are examined to explain this discrepancy. Sampling length scale has a minimal effect on age. The extent of crustal settling above the core-mantle boundary makes some difference but not enough. More frequent remelting is a possible explanation but requires the rate of crustal production to have been much higher in the past. Not introducing HIMU into the mantle prior to 2.0–2.5 Gyr before present, because of a change in the surface oxidization environment or subduction zone processes, can account for the difference, but its effect on other isotope systems needs to be evaluated. Improved treatment of the stretching of heterogeneities, which reduces them to length scales at which they cease to be identifiable magma sources, greatly reduces the Pb-Pb age. The mantle develops substantial chemical stratification from a homogeneous start, including stratification around 660 km caused by the two-component phase transitions. A deep layer of subducted crust may provide storage for some of the ‘‘missing’’ heat-producing elements. Magmatic heat transport is important in the first 2 Gyr of model time. INDEX TERMS: 1010 Geochemistry: Chemical evolution; 1025 Geochemistry: Composition of the mantle; 1040 Geochemistry: Isotopic composition/chemistry; 8120 Tectonophysics: Dynamics of lithosphere and mantle— general; 8124 Tectonophysics: Earth’s interior—composition and state (1212); KEYWORDS: thermochemical convection, phase transitions, geochemical heterogeneity, isotopic age, mantle melting, isotopic fractionation

A free plate surface and weak oceanic crust produce single-sided subduction on Earth

[1] Earth’s lithosphere is characterized by the relative movement of almost rigid plates as part of global mantle convection. Subduction zones on present-day Earth are strongly asymmetric features composed of an overriding plate above a subducting plate that sinks into the mantle. While global self-consistent numerical models of mantle convection have reproduced some aspects of plate tectonics, the assumptions behind these models do not allow for realistic single-sided subduction. Here we demonstrate that the asymmetry of subduction results from two major features of terrestrial plates: (1) the presence of a free deformable upper surface and (2) the presence of weak hydrated crust atop subducting slabs. We show that assuming a free surface, rather than the conventional free-slip surface, allows the dynamical behavior at convergent plate boundaries to change from double-sided to single-sided. A weak crustal layer further improves the behavior towards steady single-sided subduction by acting as lubricating layer between the sinking and the overriding plate. This is a first order finding of the causes of single-sided subduction, which by its own produces important features like the arcuate curvature of subduction trenches. Citation: Crameri, F., P. J. Tackley, I. Meilick, T. V. Gerya, and B. J. P. Kaus (2012), A free plate surface and weak oceanic crust produce single-sided subduction on Earth, Geophys. Res. Lett., 39, L03306, doi:10.1029/2011GL050046.

Convective heat transfer as a function of wavelength: Implications for the cooling of the Earth

[1] Attempting to reconstruct the thermal history of the Earth from a geophysical point of view has for a long time been in disagreement with geochemical data. The geophysical approach uses parameterized models of mantle cooling. The rate of cooling of the Earth at the beginning of its history obtained in these models is generally too rapid to allow a sufficient present-day secular cooling rate. Geochemical estimates of radioactive element concentrations in the mantle then appear too low to explain the observed present mantle heat loss. Cooling models use scaling laws for the mean heat flux out of the mantle as a function of its Rayleigh number of the form Q / Ra b . Recent studies have introduced very low values of the exponent b, which can help reduce the cooling rate of the mantle. The present study instead focuses on the coefficient C in the relation Q = CR a b and, in particular, on its variation with the wavelength of convection. The heat transfer strongly depends on the wavelength of convection. The length scale of convection in Earth’s mantle is that of plate tectonics, implying convective cells of wide aspect ratio. Taking into account the long wavelength of convection in Earth’s mantle can significantly reduce the efficiency of heat transfer. The likely variations of this wavelength with the Wilson cycle thus imply important variations of the heat flow out of the Earth on a intermediate timescale of 100 Ma, which renders parameterized models of thermal evolution inaccurate for quantitative predictions.