Effects of low-viscosity post-perovskite on thermo-chemical mantle convection in a 3-D spherical shell



[1] Numerical simulations of thermo-chemical, multi-phase mantle convection in a 3-D spherical shell are performed to determine how a low viscosity of post-perovskite affects dynamics and structures in the deep mantle. Low-viscosity post-perovskite weakens the deepest part of slabs, allowing them to more effectively spread over the core-mantle boundary (CMB), and it also results in a greater volume of basalt segregating, both of which increase the size of dense chemical piles, the horizontal lengthscale of regions of pooled slab material, and the steepness of piles' edges (in composition and phase), consistent with the existence of steep, sharp-sided edges found in seismic analyses. CMB heat flux is strongly enhanced in regions of low-viscosity post-perovskite (consistent with a theoretical prediction) and both CMB and surface heat flux are increased on average by a low-viscosity of post-perovskite, which could have important implications for the evolution of Earth's core and mantle.

1. Introduction

[2] Post-perovskite is now established as an important phase in the deepest mantle. High pressure experiments [Hunt et al., 2009; Yamazaki et al., 2006; Yoshino and Yamazaki, 2007] and first principle calculations of atomic diffusion [Ammann et al., 2010] indicate that the viscosity of post-perovskite is lower than that of perovskite- by a factor of O(103) to O(104) according to [Ammann et al., 2010]. Geodynamical instantaneous flow modeling has shown that the long-wavelength geoid is very sensitive to the presence of low viscosity post-perovskite regions at the base of cold subducted slabs reaching the CMB [Tosi et al., 2009; Ghosh et al., 2010]. Thus, it is important to determine the influence of low post-perovskite viscosity in long-term dynamical calculations.

[3] Dynamical calculations should also include compositional variations, because compositional anomalies (in the form of dense ‘piles’) are widely thought to exist above the core-mantle boundary (CMB) in order explain seismological observations [Trampert et al., 2004; Ni et al., 2002; To et al., 2005], often in combination with post-perovskite [Lay et al., 2006; van der Hilst et al., 2007]. Such compositional anomalies also have a strong influence on CMB topography [Lassak et al., 2007, 2010; Yoshida, 2008], although these studies did not consider post-perovskite.

[4] Other geodynamically important quantities are the heat flux across the CMB and its lateral variation, both of which have a first-order influence on the geodynamo and the evolution of the core, and which are influenced by compositional anomalies and post-perovskite [Nakagawa and Tackley, 2008, 2010]. Heat transfer by mantle convection across the CMB may well be different when the post-perovskite has a lower viscosity than perovskite, as predicted by a theoretical investigation [Buffett, 2007] and a two-dimensional isochemical study [Cizkova et al., 2010].

[5] Thus, in this study, the dynamical influences of weak post-perovskite are investigated using numerical thermo-chemical mantle convection simulations in a 3-D spherical shell, focusing on various diagnostics related to structures and dynamics in the CMB region.

2. Model Description

[6] The physical model and numerical solution method are very similar to those in our previous papers [e.g., Nakagawa and Tackley, 2005a, 2005b, 2006, 2010]), so only an overview and pertinent differences are given here. Compressibility is included using the truncated anelastic approximation, and the equations are solved in a 3-D spherical shell using the code StagYY [Tackley, 2008]. Two systems of phase transitions, those in the olivine and pyroxene-garnet systems, are included, as listed in Table 2. The density difference at the CMB is 3.6%, which corresponds to 2.16% between MORB and pyrolite. The mantle is assumed to be a mechanical mixture of basalt and harzburgite, starting with uniform pyrolite (20% basalt) [Xu et al., 2008], then compositional anomalies are generated by melt-induced differentiation producing oceanic crust.

[7] Isothermal boundary conditions are applied at both top and bottom boundaries, which are set at 300 K and 4173 K, respectively. Here the CMB temperature is fixed: core cooling is not taken into account. With the assumed CMB temperature and post-perovskite phase change parameters, a double-crossing of the perovskite to postperovskite transition [Hernlund et al., 2005] is expected.

[8] The viscosity law assumes linear diffusion creep, because [Ammann et al., 2010] find a diffusion creep viscosity that is O(103) lower than that for perovskite [Ammann et al., 2009]. It is possible that post-perovskite deforms mainly by dislocation creep (as assumed in some previous studies [Cizkova et al., 2010; van den Berg et al., 2010]), which would further lower the viscosity. The viscosity law is as by Keller and Tackley [2009] with the addition of plastic yielding to produce plate-like behavior:

equation image

where T is absolute nondimensional temperature, d is nondimensional depth, Δηij is the viscosity jump due to each phase transition, Γij is the phase function for phase i in system j (varying from 0 at low pressure to 1 at high pressure) and fj is the fraction of phase system j present. A0 is a constant calculated such that the viscosity is equal to 1 at T = 1600 K and zero depth, σ0 and σ1 are yield stress at zero depth and yield stress gradient respectively, and equation image is the second invariant of the strain rate tensor. The activation energy and volume are based on those of perovskite [Yamazaki and Karato, 2001].

[9] Physical parameters used here are listed in Table 1 and phase transition parameters are listed in Table 2.

Table 1. Mantle Model Physical Parametersa
SymbolMeaningNon-D. ValueDimensional Value
  • a

    Ra0 = ρ00ΔTsad3/κ0η0.

Ra0Reference Rayleigh number107N/A
η0Reference viscosity11.4 × 1022 Pa s
ΔηpvViscosity jump at 660 km30N/A
ΔηppvViscosity jump at the post-perovskite boundary1 or 0.001N/A
σbYield stress at surface8.5 × 104100 MPa
σdYield stress gradient3.4 × 105138.0 Pa m−1
ρ0Reference (surface) density13300 kg m−3
gGravity19.8 m s−2
α0Ref. (surface) thermal expan.15 × 10−5 K−1
κ0Ref. (surface) thermal diff.17 × 10−7 m2 s−1
ΔTsaTemperature scale12500 K
HInternal heating rate at the present time13.83.7 × 10−12 W/kg
Table 2. Physical Parameters for Two-Component Phase Changes Modified From Tackley and Xie [2003] to Include the Post-Perovskite Phase Transitiona
#Depth (km)Temperature (K)Δρph (kg m−3)γ (MPa/K)Width (km)
  • a

    The 60 km deep phase change in the pyroxene-garnet-perovskite system corresponds to the basalt-eclogite transition.


[10] The initial condition is an adiabatic temperature plus thin thermal boundary layers at the top and bottom, plus small random perturbations. The numerical resolution is 64 × 192 × 64 × 2 with 20 million tracers to track chemical composition and melt fraction.

3. Results

[11] Here two cases are examined: one with post-perovskite having the same viscosity as perovskite, and one with low-viscosity post-perovskite. Figure 1 shows the heat flux across the surface and CMB as a function of time. With low-viscosity post-perovskite the heat flux across the CMB displays a huge time variation and is generally higher than with regular post-perovskite, consistent with findings from 2-D isochemical simulations [Cizkova et al., 2010]. The surface heat flow is much less time-dependent, and is also slightly higher with low-viscosity post-perovskite. It indicates that the system has reached statistically steady state.

Figure 1.

Surface and CMB heat flux as a function of time.

[12] Figure 2 shows thermo-chemical-phase structures for regular and weak post-perovskite cases after 4.5 Gyrs of evolution. Cold slab-like downwellings penetrate to the CMB region, where they are transformed to post-perovskite, and push dense segregated basalt aside to form piles. Low post-perovskite viscosity amplifies this effect because it enables slabs to more easily deform and spread over the CMB. Additionally, in the weak post-perovskite case there is a ∼50% greater volume of segregated basalt due to some combination of more efficient separation of basalt from the slab and faster processing arising from higher velocities. For both of these reasons, ‘piles’ in the weak-pPv case are thicker and have a larger length-scale than those in the standard case. This indicates that it is density differences that are responsible for maintaining piles, not mechanical strength. An anticorrelation between the locations of dense material and post-perovskite is observed, as was previously found in similar cases in 2-D cylindrical [Nakagawa and Tackley, 2005a, 2005b] and 3-D Cartesian geometries [Nakagawa and Tackley, 2006]. Both the piles and post-perovskite regions have sharp edges, which tend to be more pronounced with low-viscosity post-perovskite.

Figure 2.

The thermo-chemical-phase state after 4.5 Ga of evolution. (top) With regular post-perovskite. (bottom) With low-viscosity post-perovskite. (left) Isosurfaces of residual temperature (red: +250 K; blue: −250 K compared to geotherm). (right) Isosurfaces of composition (green: 75% basalt) and post-perovskite (cyan).

[13] Figure 3 shows CMB topography, CMB heat flux, and temperature and composition at 2790 km depth. The amplitude of CMB topography ranges from approximately −5 km to 5 km with regular post-perovskite, being strongly negative (depressed) under slabs, positive around the edges of slabs, and neutral under ‘piles’, consistent with previous results [Lassak et al., 2007, 2010]. This range is larger than in some previous numerical mantle convection simulations [Lassak et al., 2010] and an instantaneous flow model [Yoshida, 2008]. When low-viscosity post-perovskite is included the amplitude of topography is greatly reduced, ranging from around −2 km to 2 km, the main difference being that topography is no longer strongly negative under slabs, because their low viscosity in the CMB region reduces the coupling to higher-up part of slabs and allows them to spread more. CMB heat flux is high where cold slab material pools above the CMB, which occurs in broader regions when post-perovskite viscosity is low, thereby enhancing the total CMB heat flux. Additionally, the maximum CMB heat flux is higher with low-viscosity post-perovskite. This observed enhancement of CMB heat flux was previously predicted from a theoretical estimate between the velocity of subduction, the viscosity in the CMB region and CMB heat flux [Buffett, 2007]. In general, a low post-perovskite viscosity appears to suppress small-scale structures.

Figure 3.

CMB topography and heat flux, and temperature and composition at 2790 km depth (100 km above the CMB) (from left to right, respectively for the same cases and time as Figure 3. (top) Regular post-perovskite. (bottom) Low-viscosity post-perovskite.

[14] Figure 4 shows the viscosity at 2790 km depth, where the post-perovskite phase transition is found. Comparing this to the temperature distribution shown in Figure 3, a viscosity reduction in cold pooled slab regions is clearly visible. This causes the reduced CMB topography and enhancement of CMB heat flux discussed above.

Figure 4.

Viscosity at 2790 km depth (100 km above the CMB). (a) Regular post-perovskite. (b) Weak post-perovskite.

4. Summary and Discussion

[15] Here we have investigated the effect of low-viscosity post-perovskite in the CMB region on thermo-chemical mantle convection. The major findings are as follows.

[16] 1. Low post-perovskite viscosity amplifies the size of dense compositional piles above the CMB, because it enables cold slab material to spread more easily above the CMB, pushing dense segregated basalt aside into piles, and also because a larger volume of basalt segregates at the CMB when the post-perovskite viscosity is low. It is plausible, although not studied here, that this greater segregated basalt volume is because low viscosity facilitates more efficient segregation of the basaltic and harzburgitic parts of the slab. As a result, structures in the CMB region tend to be of longer wavelength when low-viscosity post-perovskite is present. Steep, sharp-sided edges of both post-perovskite regions and dense piles are enhanced by the effects of low-viscosity post-perovskite, consistent with seismic waveform analyses suggesting the existence of steep, sharp-sided edges between slow and fast anomalies [Ni et al., 2002; To et al., 2005]. We find steep, sharp edges even when the dense material has an identical compressibility, contrary to Tan and Gurnis [2005], which is something that could be further tested in the future.

[17] 2. CMB topography is reduced by the presence of low-viscosity post-perovskite. With regular-viscosity post-perovskite, the CMB is depressed where slabs arrive and neutral elsewhere [Lassak et al., 2010], resulting in a strong correlation between CMB topography and temperature above the CMB. With low-viscosity post-perovskite, slab pools are weak and broad and do not depress the CMB, which removes most of this correlation. Thus the correlation (or lack of it) between temperature above the CMB and CMB topography inferred from seismic waveform analyses [Tanaka, 2010] could be used as a diagnostic to test for the viscosity of post-perovskite. A previous instantaneous mantle flow model [Yoshida, 2008] pointed out the effect of a low-viscosity D″ in reducing CMB topography but there, low-viscosity was imposed everywhere above the CMB, whereas here it is due low-viscosity post-perovskite in cold regions and temperature-dependent viscosity in hot regions (containing piles).

[18] 3. Low-viscosity post-perovskite substantially increases heat transfer across the CMB by increasing the pooling of cold slab material above the CMB. This is consistent with a theoretical prediction between the viscosity of post-perovskite and CMB heat flux [Buffett, 2007], and isochemical 2-D calculations [Cizkova et al., 2010]. As a result it also slightly increases heat flux across the surface. This would have a significant effect on core cooling and hence the thermal evolution of the mantle and core, which are not studied here for the purpose of simplicity.

[19] There are several other interesting effects of low viscosity post-perovskite that we plan to study in future. The effect on geoid found in instantaneous flow models [Tosi et al., 2009; Ghosh et al., 2010] should be tested in full convection models. The pattern of anisotropy in the deep mantle, an important seismological observation [e.g., Wookey et al., 2005], is expected to be strongly influenced both by strongly anisotropic post-perovskite seismic velocity and by the change in flow patterns caused by low post-perovskite viscosity. The dependence of results on uncertain parameters such as the density difference between basalt and harzburgite in the deep mantle and exact viscosity reduction, should be systematically evaluated.


[20] All computations are performed on the Brutus cluster of ETH Zurich. We thank two anonymous reviewers for helpful suggestions.

[21] M. E. Wysession thanks John Hernlund and one anonymous reviewer.