SESolid EarthSESolid Earth1869-9529Copernicus GmbHGöttingen, Germany10.5194/se-6-93-2015Effective buoyancy ratio: a new parameter for characterizing thermo-chemical mixing in the Earth's mantleGalsaA.gali@pangea.elte.huHereinM.LenkeyL.FarkasM. P.TallerG.Department of Geophysics and Space Sciences, Eötvös
Loránd University, Budapest, HungaryInstitute for Theoretical Physics, Eötvös Loránd
University, Budapest, HungaryDepartment of Engineering Geophysics, Geological and Geophysical
Institute of Hungary, Budapest, HungaryA. Galsa (gali@pangea.elte.hu)28January2015619310228July20141September201419November20142December2014This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://www.solid-earth.net/6/93/2015/se-6-93-2015.htmlThe full text article is available as a PDF file from https://www.solid-earth.net/6/93/2015/se-6-93-2015.pdf
Numerical modeling has been carried out in a 2-D cylindrical shell domain to
quantify the evolution of a primordial dense layer around the core–mantle
boundary. Effective buoyancy ratio, Beff was introduced to characterize
the evolution of the two-layer thermo-chemical convection in the Earth's
mantle. Beff decreases with time due to (1) warming of the compositionally
dense layer, (2) cooling of the overlying mantle, (3) eroding of the dense layer
through thermal convection in the overlying mantle and (4) diluting of the dense
layer through inner convection. When Beff reaches the instability point,
Beff=1, effective thermo-chemical convection starts, and the mantle
will be mixed (Beff=0) over a short time period. A parabolic relationship was
revealed between the initial density difference of the layers and the mixing
time. Morphology of large low-shear-velocity provinces and results
from seismic tomography and normal mode data suggest a value of
Beff≥1 for the mantle.
Introduction
The most prominent feature of the lowermost part of the Earth's mantle is
the two seismically slow domains beneath the Pacific and Africa (e.g., Dziewonski
et al., 1993; Garnero et al., 2007a). The nearly antipodal large low-shear-velocity provinces (LLSVPs) are characterized by -2 to -4 % shear wave and
-1 to -2 % primary wave anomaly, several thousand kilometers lateral
extent and 800–1000 km elevation from the core–mantle boundary (CMB)
(Mégnin and Romanowicz, 2000; Masters et al., 2000; Lay, 2005; Zhao,
2009). The margins of the anomalies, where the lateral shear wave velocity
gradients are the most pronounced, have sharp sides (Ni et al., 2002; Wang
and Wen, 2004; Ford et al., 2006; Garnero and McNamara, 2008) and correlate
with hot spot volcanism (Thorne et al., 2004; Torsvik et al., 2010). The
existence and the morphology of LLSVPs cannot be satisfactorily explained by
the variation in temperature, mineralogical phases or melts. Compositionally
dense and thus stable material accumulated above the CMB is necessary in a
consistent mantle model (Trampert et al., 2004; Ishi and Tromp, 2004;
Garnero et al., 2007b; Bull et al., 2009).
A compositionally dense layer around the core is expected to hinder the
mantle convection through reducing the heat transport from the Earth's core
(Nakagawa and Tackley, 2004). Thus, a chemically dense layer at the base of
the mantle has a stabilizing role (Sleep, 1988; Deschamps and Tackley,
2009). On the other hand, the heat coming from the core is trapped in the
dense layer leading to a hot and unstable bottom thermal boundary layer.
The dominant process of the two opposite effects can be predicted by the
buoyancy ratio (Davaille et al., 2002),
B=βαΔTm,
which is the ratio of the stabilizing chemical density difference and the
destabilizing thermal density difference. β denotes the relative
chemical density difference between the layers, α is the thermal
expansion coefficient and ΔTm is the temperature difference
across the mantle. When B is larger than 1, the dense layer is thought to
be stable, but in the case of B < 1, the density decrease through thermal
expansion is strong enough to break up and mix it with the overlying mantle
through thermo-chemical convection (TCC).
As early as the 1980s, pioneer numerical simulations were made to
investigate the effect of the compositionally dense lower layer on the
mantle dynamics (Christensen and Yuen, 1984; Hansen and Yuen, 1988).
Laboratory experiments and numerical models of mantle convection have shown
that a chemically dense primordial layer can survive for the age of the
Earth if B is large enough (e.g., Davaille et al., 2002; Jellinek and Manga,
2002; Lin and Van Keken, 2006). Depending on the density contrast and the
initial thickness of the dense layer thermo-chemical domes/piles are formed
in these models which morphologically resemble the seismological LLSVPs
(Trampert et al., 2004; Bull et al., 2009). Deschamps and Tackley (2008,
2009) investigated systematically the influence of some important parameters
(depth-, temperature- and concentration-dependent viscosity, internal
heating, chemical density contrast, mineralogical phase change at 660 km) on
the evolution of the initial dense layer and compared the power spectra of
density and thermal anomalies obtained from seismic tomography and numerical
models. They mapped the parameter space of the thermo-chemical convection
and suggested the essential ingredients for a successful mantle convection
model.
In these thermo-chemical models, B is time-independent during the simulations.
However, the primordial dense layer might change greatly due to the heat
from the core and possibly from the decay of enriched radioactive elements,
the surface erosion of dense material through convection occurring in the
overlying mantle, internal convection within the dense layer and termination
of subducted slabs at CMB (Nakagawa and Tackley, 2004; Lay, 2005; McNamara
and Zhong, 2005; Lay et al., 2006; Garnero et al., 2007a). In this paper we
present the results of numerical model calculations made with different
values of B including values larger than 1. We studied the evolution of the
convection, and we suggest the introduction of the time-dependent effective
buoyancy ratio which characterizes better the dynamics of the TCC.
Model description
Boussinesq approximation of the equation system governing the
thermo-chemical convection was applied (Chandrasekhar, 1961; Hansen and
Yuen, 1988; Čížková and Matyska, 2004). The dimensional
equations expressing the conservation of mass, momentum as well as the heat
and the mass transport are
∂ui∂xi=0,0=ρgei-∂p∂xi+∂σij∂xj,∂T∂t=κ∂2T∂xi2-ui∂T∂xi+Q,
∂c∂t=-ui∂c∂xi,
where the unknown variables are the density, the pressure, the flow
velocity, the temperature of the fluid and the concentration of the dense
material, ρ, p, ui, T and c, respectively. In a two-dimensional model
domain there are five equations to determine six variables. Therefore, a
simple linear relationship is given among the density, the temperature and the
concentration by the equation of state,
ρ=ρR1-αT-TS+βc,
where ρR and TS denote the reference density and the surface
temperature, β is the initial relative density difference between the
dense layer and the overlying mantle. Q and σij are the internal
heat production and the deviatoric stress tensor for incompressible
Newtonian fluid, respectively. The space coordinates and the time are
denoted by xi and t, respectively; ei shows the direction of the
gravitational acceleration, downwards. According to the Boussinesq
approximation, other parameters in Eqs. (2–6) are supposed to be constant
(Table 1) (Van Keken, 2001). Focusing on the processes of the disintegration and
homogenization of the primordial dense layer above the core–mantle boundary,
dynamic viscosity was chosen to characterize the deep mantle instead,
resulting in less intense convection with a thermal Rayleigh number of about
6×106.
Finite element method was applied to solve the partial differential equation
system of Eqs. (2–5) using COMSOL Multiphysics software package
(Zimmerman, 2006). A field method was applied to calculate the concentration
distribution of dense material. The applied numerical scheme was tested, and
the comparison with the benchmark study of Van Keken et al. (1997) is
presented in the Supplement. Two-dimensional cylindrical shell
geometry was used to approximate the shape of the Earth's mantle.
Geometrical scaling was adopted from Van Keken (2001) to maintain the ratio
of the CMB and the Earth's surface (≅0.3) and not to overstate the role of
the deep mantle; thus, the outer and inner radius of the mantle were 4123 km
and 1238 km, respectively. The boundaries were isothermal as well as
symmetrical and impermeable with respect to the velocity and the
concentration.
Simulation was started from a quasi-stationary state of the temperature
field obtained from a chemically homogeneous, purely thermal convection
model. Concentration of dense material was set to 1 for the dense layer and
0 above; the transition was adjusted using a smoothed Heaviside function
with continuous first derivative and interval thickness of 50 km. The
initial thickness of the dense layer was 300 km around the core. Maximum
element size was 50 km within the model domain, 30 km along the surface and 15 km
along the CMB and the surface of the initial dense layer (300 km above the CMB)
to ensure sharp variation in the thermal and/or
chemical boundary layer.
Model constants.
DefinitionSymbolValueGravitational accelerationg10 ms-2Dynamic viscosityη1022 Pa⋅sHeat diffusivityκ10-6m2s-1Thermal expansivityα2×10-5K-1Reference densityρR4500 kgm-3Temperature drop across the mantleΔTm3000 KThickness of mantled2885 km
During the systematical model calculations, the mantle was taken as isoviscous
without internal heating. The only parameter modified during the simulation
was the initial relative density difference between the dense layer and the
light overlying mantle, β; it ranged between 0–8 %
(B=0-1.33). We investigated the effect of β on the monitoring
parameters; heat flux, velocity, temperature and concentration time series
were calculated in the upper and the lower layer. Hence we use the lower and
upper layer expression in geometrical meaning as the deepest 300 km thick
part of the mantle and the overlying zone, respectively. For example,
c0=1A0∫A0cdAandc1=1A1∫A1cdA
denote the concentration of the dense material in the upper and the lower
layer, respectively, and A0 and A1 the area of the mantle above and
beneath 300 km above the CMB. Other volumetric parameters such as the temperature
and the velocity are calculated in the same manner (Table 2). The concentration and
temperature difference between the layers is calculated as
Δc=c1-c0andΔT=T1-T0.
Indices S,D and CMB denote the values at the surface, at the depth of 300 km above
the CMB and at the CMB, respectively. Time is defined as non-dimensional
diffusion time. In addition, we compiled a model with complex rheology
(depth-, temperature- and composition-dependent viscosity) and
composition-dependent internal heating to test their influence on the
effective buoyancy ratio.
Monitoring parameters.
SymbolDefinitionqSSurface heat flowqCMBHeat flow at CMBqDHeat flow at the top of the dense layerv0Rms velocity of the upper layerv1Rms velocity of the lower layervRms velocity of the mantleT0Temperature of the upper layerT1Temperature of the lower layerTTemperature of the mantlec0Concentration of the upper layerc1Concentration of the lower layerchetHeterogeneity of the concentrationqDCConcentration flux at the top of the dense layerΔcConcentration difference between the lowerand upper layerΔTTemperature difference between the lowerand upper layerBeffEffective buoyancy ratioResults
Five stages characterizing the evolution of the thermo-chemical
convection as a funktion of non-dimensional time. Left: time series of monitoring parameters (heat flux, velocity,
temperature, concentration, see in Table 2), vertical lines denote the
stages shown in the right side. Right: the evolution of the concentration of
the dense material and the temperature field.
(a) The concentration, (b) the temperature differences between
the lower and upper layers and (c) the effective buoyancy ratio as a
function of time at different values of the initial compositional density
contrast, β. Dashed blue line denotes the complex model (see in
text).
Figure 1 illustrates the influence of a basal dense layer on the heat flux,
velocity, temperature and concentration time series (left) as well as on the
evolution of the concentration and temperature field (right). The initial
density difference was β=6 % between the layers that results in
B=1 for the buoyancy ratio. The initial state (stage a) is given by a
temperature field obtained from a purely thermal convection calculation and
a compositionally dense basal layer placed instantaneously above the CMB.
After approximately 1 Gyr (stage b) two-layer convection is being evolved
separately in the upper and the lower layers. Inner convection within the
dense layer and cold downwellings in the overlying mantle deform the surface
of the dense layer. At this stage, the temperature of the dense layer reaches
its maximum (T1), and the heat flux (qS, qCMB, qD) decreases
to a low quasi-stationary level. The erosion of the dense layer through thermal
convection in the overlying mantle reduces the concentration of the dense
material in the lower layer (c1) and increases it in the upper one
(c0). The concentration variation shows a linear trend. A similar linear
reduction in the volume of the dense layer was found by Zhong and Hager
(2003), who studied the entrainment of the dense material by examining one stationary
thermal plume. 4.5 Gyr later (stage c) the dense layer disintegrates,
it becomes unstable and effective thermo-chemical convection (TCC) starts.
The TCC mixes the layers quickly, the flow accelerates (v0, v1), the
heat flux increases (qS, qCMB, qD), the dense layer cools
(T1), while the upper layer warms (T0). The mass flux of the dense
material (qDC) starts up and the heterogeneity of the concentration
(chet, normalized standard deviation of the concentration) decreases
suddenly. In other words, the thermal energy of the dense layer transforms
to kinetic energy in a short period of time. After 5.1 Gyr (stage d) the dense
layer ceased, having been mixed in the mantle, the system reached the stable state. Time series converge to the values characterizing the pure thermal
convection, concentration time series tend to the average value of 0.0538. The
heat flux (qS, qCMB, qD) and velocity (v0, v1) time
series have higher values and larger fluctuations than in the two-layer
convection regime (from stage a to d) that underlines the retaining role of
the chemically dense bottom layer. Of course, the homogenization continues
protractedly, and after 7.8 Gyr (stage e) the heterogeneity
(chet) decreases below 1 %. The heating of the mantle (T) requires
billions of years.
Figure 1 illustrates that although the buoyancy ratio is B=1 – that is,
the stabilizing chemical density difference and the destabilizing thermal
density difference is balanced – the dense layer evolves considerably,
moreover disappears during disappears after about 5 Gyr. Additional model calculations
revealed that mixing of the layers occurred for both B < 1 (β < 6 %) and B > 1 (β > 6 %).
Therefore, we suggest introducing the effective buoyancy ratio in order to
characterize the evolution of the dense layer and the dynamics of the
thermo-chemical convection. The effective buoyancy ratio,
Beff(t)=βc1(t)-c0(t)αT1(t)-T0(t)=βΔc(t)αΔT(t),
is time-dependent and includes Δc concentration and ΔT
temperature differences between the bottom layer (i.e., the lower 300 km of
the mantle) and the overlying mantle.
Figure 2 shows the concentration and temperature differences between the layers as
well as the calculated effective buoyancy ratio at different values of
β. As the dense layer warms up from heat coming from the core and
the overlying mantle cools down from retained heat transport due to
two-layer convection, the temperature difference increases. It results in
the initial rapid decrease of Beff. The concentration difference is
decreased monotonically through the erosion of the dense material that later
becomes the dominant process in reduction of Beff. Gonnermann et al.
(2002) observed a similar decrease of the time-dependent buoyancy ratio in
their laboratory experiments. However, they used the temperature drop across
the interface of the two layers and the temperature difference between the
bottom of the tank and the lower layer for the estimation of the chemical
and the thermal density difference, respectively, to define the buoyancy
ratio. When the effective buoyancy ratio reaches the value of
Beff=1, that is, the instability point of the system (stage c in
Fig. 1), one-layer thermo-chemical convection (mixing) starts. Mixing results in
the quick reduction of the temperature and concentration differences. When
the effective buoyancy ratio reaches the value of Beff=0 (stage d in
Fig. 1), the dense layer ceases, the mantle becomes mixed. Overturns of
dense material cause temporarily negative values in Beff, especially
in the cases of lower initial density contrast (β). It is obvious that
larger initial density contrast entails more stable layering, however the
mixing occurs in each model even for B > 1.
We attribute the occurrence of the effective thermo-chemical convection in
each model to four main physical processes:
Heat coming from the core warms up the dense layer reducing its
density through thermal expansion.
The overlying mantle cools down through retained heat transport due to
two-layer convection.
Thermal convection forming in the upper layer erodes the surface
of the dense layer through viscous drag.
Inner convection within the dense layer intermixes light
material from the overlying mantle.
Processes (1) and (2) result in the increase of the temperature difference
between the layers, the processes (3) and (4) cause a decrease in the
concentration difference. While the first two phenomena are constrained by
the total temperature drop across the mantle (practically ΔTm/2, see Fig. 2b), the latter two are not. Erosion (3) and dilution
(4) gradually reduce the chemical density difference between the layers
until the system reaches the instability point (Beff=1) when mixing
begins. Mixing occurs in every case, even if the time might exceed the
Earth's age (B≥1). Figure 3 illustrates the phenomena of the erosion and
dilution of the dense layer in the concentration and the temperature fields.
Black arrows denote (a) the mass flux of the dense material and (b) the
velocity of the flow.
(a) Concentration of the dense material and (b) temperature field
demonstrating the processes of (3) erosion and (4) dilution of the dense
layer. Black arrows denote the logarithmically scaled (a) mass flux of the
dense material and (b) flow velocity.
We investigated how the occurrence time of the two most characteristic
events (the onset and the end of the effective TCC) depends on the initial
chemical density difference, β (Fig. 4a). Obviously, larger β results
in a more stable, long-lived dense layer and larger occurrence time. A
parabolic relationship was found between the occurrence time of Beff=1
(onset of mixing) and β. Davaille (1999a) observed a similar
relationship in their laboratory experiments studying the effect of the buoyancy ratio (and
other parameters) on the entrainment rate. Parabolic function fits well on
data of Beff=0 (end of mixing) too.
As shown in Fig. 2, both the erosion/dilution phase (leading up to stage c) and
the effective TCC phase (between stage c and d) can be characterized by a
linear decrease in Δc. The effective buoyancy ratio displays a
similar feature apart from its initial phase, which is due to the transient
heating of the dense layer and the cooling of the overlying mantle (from
stage a to b). Figure 4b illustrates the slope of the linear curves fitted on Δc and Beff time series during the erosion/dilution phase. It is
established that larger initial density contrast (β or B) entails more
stable layering owing to the less effective erosion/dilution process. Figure 4b presents
a power function relationship between the slopes of time series and
β (Δc∼β-1.91 or Beff∼β-2.35). Both the parabolic relationship in Fig. 4a and the power function relationship in Fig. 4b support the idea that
mixing of the layers occurs for arbitrary density contrast. It is worth
noting that the effective TCC phase demonstrates also a linear decrease in
Δc and Beff, but with steeper slope (Fig. 2). The slope of the
linear curves fitted on the time series shows a slight decrease as β
increases (not shown).
Focusing on the erosion phase (from stage b to c) the linear decrease of the
concentration difference between the layers, or in other words, the constant
entrainment rate has been shown earlier (e.g., Davaille, 1999b; Gonnermann et
al., 2002; Zhong and Hager, 2003). The entrainment of the dense material
through a thin tendril can be calculated using the balance between the viscous force
dragging the dense material upward and the buoyancy force drawing it back
(Jellinek and Manga, 2002),
ηvpl2gΔρ≈1,
where vp, l and Δρ denote the plume velocity, the thickness
of the tendril and the density difference between the layers, respectively.
The tendril thickness from Eq. (8) is
l≈ηvpgΔρ.
The concentration of the dense material in the lower layer decreases through the
dense material entrained by hot plumes,
c1=A1-NpvpltA1,
where Np is the number of plumes and t is the elapsed time. Thus, the
entrainment rate which is the concentration variation in the lower layer is
dc1dt=-NpvplA1.
At the relative density difference between the layers of β=0.06 the
plume velocity varies from 3×10-11 m s-1 to 10-10 m s-1 in the
numerical model during the erosion phase just above the lower layer
resulting in a tendril thickness of 10–20 km (Table 1). Applying Eq. ()
the concentration decrease caused by hot plumes of about Np=7 (Fig. 1b and c) gives a value of
0.85–5.2×10-18 s-1. On the other
hand, in Fig. 1 the concentration decrease of the lower layer during the
erosion phase has a slope of 3.3×10-18 s-1, or in
non-dimensional form, 27.2.
(a) Occurrence time of the two most characteristic events:
Beff=1 (onset of mixing) and Beff=0 (end of mixing) as well as
(b) slope of the decrease of the concentration difference and the effective
buoyancy ratio during the erosion/dilution phase as a function of β.
These conclusions were drawn from a simple isoviscous model. However, the
TCC leading to the dissolution of the dense layer strongly depends on the
viscosity. Therefore, a more complex model including depth- temperature- and composition-dependent viscosity and composition-dependent internal
heating was calculated in order to investigate the dynamics of the TCC and
the variation of the effective buoyancy ratio. Parameters controlling the
viscosity and the internal heating were assigned based on the results of
Deschamps and Tackley (2008, 2009). An Arrhenius-type law determined the
depth-, and temperature-dependence of the viscosity, which increased 1
order of magnitude from the surface to the CMB and decreased 6 orders of
magnitude with the temperature. A viscosity jump with a factor of 30 was
superimposed at the depth of 660 km, reflecting the effect of mineralogical
phase change on the viscosity. The viscosity of the dense material (c=1) is
half of that of the light material (c=0) with a linear transition. Internal
heating was adjusted to produce 65 mWm-2 average heat flux on the
surface, but the heat production of the dense material was increased by a
factor of 10 due to the higher abundance of radioactive elements. The
initial compositional density contrast between the layers was β= 6 %, which corresponds with the model presented in Fig. 1. The simulation
started from a quasi-stationary state of the temperature field obtained from
a chemically homogeneous, purely thermal convection model with depth- and
temperature-dependent viscosity and homogeneous internal heating.
A quasi-stationary state of the (a) temperature, (b) viscosity, (c) concentration of the dense
material and (d) velocity for the complex model (see text) at 3.5 Gyr (t=0.01325). Viscosity
is non-dimensionalized as log10(η/ηS) where ηS denotes the surface viscosity.
Figure 5 illustrates the pattern of the TCC for the complex model at 3.5 Gyr after
the inset of the dense layer when the effective buoyancy ratio is approximately 1.13. Over a period of 3.5 Gyr the dense layer disintegrated and two hot,
compositionally dense, nearly antipodal piles formed with sharp sides. Due
to the concentration-dependent internal heating, the temperature within piles
exceeds the CMB temperature; thus, the viscosity decreases considerably. The
concentration and velocity field attest to a sluggish internal convection
forming within the piles. A stagnant lid regime evolved owing to the strongly
temperature-dependent viscosity (Solomatov, 1995), which does not participate
in the convection. Beneath the stagnant lid, vivid small-scale convection
occurs in the upper mantle (Kuslits et al., 2014). Due to the lack of the
endothermic phase transition, advective mass and heat transport exists
between the upper and lower mantle.
Figure 2 displays the variation of the concentration and temperature
differences between the layers and the effective buoyancy ratio for the
“mantle-like” model (mm_6 %). As a consequence of the
stagnant lid regime, ΔT decreased compared to the isoviscous case, but
the character of the curve remained similar. The rate of the decrease in
Δc through erosion and dilution processes became steeper owing to the
reduced viscosity of the hot, dense thermo-chemical layer. As a result, the
effective buoyancy ratio has a similar nature with a steeper erosion/dilution
phase and less steep mixing phase. In summary, the stability of the dense
layer in the complex model with varying viscosity and internal heating was
reduced compared to isoviscous model by about 20 %, but the physical
processes acting in the two models were the same.
Discussion and conclusions
A new parameter, the effective buoyancy ratio, Beff was defined to
characterize the dynamics of thermo-chemical convection occurring in the
Earth's mantle. Buoyancy ratio, B, in its classical meaning (Davaille et al.,
2002) is a constant and predicts the resistance of the lower compositionally
dense but hot layer against mixing, and so it is insensitive to the behavior
of the system. Additionally, our calculations show that mixing also occurs
in the case of B > 1 suggesting the instability of two-layer convection
for arbitrary value of B (Davaille, 1999a). On the other hand, the effective
buoyancy ratio, Beff, is a time-dependent parameter which represents the
instantaneous stability of the thermo-chemical system. During the numerical
modeling, Beff decreases monotonically and when its value reaches 1
(the instability point, when stabilizing chemical and the destabilizing
thermal buoyancy is balanced), the pattern of the flow system changes
considerably; the two-layer convection is replaced with a one-layer
thermo-chemical mixing. Thus, the effective buoyancy ratio is a good
diagnostic tool to determine the actual state of two miscible fluid-like
layers. Additionally, the time of Beff=0 might define the time when
the two layers are mixed. Beff illustrates well the evolution of the
initial dense layer above the CMB consisting of four phases: (i) transition
phase of warming dense layer; (ii) erosion and dilution of the dense layer;
(iii) effective thermo-chemical convection (mixing of layers); (iv) homogenization.
There is no exact knowledge of the early stage of the mantle evolution, that
is, the initial condition of the numerical and laboratory models is pending.
Still, there are some hypotheses which make it plausible that the
compositionally dense layer might have formed during the first 100–200 Myr
of the Earth's history. Deschamps and Tackley (2008) and Tackley (2012)
detail this problem and mention that (1) mixing between the liquid iron of
the outer core and silicate deep mantle (Mao et al., 2006); (2) early
differentiation of the magmatic mantle (Agee and Walker, 1988; Kellogg et
al., 1999); (3) crystallization of the basal magma ocean (Labrosse et al.,
2007; Lee et al., 2010) forming iron-rich and therefore dense material would
result in a compositionally dense layer above the core–mantle boundary in
the early phase of the Earth's evolution. On the contrary, there are
arguments for mechanisms that the dense material generates over time, e.g.,
through the recycling and segregation of oceanic crust (e.g., Christensen and Hofmann,
1994). Undoubtedly, there are arguments for and against the formation of a
dense layer in the deepest mantle at the beginning of the Earth's evolution,
though the dense material accumulated in the Archean deepest mantle is a
geologically realistic initial condition. Additionally, it is popular
because it can be implemented easily both in numerical (e.g., Van Summeren et
al., 2009; Li et al, 2014) and laboratory models (e.g., Jellinek and Manga,
2002; Gonnermann et al., 2002).
In order to make a comparison among different numerical models, Tackley
(2012) rescaled the results for the heat expansion of α=10-5K-1 as a more realistic value in the deep, compressible mantle (Mosenfelder
et al., 2009). Applying smaller heat expansion requires less initial
compositional density contrast to obtain the same Beff. Re-scaling our
model (Fig. 1) for reduced heat expansion minimum β=3 %, initial
compositional density contrast is needed to maintain the dense layer over
the age of the Earth. It is in accordance with the results of Tackley (2012),
who arrived at a density difference of 2–3 % based on different model
calculations.
Using tomographic likelihoods, Trampert et al. (2004) separated the total
density variation in the mantle into temperature and chemical density
variation. They established that the present compositional density variation
is dominant in the lower 1000 km of mantle and it is likely to
exceed 2 %. It corresponds to our models with initial density contrast of
β=3 % assuming reduced heat expansion because the density
difference decreases gradually due to erosion and dilution processes (Fig. 2).
Several normal modes of the Earth show a significant sensitivity to the
density/shear velocity ratio in the deep mantle (Koelemeijer et al., 2012).
Ishi and Tromp (2004) revealed a total density increment of approximately 0.5 %
beneath Africa and the Pacific in which the opposite effect of temperature
and compositional variation is superimposed. Taking into account the compositional density increase of more than 2 % and the total density
increase of only 0.5 %, a rough estimate of the effective buoyancy ratio
gives a value of slightly above 1. Based on our model results at this stage,
the TCC system in the Earth's mantle might be just before the instability
point. It agrees well with the present strongly deformed, disintegrated
morphology of LLSVPs (e.g., Garnero et al., 2007a).
The Supplement related to this article is available online at doi:10.5194/se-15-93-2015-supplement.
A. Galsa built up and tested the model, A. Galsa, M. P. Farkas and G. Taller
ran and evaluated the simulations. A. Galsa, M. Herein and L. Lenkey
interpreted the results and A. Galsa prepared the manuscript with
contributions from all authors.
Acknowledgements
The authors are grateful to P. J. Tackley and the anonymous reviewer for
their constructive remarks and improving the manuscript considerably. This
research was supported by the European Union and the State of Hungary,
co-financed by the European Social Fund in the framework of TÁMOP 4.2.4.
A/1-11-1-2012-0001 National Excellence Program. This research was also
supported by the Hungarian Scientific Research Fund (OTKA K-72665 and OTKA
NK100296) and it was implemented thanks to the scholarship in the
framework of the TÁMOP 4.2.4.A-1 priority project.
Edited by: T. Gerya
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