Auxiliary material for
Deep recycling of oceanic asthenosphere material during subduction
Lijun Liu, Quan Zhou
Department of Geology, University of Illinois at Urbana-Champaign
Geophysical Research Letters, 2015
Introduction
This file contains a supplementary text, one table and five additional figures in
support of the main manuscript.
Supplementary Text
1. Numerical Method
We simulate subduction and mantle convection using the finite element code
CitcomS (Zhong et al., 2000; Tan et al., 2006). We approximate the mantle as an
incompressible fluid with variable viscosity under the Boussinesq approximation.
The non-dimensional governing equations the model solves include:
(1)
(2)
(3)
¶C
+ u × ÑC = 0
¶t
(4)
1
where
is velocity, P dynamic pressure, η dynamic viscosity, ρm ambient mantle
density, α thermal expansion coefficient, g gravitational acceleration, DT
temperature increase from surface to the Earth interior, er unit vector in radial
direction, T temperature, κ thermal diffusivity, C composition, respectively.
We use 2-dimensional models to track the temporal evolution of the slabasthenosphere system and neglect the effect of 3-dimensional toroidal flow around
slab edges. This is because most subduction trenches are longer than 1000 km,
below which trench-parallel sub-slab mantle flow starts to become apparent along
the entire trench (Stegman et al., 2006). The model covers a 4000 km × 2000 km
physical domain in the east-west and radial direction, respectively (Fig. S1a). This
domain is divided into a 600 by 200 finite element mesh with regional mesh
refinement applied in the central and upper half of the box, which leads to a
minimum of 4 km grid resolution for the uppermost 200 km. The grid size in the
vertical direction gradually increases to ~5 km at 300 km and ~10 km at 600 km
depths. Horizontal grid size remains ~4 km from the surface to the lower mantle.
This mesh can sufficiently resolve the thermal (Davies et al., 2007) and rheological
gradients (Moresi et al., 1996) inside the subducting slab and the underlying
asthenosphere all the way into the lower mantle.
2. Boundary Conditions & Rheology
On the top of the model domain, we include an age-dependent thermal
boundary layer to represent oceanic plates (Fig. S1a, b). The model has a subducting
plate with a constant age at 80 million years old (Ma), forward subduction speed at
5 cm/year, and a trench retreat speed at 1 cm/year, unless otherwise noted. The
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ambient mantle either assumes a constant viscosity across the entire upper mantle,
or adopts a graduate viscosity increase with depth (by a factor of 3) to reflect the
depth-dependence. In all cases, the transition zone viscosity is fixed at 1.5×1021 Pa s,
and the lower mantle viscosity at 3×1022 Pa s. A list of model parameters are in
Table 1.
In order to keep the continent from getting subducted, we assign positive
compositional buoyancy to the continental crust using tracers and keep the
lithosphere at mantle temperature. On the bottom of the model domain, we assume
a constant temperature condition. The model has free-slip boundary conditions on
the bottom and sidewalls. In order to generate subduction from the top thermal
boundary layer, we impose velocity conditions at the surface. Both the seafloor age
and velocity boundaries are synchronized to allow for horizontal motions of the
trench. For simplicity, we neglect the effects of phase transformations at 410 and
660 km, which is not critical for the main topic of this paper.
We use depth-, temperature-, composition- and stress-dependent (or viscoplastic) mantle viscosity (Fig. S1b), similar to that used in earlier research (Zhong et
al., 1996; Faccenna et al., 2010). Viscosity jumps at depth 200km and 660 km.
Smoothing is applied to these two depths. The dependence of viscosity on
temperature is
æ
E
E
è T + Toff 1+ Toff
h =hr exp çç
ö
÷÷
ø
(5)
3
where ηr is the reference viscosity, E is the activation energy, Toff is surface
temperature (300 °C). Both the background (i.e., reference) viscosity change with
depth and its temperature-dependence are shown in Figure S2.
Special attention is needed for treatment of plate boundary and lithospheric
rheology, in order to generate self-evolving subducting slabs (Liu & Stegman, 2011)
and deformation within the overriding plate (Capitanio et al., 2011). We adopt a
weak plastic crust within the subducting plate such that the slab can mechanically
decouple from the overriding plate at the trench and bend naturally as it enters the
mantle. The plasticity is applied in the overriding lithosphere as well, which allows
the continent to stay as a coherent strong body but focus deformation within
narrow zones. With both the weak oceanic crust and plasticity, we can successfully
avoid any artificial weak zones commonly used in numerical models to generate
asymmetric subduction.
3. Composition Dependent Buoyancy and Viscosity
Due to the uncertain nature of asthenosphere, we allow its density and
composition to vary independently and use a composition-dependent viscosity and
buoyancy to simulate dynamic properties of the oceanic asthenosphere. In practice,
we use the particle-in-cell tracer method (Tackley & King, 2003) to define and
advect chemical compositions. This method was improved to define compositiondependent viscosity (Bower et al., 2010), in which materials have distinct intrinsic
viscosity values that are multiplied to the background viscosity profile. We make
further modifications based on these existing functions, such as we define materialbased yield stress and the results are shown in this paper.
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In reality, a weak asthenosphere may result from excess temperature, partial
melt, and/or strain-rate weakening. In order to cover the likely amount of viscosity
reduction due to these mechanisms, we consider an asthenosphere that is up to
three orders of magnitude weaker relative to the underlying upper mantle. In
practice, we use a tracer-defined channel to simulate the asthenosphere, which is
placed right below the thermal boundary layer representing the oceanic plate (Fig.
S1b). Based on the seismically detected slow velocity channel beneath ocean basins
(Revenaugh & Jordan, 1991; Tan & Helmberger, 2007), we assume a 70-km thick,
cold and strong oceanic lithosphere, underlain by a buoyant and weak
asthenosphere that extends down to ~200 km depth; these dynamic properties of
the asthenosphere are implemented either by depth (assuming the asthenosphere is
chemically the same as the ambient mantle) or by tracers (assuming a thermally or
chemically different asthenosphere). Note that due to the positive buoyancy of
asthenosphere, the initially prescribed weak channel will thin over time, so we add
in tracers from below and keep the bottom of the channel to be no shallower than
200 km depth.
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Table 1
Model parameters that are fixed in all simulations
Parameter
Value
Temperature change across lithosphere
1250 °C
Yield stress for overriding plate
10 MPa
Reference Viscosity η0
1021 Pa s
Activation Energy E
31 kJ/mol
Maximum Temperature Tmax
1250 °C
Maximum viscosity cutoff
1024 Pa s
Minimum viscosity cutoff
1018 Pa s
Minimum oceanic crust viscosity
1018 Pa s
Density anomaly of continent
-10% of ambient mantle
6
Figure S1. Model setup and the initial condition. A) The 2D model domain and the
initial temperature boundary layer representing the oceanic plate. A layer of tracers
(black dotted region) right below the oceanic lithosphere is used to realize the
viscosity and density anomaly within the asthenosphere. B) Close up view of the
middle part of the model domain, showing the viscosity structure including a strong
oceanic plate, plastic overriding plate, and a weak oceanic asthenosphere, together
with the velocity field (arrows). The average upper mantle viscosity is 1×1021 Pa s
and that in the lower mantle 3×1022 Pa s.
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Figure S2. Depth- and temperature-dependence of viscosity. Left: Background
viscosity variations with depth. Right: Viscosity changes due to temperature. At low
temperature, the viscosity will be extremely strong, thus a cut-off value of 1024 Pa s
is applied.
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Figure S3. Subduction model with a two-layer asthenosphere at three snapshots.
The upper layer has a viscosity at 5×1018 Pa s and the lower layer has 5×1019 Pa s.
This is to test if a weaker upper asthenosphere layer, such as due to partial melt,
would cause significant reduction of the asthenosphere entrainment, and the
modeling results suggest this is a minor effect.
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Figure S4. Snapshots of asthenosphere entrainment after 50 million years of
subduction, with a fixed asthenosphere viscosity at 2×1019 Pa s and a 20-Ma
subducting slab. A-C: Asthenosphere density anomaly increases from 0.3% to 1.0%.
The observation that the slab dip decreases with increasing asthenosphere
buoyancy suggests that in order for the 20-Ma slab to subduct into the deep mantle,
the maximum asthenosphere density anomaly magnitude should be between 0.5%
and 1.0%, with a plausible value being 0.75%.
10
Figure S5. Subduction model with a weak slab (100× of ambient mantle viscosity).
The asthenosphere density anomaly is -0.5%, and viscosity at 2×1019 Pa s. After 20
Myr of subduction (A), a thick layer of asthenosphere is entrained. At 30 Myr (B),
the entrainment asthenosphere breaks the overlying slab. Eventually at 40 Myr (C),
the initially entrained asthenosphere escape into the mantle wedge, leading to little
entrainment.
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Figure S6. Translation of asthenosphere deformation pattern into the deep mantle
during subduction. In this model, the asthenosphere is considered a layered channel
following Kawakatsu et al. (2009). Multiple tracer layers are used to define initial
asthenosphere viscosity and buoyancy structures and to track the internal
deformation over time.
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