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Geochemistry, Geophysics, Geosystems
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Supporting Information for
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Eduction, Extension and Exhumation of Ultra-High Pressure Rocks in
Metamorphic Core Complexes due to Subduction Initiation
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Kenni Dinesen Petersen1,2 and W. Roger Buck2
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1Department of Geoscience, Aarhus University, Aarhus, Denmark.
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2Lamont-Doherty Earth Observatory of Columbia University, Palisades, New York.
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Contents of this file
Text S1
Table S1
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Introduction
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Text S1 provides a description of the numerical method employed in the main paper.
Assumed model parameters appear in Table S1. References for both Text S1 and Table
S1 are provided at the end of this document.
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Text S1.
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The code is based on the marker-in-cell technique described in Gerya [2010] and
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represents simultaneous viscous, elastic and plastic (brittle) deformation under the
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assumption of conservation of energy, momentum and mass in 2 dimensions (i=1,2):
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
xi
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Model Description and Numerical Method

T 
DT
  k
  c
 Hr  H A  HS
xi 
Dt

 ij'
x j
v j
x j
 gi 
(1)
P
0
xi
(2)
0
(3)
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1
'
Where  ij is the deviatoric stress tensor, v j is the velocity field vector, P    kk is
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pressure and H r  H A  H S is the total rate of energy change due to radiogenic, adiabatic
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and shear heating respectively.
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adiabatic heat production is approximated [Gerya and Yuen, 2003a] as Ha≈Tαvzg.
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1 v
Strain rate is related to the velocity field by ij   i  j  and is assumed to be the
2  x j xi 
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mutual contribution from brittle, elastic and viscous deformation:
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  
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Where the plastic multiplier, χ is nonzero only if  II   yield which is the Mohr-Coulomb
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failure limit:
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 yield  C  P sin(  )
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The brittle strength is taken to decrease with increasing brittle strain though a linear
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reduction of the friction angle [e.g. Buiter et al., 2006] until a value of 0 is reached at a
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strain of 0.1. It is this strain weakening that allows for a localized interface between the
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upper and lower plates of a subduction zone. The viscous rheology depends on
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composition, temperature, pressure and stress:
2
DT
is the material time derivative of temperature. The
Dt

'
ij
'
ij elastic
 
'
ij  plastic
 
'
ij viscous
v 
'
 ij'
1 D ij
1



 ij'
2 Dt
2 II 2 ( viscous)
(4)
(5)
2
1
 E  PV 
exp 

 RT 
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
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Following Duretz et al. [2011] we also account for the effect of exponential creep in the
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mantle by calculating an effective viscosity that is consistent with the flow law of
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Katayama and Karato [2008]:
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
 H
  Ap II2 exp  
 RT

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Practically, this is implemented such that this mechanism activates and predominates
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when the effective viscosity for exponential creep is less than that for power-law creep.
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Densities are temperature-dependent, and for the mantle we employ a temperature-
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dependent coefficient of thermal expansion [Gillet et al., 1991]. For remaining lithologies
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we assume a constant (with temperature) coefficient of expansion [McKenzie et al.,
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2005]. Following the Boussinesq approximation [Ranalli, 1995], density changes due to
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temperature changes are assumed to affect only the momentum equation (2), but are
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ignored in the continuity equation (3).
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For definitions of the remaining terms we refer to earlier works using similar
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nomenclature and methods [Gerya and Yuen, 2007; Petersen et al., 2010] and Table S1.
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A stress-free surface is represented by employing a ‘sticky-air’ approach [Crameri et al.,
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2012] by letting the initial upper 40 km of the modelling domain have little mass and low
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(relative to the time scale of thermal evolution of the lithosphere) viscosity of 1020 Pa s.
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Furthermore, we ensure that negligible surface stresses form by also setting a plastic yield
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limit of 0.1 MPa (similar to the numerical precision of the modelling method) for the ‘air’
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layer [Petersen et al., 2015]. This renders the surface effectively stress-free even during
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rapid surface movements and dynamically limits the effective viscosity only when
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needed (a beneficial property for especially iterative thermo-mechanical solution
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strategies). The numerical precision of 0.1 MPa of the modelling method is specified
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explicitly for multigrid iterations that are repeated until residuals of both the momentum
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and continuity equations correspond to errors that are less than this amount [Taras Gerya,
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pers. comm.].
n 1
2 A II
 
1   II
   p2
 
(6)




2




(7)
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Surface processes are represented as a simple diffusion process [Kooi and Beaumont,
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1994], but with a diffusivity of only 10-8m2/s. For a time scale of 20 Myr this corresponds
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to a length scale of ~3.5 km. This implies that such diffusion does not affect large-scale
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topographic variation, but only local areas with high convexity. In particular, trenches
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that form upon subduction initiation will be affected by this by having their relief
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smoothed. Practically, erosion and sedimentation are implemented by converting markers
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to air or sediment, respectively [Gerya and Yuen, 2003b]. The employment of such short-
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wavelength erosion/sedimentation appears to increase numerical stability in the present
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modelling experiments.
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Table S1. Assumed model parameters.
Description
Symbol
Value
Viscosity
Η
1020 Pas
Yield strength
σy
0.1 MPa
Shear modulus
Μ
1 GPa
Density
Ρ
1 kgm-3
Angle of internal friction [Buiter et al., 2006]
φ
Cohesion [Ranalli, 1995]
C
36° (linearly reduced to 0° as plastic strain
approaches 0.5)
10 MPa
Coefficient of thermal expansion [Parsons and Sclater,
1977]
Isobaric heat capacity
α
3.28·10-5K-1
Cp
800 Jkg-1K-1
Shear modulus
μ
25 GPa
Reference density at 273 K
ρ0
2800 kgm-3
Radiogenic heat production
Hr
1.0 μWm-3
Thermal conductivity
k
2.5 Wm-1K-1
Activation energy [Ranalli, 1995]
E
238 kJmol-1
Power-law exponent [Ranalli, 1995]
n
3.2
Power-law constant [Ranalli, 1995]
A
2.08·10-23Pa-ns-1
Reference density at 273 K
ρ0
2300 kgm-3
Radiogenic heat production
Hr
1.0 μWm-3
Activation energy [Ranalli, 1995]
E
154 kJmol-1
Power-law exponent [Ranalli, 1995]
n
2.3
Power-law constant [Ranalli, 1995]
A
5.07·10-18Pa-ns-1
Thermal conductivity
k
2.0 Wm-1K-1
Reference density at 273 K
ρ0
3000 kgm-3
Radiogenic heat production
Hr
1.0 μWm-3
Thermal conductivity
k
2.5 Wm-1K-1
Activation energy [Ranalli, 1995]
E
238 kJmol-1
Power-law exponent [Ranalli, 1995]
n
3.2
Power-law constant [Ranalli, 1995]
A
2.08·10-23Pa-ns-1
Reference density at 273 K
ρ0
3300 kgm-3
Coefficient of thermal expansion [Gillet et al., 1991]
α
2.77·10-5K-1+0.97·10-8K-2T+0.32 KT-2
Thermal conductivity [McKenzie et al., 2005]
k
4.08 Wm-1K-1(298K/T)0.406
Isobaric heat capacity [Berman and Brown, 1986]
Cp
[1.69·10-3-1.42·104(T/K)0.5-8.27·108(T/K)-3]
Jkg-1K-1
Shear modulus [Karato and Wu, 1993]
μ
80 GPa
Activation energy [Karato and Wu, 1993]
E
540 kJmol-1
Power-law exponent [Karato and Wu, 1993]
n
3.5
Power-law constant [Karato and Wu, 1993]
A
2.41·10-16Pa-ns-1
Activation volume [Karato and Wu, 1993]
V
15 cm3mol-1
Freely deforming upper layer
All lithologies (except ‘seeds’)
Crust (all lithologies)
-Continental (upper and lower)
-Sediments
-Oceanic
Mantle
-Dislocation creep
-Exponential creep
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Exponential-law constant [Katayama and Karato, 2008]
Ap
6.31·10-5Pa-2s-1
Peierls stress [Katayama and Karato, 2008]
σp
2.87 GPa
Activation enthalpy at zero stress [Katayama and Karato,
2008]
H
512 kJmol-1
Seeds have identical rheological properties as the mantle except that plastic yield limit is
1 MPa.
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