Auxiliary material for
Deep water recycling through time
Valentina Magni, Pierre Bouilhol, Jeroen van Hunen
Department of Earth Sciences, Durham University, Science Labs, Durham DH13LE,
United Kingdom
Geochemistry, Geophysics, Geosystems (G-Cubed)
Introduction
In the following text we provide details on 1) the numerical method, 2) the
thermodynamic model, 3) the different thermal structures of the subduction zone, and
4) the phases involved in the first dehydration reaction for present-day conditions.
Figures list and captions
Figure s01: (a) P-T diagram in the NCFMASH closed system showing the fields of
stability of hydrous phases calculated for sample LTBC, with 2 wt% H2O (modified
from Bouilhol et al., under review). (b) P-T diagram calculated for the depleted
mantle composition [Workman and Hart, 2005] with 2 wt% H2O; (c) T-X diagram for
the DMM that shows the stability field of hydrous phases at P=3 GPa and varying
water content (0-12 wt%). (d) P-X diagram for the DMM that shows the stability field
of hydrous phases at T=500°C and varying water content (0-12 wt%). Dry
eclogites=Cpx+Grt. SiO2 in excess. Amph=Amphibole; Atg=Antigorite; Ph-A=phase
A; Br=Brucite; Chl=Chlorite; Ctd=Chloritoid; Ep=Epidote; Grt=Garnet;
Law=Lawsonite; T=Talc
Figure s02: Thermal structure of different models (a) a=40 Myr, Tm=1350°C, and
vs=2.5 cm/yr (dashed magenta contours) vs. vs=10 cm/yr (solid black contours); (b)
vs=5 cm/yr, Tm=1350°C, and a=40 Myr (dashed magenta contours) vs. a=80 Myr
(solid black contours); (c) a=40 Myr, vs=5 cm/yr, and Tm=1350°C (dashed magenta
contours) vs. Tm=1550°C (solid black contours). The green area shows where the slab
crust is. Contours are every 200°C, from 200°C to 1200°C.
Figure s03: Equilibrium paragenesis and phases amount (%) at the first water released
from the crust for models with Tm 1350°C. Slab age has no or very little effect on the
phases involved in the first crust dehydration reaction. Amphibole is present for fast
subductions, whereas Talc is involved in the dehydration for slower slabs.
Figure s04: Phases amount (%) as shown in Fig.2c. Example of (a) a model in which
the lithospheric mantle gets entirely dehydrated due to the breakdown of chlorite
(model with a=40 Myr, vs=5 cm/yr and Tm=1350°C); and (b) a model in which H2O
stays bound in the middle part of the hydrated DMM layer as the stability field of
phase-A is reached before Chl breakdown occurs.
1. Numerical method of the thermo-mechanical modelling
We use the finite element code Citcom [Moresi and Gurnis, 1996; Zhong et al.,
2000; van Hunen et al., 2005] to compute the thermal structure of the subduction
system. The equations of conservation of mass, momentum and energy are solved in a
Cartesian geometry assuming an incompressible flow and adopting the Boussinesq
approximation (symbols defined in Table 1):
𝜕𝑇
𝜕𝑡
∇∙𝑢 =0
(1)
−∇𝑝 + ∇ ∙ (𝜂(∇𝑢 + ∇𝑢𝑇 )) = 0
(2)
+ 𝑢 ∙ ∇𝑇 = ∇2 𝑇
(3)
The computational domain is 300 km deep and 600 km wide and the finite
element mesh has a resolution of 0.6 km, which is sufficiently high to solve the
governing equations even when the viscosity contrast is high and at the mantle wedge
corner [van Keken et al., 2008]. The slab subducts with a constant dip α = 30° and a
constant velocity, which is prescribed at the left-hand side and bottom boundary.
Similar model setups have been used in other studies [van Keken et al., 2008;
Syracuse et al., 2010]. A stress-free inflow/outflow boundary condition is imposed for
the right-hand side of the domain, whereas the top has a no-slip boundary condition.
The temperature is prescribed in the top boundary (T=0°C), and the left-hand side
boundary (the thermal structure of the incoming plate is computed for a given slab
age from the half-space cooling solution [Turcotte and Schubert, 2002]), while a zero
conductive heat flux applies on the right and bottom boundaries. The initial
temperature field is computed beforehand in a model in which the subduction of a
slab with a given age evolves until it a thermal steady state solution. This solution is
then used as the initial temperature field of the models. An a posteriori adjustment of
0.5 K/km is applied to the temperature to take into account the effect of adiabatic
heating. Subduction is enabled by the presence of a 2-km wide weak fault zone
(ηwz=η0) that decouples the plates. In the mantle wedge the deformation is
accommodated with a diffusion creep mechanism, in which the viscosity is described
as:
𝜂𝑑𝑖𝑓𝑓 = 𝜂0 exp (
𝐸
𝑅𝑇𝑎𝑏𝑠
−
𝐸
𝑅𝑇𝑚
)
(4)
A maximum value of viscosity of 1023 Pa s is imposed for the mantle wedge and a
fixed value of 1026 Pa s is imposed for the plates. The mantle wedge flow is purely
slab-driven, as we neglect the gravitational force.
Table 1: Symbols, units and default model parameters
Parameters
Temperature
Mantle potential temperature
Reference mantle viscosity
Diffusion creep viscosity
Maximum mantle viscosity
Lithosphere viscosity
Weak zone viscosity
Gas constant
Activation Energy
Water retention
Deviatoric pressure
Time
Velocity
Plate velocity
Plate age
Mesh resolution
Symbols (unit)
Tabs (K)
Tm(°C)
η0 (Pa s)
ηdiff(Pa s)
ηmm (Pa s)
ηl (Pa s)
ηw (Pa s)
R (J/mol K)
E (kJ/mol)
W (%)
p (Pa)
t (s)
u (m/s)
vs (cm/y)
a (Myr)
km2
Value
1350-1550
1021
1024
1026
1021
8.3
360
2.5-10
40-80
0.6x0.6
2. The Thermodynamic model
The metamorphic processes are investigated in the chemical space Na2O-CaO-FeOMgO-Al2O3-SiO2-H2O (NCFMASH system). Our choices of solid-solutions
reproduce fairly well the sub-solidus crustal parageneses and solidus shape of LTBC
as well for the DMM and primitive mantle compositions (see Bouilhol et al., under
review). The solid solutions models are those of Holland and Powell [1998], except
for spinel [Jamieson and Roeder, 1984] and plagioclase [Newton et al., 1980]. The
thermodynamic behaviour of water is dictated by the equation of state of Holland and
Powell [1991].
3. Thermal solution
The thermal structure of a subduction zone, together with the slab composition,
determines the reactions involved in the slab dehydration processes. Each of the three
parameters that are varied in the models (subduction velocity vs, slab age a, and
mantle potential temperature Tm) has an effect on the temperature field. In general, a
cold subduction zone is obtained for old and fast slabs and low mantle potential
temperature. However this is not always the case when looking at different parts of
the slab.
Fig. s02a shows the different temperature fields obtained for two models with the
same slab age (40 Myr) and same potential mantle temperature (1350°C), but with
different subduction velocity (2.5 cm/yr and 10 cm/y). The subduction velocity has no
effect on the thermal state of the plate before it enters the trench, thus, at the left-hand
side boundary there is no difference between the models. With vs of 10 cm/yr the
isotherms near the slab surface are much closer to each other than those in the model
with vs of 2.5 cm/yr. This difference in the thermal structure of the system has two
main consequences. The first one is that the top of the slab is hotter for high vs, or,
more precisely, isotherms above 200°C cross the top of the slab shallower for high vs.
The second consequence is a difference in the slope of the isotherms, which are more
parallel to the slab surface for vs=10 cm/yr than for vs=2.5 cm/yr. This means that
although the top of the slab reaches high temperatures sooner when subduction is fast,
for a point that is only few kilometers deeper in the slab, for instance at the Moho, the
opposite is true: it takes longer for that point to reach the same temperature if vs is
high. The reason for these differences in the temperature field is that high subduction
velocities (7.5-10 cm/yr) create vigorous convection in the mantle wedge, causing the
advection of heat to be very efficient. Thus, hot mantle material is brought very close
to the top of the slab resulting in higher temperatures at shallower depths for fast slabs
compared to the slower ones (2.5-5 cm/yr). This is consistent with other thermal
modeling results of a subduction system [England and Wilkins, 2004; Rüpke et al.,
2004; Wada and Wang, 2009]. On the other hand, the mantle wedge convection does
not affect the temperature deeper in the slab, and the high efficiency of heat advection
for fast subducting plates brings cold material in the core of the slab at greater depths.
The effect of slab age on the thermal structure of the subduction system can be
observed in Fig. s02b that shows two models with the same vs of 5 cm/yr, the same
Tm of 1350°C and different slab age (40 Myr vs 80 Myr). Young slabs are hotter
compared to old slabs as their temperature is defined by the half-space cooling
solution. Therefore, the largest temperature difference between the two models of Fig.
s01b is found deep in the slab (far away from the slab surface). Indeed, at the slab
surface the temperature field is very similar, since the convection in the mantle wedge
is not affected at all by the slab age.
Finally, the effect of a different potential mantle temperature is shown in Fig.
s02c with the results from two models with the same vs =5 cm/yr, the same a = 40
Myr, and different Tm (1350°C vs 1550°C). Here, a combination of what we observed
in the comparisons described above can be seen. A different Tm affects both the initial
thermal structure of the incoming plate (as for the slab age) and the mantle wedge
convection (as for the subduction velocity) due to the temperature-dependent mantle
wedge viscosity. With high Tm the subducting plate is hotter from the beginning, and
isotherms in the core of the slab go deeper when mantle potential temperature is low.
Moreover, a direct consequence of the high Tm is that the temperature at the top of the
slab is higher, since a weaker mantle wedge allows a more localized shearing and,
thus, hot mantle material is brought close to the slab surface.
4. Phases involved in the first dehydration reaction for present-day conditions
As described in the Section 3.2.1, when slabs are slow (2.5 and 5 cm/yr) the
dehydration of the crust starts deeper than for fast slabs (7.5 and 10 cm/yr). The main
consequence of this is that amphibole is present when water is released at shallow
depths (25 ≤ P ≤ 29 kbar), so for vs=7.5 and 10 cm/yr, whereas it is absent in the
case of vs=2.5 and 5 cm/yr, as the dehydration reactions occur at greater depths (31 ≤
P ≤ 40 kbar) where amphibole is not stable anymore (Fig. s03). For those low
velocities talc is responsible for releasing water, with the following paragenesis: Cpx
(41-42%), Gt (31-32%), coe (6%), talc (6-8%), Law (13-15%), and free H2O. This
does not change significantly when the slab age is varied. If the subduction velocity is
7.5 cm/yr both amphibole (14%) and talc (5%) are present (except for the 80 Myr old
slab case), together with Law (14%), Cpx (33%), Gt (29%), and coe (5%). In this case
it is the amphibole that goes unstable first and releases water. In the 10 cm/yr cases
talc is absent and the amount of amphibole present is much larger than for the 7.5
cm/yr cases. Indeed, the equilibrium paragenesis is: Cpx (29%), Gt (32%), Q (6%),
Amph (21%), and Law (11%).
References
Bouilhol, P., V. Magni, J. van Hunen, and L. Kaislaniemi, A numerical approach to
melting in warm subduction zones, submitted to Earth Planet Sc Lett.
England, P., and C. Wilkins (2004), A simple analytical approximation to the
temperature structure in subduction zones, Geophys J Int, 159(3), 1138-1154.
Holland, T.J.B., and Powell, R., (1998), An internally consistent thermodynamic data
set for phases of petrological interest, J. Metamorph. Geol., 16, 309-343.
Jamieson, H. E., and P. L. Roeder (1984), The distribution of Mg and Fe (super 2+)
between olivine and spinel at 1300 degrees C, American Mineralogist, 69(3-4),
283-291.
Moresi, L., and M. Gurnis (1996), Constraints on the lateral strength of slabs from
three-dimensional dynamic flow models, Earth Planet Sc Lett, 138(1-4), 15-28.
Newton, R. C., T. V. Charlu, and O. J. Kleppa (1980), Thermochemistry of the high
structural state plagioclases, Geochim Cosmochim Ac, 44(7), 933-941.
Rüpke, L. H., J. P. Morgan, M. Hort, and J. A. D. Connolly (2004), Serpentine and
the subduction zone water cycle, Earth Planet Sc Lett, 223(1-2), 17-34.
Syracuse, E. M., P. E. van Keken, and G. A. Abers (2010), The global range of
subduction zone thermal models, Phys Earth Planet In, 183(1-2), 73-90.
Turcotte, D. L., and G. Schubert (2002), Geodynamics: Applications of continuum
physics to geological problems. Second Edition, Cambridge University Press.
van Hunen, J., S. Zhong, N. M. Shapiro, and M. H. Ritzwoller (2005), New evidence
for dislocation creep from 3-D geodynamic modeling of the Pacific upper mantle
structure, Earth Planet Sc Lett, 238(1-2), 146-155.
van Keken, P. E., et al. (2008), A community benchmark for subduction zone
modeling, Phys Earth Planet In, 171(1-4), 187-197.
Wada, I., and K. Wang (2009), Common depth of slab-mantle decoupling:
Reconciling diversity and uniformity of subduction zones, Geochemistry,
Geophysics, Geosystems, 10(10), Q10009.
Zhong, S. J., M. T. Zuber, L. Moresi, and M. Gurnis (2000), Role of temperaturedependent viscosity and surface plates in spherical shell models of mantle
convection, J Geophys Res-Sol Ea, 105(B5), 11063-11082.