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J. Huw Davies, Dept. Earth Sciences
Hydrofrac Model
Davies, Nature, 1999
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J. Huw Davies, Dept. Earth Sciences
Temperature dependent rheology
Starting
Model
Model a
little time
later – not
steadystate
Model with temperature dependent
rheology, example here would ‘eat’
all the way to the surface.
Possible to get freezing out –see
Kincaid and Sacks. We know we
get magmas therefore I prefer hot
end-point => need means to stop
eating all the way to surface.
Possibly lithosphere in wedge
corner is crust (i.e. buyoancy not
rheology keeps things near surface)
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J. Huw Davies, Dept. Earth Sciences
Water reacts with mantle –
Davies (1994) Davies and Stevenson (1992)
Water reacts with largely
dry peridotite
melting
Mantle largely dry
Path of water
in hydrated
mineral
Water enters
wedge
Water flow as free phase
Flow of mantle
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J. Huw Davies, Dept. Earth Sciences
Equilibrium, 130Ma,
6cm/yr
My Favourite
Model
(Iwamori,
EPSL,1998)
Equilibrium, 10Ma,
6cm/yr
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J. Huw Davies, Dept. Earth Sciences
Iwamori (EPSL, 1998)
Disequilibrium, 130Ma, 6cm/yr
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J. Huw Davies, Dept. Earth Sciences
Iwamori (EPSL, 1998 – Fig Cap for Fig 5)

Fig. 5. Distribution of H2O (left) and melt (right). (a) For a relatively cold slab (age 130 Myr) with a
constant subduction velocity, of ~6 cm/year. A cross-sectional area of 250x250 km region with a fixed
crust of 30 km thick is divided into a regular grid for numerical calculations, with a finer triangular grid
at the slab¯wedge interface and at the bottom of the slab for preventing artificial diffusion of H2O. The
thickness of rigid slab can be defined as 2.32 (kt)1/2 where k is the thermal diffusivity. If k = 10-6 m2 s-1,
then thickness = 150km. In both the oceanic side (lower left corner) and the mantle wedge side (upper
right) of the rigid slab, the solid flow is assumed to be described by analytic corner flow solutions of
incompressible fluid with constant viscosity. The dotted lines in the mantle wedge indicate the stream
lines. The thermal boundary conditions are as follows: a surface temperature of 273 K; an error function
gradient for the plate age of 130 Myr and an adiabatic gradient underneath for the oceanic side
boundary; a linear gradient within the crust and within a thermal boundary layer of 12 km beneath the
crust to produce the surface heat flux of 0.115 W/m2, and an adiabatic gradient underneath the arc side
boundary, which gives the potential temperature ~1250°C; zero heat flux at the bottom boundary.The
solid lines indicate the isothermal contours with a 200K interval. A steady geothermal structure for H2Ofree subduction of the slab was assumed for an initial condition where no melt exists, then the slab with
6 wt% H2O started to subduct. The elapsed time for this snapshot is 7.1 Myr. (b) For a hot slab (age of
10 Myr) with a constant subduction velocity of ~6 cm/year. The thickness of rigid slab is 40km. The
other conditions are the same as in (a). The elapsed time for this snapshot is 4.1 Myr. (c) For a case
involving disequilibrium transportation of H2O. A small portion of the aqueous fluid (8% of the aqueous
fluid present in each local system) is assumed to be isolated chemically in the local system.
Consequently, once the aqueous fluid is produced, it can survive and continue to migrate even if the
surrounding solid and melt are not saturated with H2O. The other conditions are the same as in (a). The
elapsed time for this snapshot is 2.9 Myr.
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J. Huw Davies, Dept. Earth Sciences
Iwamori
(EPSL, 1998)
Fig 6
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J. Huw Davies, Dept. Earth Sciences
Physical and Chemical Constraints on SZ processes

Physical – (Many subduction zones – many experiments)



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

Plate velocities, Age of subducting lithosphere, thickness overriding plate crust
Shape of Benioff zone, double zone? Dip?
Location of magmatism – See below. Rate of magmatism, temp. of lavas
Surface shape – trench depth, outer arc rise – GPS, satellite
Heat flux – Broad scale good, but at local scale there are many poorly understood
processes
Seismology,

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Tomography – Velocity (P,S), Attenuation, low vel. zone (crust?)
Anisotropy – interpretation – water?
Focal mechanisms, stress regimes
3D seismic – ANCORP, Shipley et al., Banks et al.,
Down- and up-dip extent of mega-thrust plane
Lab measurements – rheology, anisotropy, dihedral angle
Electrical conductivity
Gravity and geoid – low density/low viscosity
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J. Huw Davies, Dept. Earth Sciences
Chemistry – help!


Inputs – Drilling of ocean sediments and basalts
Outputs – Composition

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Expts. – Melting expts. –

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Major elements – differentiation, primary magmas eq. temp, degree of melting
Trace elements – LILE/HFSE, B, degree of melting
Xenoliths
Isotopes - Stable/Radiogenic – Be10, U versus Pb, Th versus Be
Fluid/Melt Inclusions – water contents
Uranium decay chain isotopes – time scales – fast
Volatiles - fluxes
Sediments, Peridotite, Basalt +/- water, composition – diamond aggregates
Partitioning – including improved theory
Thermodynamic databases – MELTS – extend to hydrous systems
Outputs from other parts of the mantle; e.g. OIB - recycled SZ plates?
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J. Huw Davies, Dept. Earth Sciences
Location of arc relative to Benioff zone – h
Volcanic Front
o.c.
slab
h
mantle
earthquakes
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J. Huw Davies, Dept. Earth Sciences
h (km) – constant along arc segments, but different from
segment to segment – England, Engdahl et al.
(unpublished)
65
80
85 105
105
135
120
120
125
105
110
115
105
105
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J. Huw Davies, Dept. Earth Sciences
Subduction Tomography – Zhao + Hasegawa (1993)
Non-unique
but a 3D
constraint
Resolution?
Combine
with 3D
reflection
seismics?
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J. Huw Davies, Dept. Earth Sciences
Temperature of Primary Magmas
Tatsumi et al., Nye and Reid, etc.
 Questions –

 Is
this how magmas form? i.e. equilibrium, batch
 Do we sample and can we identify primary magmas?
Tatsumi et al., 1983
l
Temperature
opx+l
1320oC
ol+l
opx+cpx+l
ol+cpx+l
High Alumina Basalt +
1.5% water
ol+opx+cpx+l
50km
Pressure/Depth
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J. Huw Davies, Dept. Earth Sciences
Chemical correlations
Stolper and Newman – Water and Chemistry
 Plank and Langmuir – Sediment input and
volcanic output
 Elliott et al.  Etc

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J. Huw Davies, Dept. Earth Sciences
Melting of sediments


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Claims that sediments do melt
Experiments constrain temperature of sediment melting
Therefore constraint on temperature at sediment – wedge
boundary
Temperatures are generally higher than predicted by
numerical thermal models (but models, while precise are
not very accurate – equally interpretation of presence of
melt is debatable – remember difference between fluid
with high silica content and melt with high fluid contents
might be small)
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J. Huw Davies, Dept. Earth Sciences
Constraints – Huw Stops (You start)
– geometry
 Seismic tomography
 Sediment melting
 Chemical correlations – including
timescales
 Temperature of primary magmas
h
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