Geology Reference
In-Depth Information
Table B.3.
Parameters of the numerical thermal evolution
model of Figure 9.2.
Quantity
Symbol
Value
Inputs:
Reference mantle temperature
1300
◦
C
T
r
10
20
Pa s
Reference upper-mantle viscosity
μ
r
3
×
10
22
Pa s
Reference lower-mantle viscosity
E
∗
Viscous activation energy
325 kJ/mol
1650
◦
C
Initial temperature
Initially estimated Urey ratio
Ur
0.71
Outputs:
Final temperature, upper mantle
1284
◦
C
T
U
1269
◦
C
Final temperature, mean mantle
T
Final surface heat loss
Q
S
40.1 TW
Final radiogenic heating
Q
R
35.7 TW
Final Urey ratio
Ur
0.89
melting depth in the models is estimated from the mean upper-mantle temperature and an
approximation to the eclogite solidus versus depth of Yasuda
et al.
[80]:
1020
.
(B.2)
The variation of crustal thickness with temperature in undepleted mantle is taken from
McKenzie and Bickle's estimates [243] for fertile (undepleted) mantle, calibrated to yield
7 km at 1280
◦
C:
0
.
478
T
up
−
z
melt
=
1280)
.
(B.3)
Units in both formulae are km and
◦
C. The method of estimation of the crustal thickness is
not strictly consistent with the eclogite melting implied by the melting model, but it is
assumed to usefully represent the trend for this exploration.
Subduction returns the crustal layer and the depleted layer to the mantle, where they
are stirred by mantle convection. These and other features of the model are described in
more detail by Davies [203]. The simulated melting is suppressed under the 'continental'
region in the centre, since the upper boundary there is taken to be the base of continental
lithosphere at around 200 km depth, under which little melting should occur.
Because heavy tracers tend to accumulate at the bottom of the model, it is necessary to
ensure that their concentration does not exceed that corrresponding to pure basaltic
component. This is done during the tracer advection process by checking for each tracer
whether the limit has already been exceeded for the local grid cell. If so, the tracer is
moved up until it reaches a cell whose concentration is below the limit.
d
crust
=
7
+
0
.
085 (
T
up
−
B.5 Models with basalt tracers
The results shown in Figure 9.5 are from an unpublished model, and those in Figure 9.10
are Case 2 of Davies [156], where full details can be found. Figure 9.5 is similar to Case 1
