Geoscience Reference
In-Depth Information
o
Temperature ( C)
0
500
1000
1500
A = 4.2
10
CRUST
20
A = 0.8
30
MANTLE
Q = 63
Figure 7.4.
A two-layer model for the crust and equilibrium geotherm in the
Archaean. Heat generation
A
is in Wm
−3
; heat flow from the mantle
Q
is in
10
−3
Wm
−2
. Recall that, during the Archaean, heat generation was much greater
than
t
is now (Table 7.2). (After Nisbet and Fowler (1982).)
Consider a two-layer model:
A
=
A
1
for 0
≤
z
<
z
1
A
=
A
2
for
z
1
≤
z
<
z
2
T
=
0on
z
=
0
with a basal heat flow
Q
=−
Q
2
on
z
=
z
2
.Inthe first layer, 0
≤
z
<
z
1
, the
equilibrium heat-conduction equation is
2
T
∂
∂
A
1
k
=−
(7.29)
z
2
In the second layer,
z
1
≤
z
<
z
2
, the equilibrium heat-conduction equation is
2
T
∂
z
2
∂
A
2
k
=−
(7.30)
The solution to these two differential equations, subject to the boundary condi-
tions and matching both temperature,
T
, and temperature gradient,
∂
/∂
T
z
,onthe
=
boundary
z
z
1
,is
Q
2
k
+
z
A
1
2
k
z
2
A
2
k
A
1
z
1
k
T
=−
+
(
z
2
−
z
1
)
+
for 0
≤
z
<
z
1
(7.31)
Q
2
k
+
z
+
A
1
−
A
2
2
k
A
2
2
k
z
2
A
2
z
2
k
z
1
T
=−
+
for
z
1
≤
z
<
z
2
(7.32)
Figure 7.4 shows an equilibrium geotherm calculated for a model Archaean
crust. The implication is that, during the Archaean, crustal temperatures may
have been relatively high (compare with Fig. 7.3.).
