Geoscience Reference
In-Depth Information
Table 7.6
Some continental heat-flow provinces
Mean
Q
0
(10
−3
Wm
−2
)
Q
r
(10
−3
Wm
−2
)
Province
D
(km)
Basin and Range (U.S.A.)
92
59
9.4
Sierra Nevada (U.S.A.)
39
17
10.1
Eastern U.S.A.
57
33
7.5
Superior Province
(Canadian Shield)
39
21
14.4
U.K.
59
24
16.0
Western Australia
39
26
4.5
Central Australia
83
27
11.1
Ukrainian Shield
37
25
7.1
Source
: Sclater
et al
.(1980).
We consider here two extreme models of the distribution of the radioactive
heat generation in the crust, both of which yield a surface heat flow in agreement
with this observed linear observation.
1.
Heat generation is uniformly concentrated within a slab with thickness D
.
In this case, using Eq. (7.16), we obtain
∂
2
T
∂
A
0
k
=−
for 0
≤
z
≤
D
z
2
Integrating once gives
∂
T
∂
z
=−
A
0
k
z
+
c
(7.76)
where
c
is the constant of integration. At the surface,
z
=
0, the upward heat flow
Q
(0) is
z
=
0
Q
(0)
=
Q
0
=
k
∂
T
∂
z
=
kc
(7.77)
Therefore, the constant
c
is given by
Q
0
k
c
=
At depth
D
, the upward heat flow is
Q
(
D
)
=
k
A
0
D
k
Q
0
k
−
+
=−
A
0
D
+
Q
0
=
Q
r
(7.78)
Thus, in this case, the heat flow
Q
(
D
) into the base of the uniform slab (and the
base of the crust, since all the heat generation is assumed to be concentrated in
the slab) is the
Q
r
of Eq. (7.75).
