Heat - The Solid Earth - page 278

Figure 7.3. Equilibrium geotherms calculated from Eq. (7.28) for a
50-km-thick column of rock. Curve a: standard model with
conductivity 2.5 W m −1 ◦ C −1 , radioactive heat generation
1.25 Wm −3 and basal heat flow 21 × 10 −3 Wm −2 . Curve b:
standard model with conductivity reduced to 1.7 W m −1 ◦ C −1 .
Curve c: standard model with radioactive heat generation
increased to 2.5 Wm −3 . Curve d: standard model with basal heat
flow increased to 42

o

Temperature ( C)

0 500 1000 1500

0

20

10 −3 Wm −2 . Curve e: standard model with
basal heat flow reduced to 10.5

×

40

10 −3 Wm −2 . (From Nisbet and

×

ea dbc

Fowler (1982).)

are varied. This model column is 50 km thick, has conductivity 2.5 W m − 1 ◦ C − 1 ,
radioactive heat generation 1.25 Wm − 3

and a heat flow into the base of the

10 − 3 Wm − 2 . The equilibrium geotherm for this model column
is given by Eq. (7.28) and is shown as curve a in Fig. 7.3;atshallow levels
the gradient is approximately 30 ◦ Ckm − 1 ,whereas at deep levels the gradient is
15 ◦ Ckm − 1 or less.

column of 21 ×

Conductivity
Reducing the conductivity of the whole column to 1.7 W m − 1 ◦ C − 1 has the effect
of increasing the shallow-level gradient to about 45 ◦ Ckm − 1 (see curve b in
Fig. 7.3). Increasing the conductivity to 3.4 W m − 1 ◦ C − 1 would have the opposite
effect of reducing the gradient to about 23 ◦ Ckm − 1 at shallow levels.

Heat generation
Increasing the heat generation from 1.25

Wm − 3 raises the
shallow-level gradient to over 50 ◦ Ckm − 1 (curve c in Fig. 7.3); in contrast, reduc-
ing the heat generation to 0.4

Wm − 3

to 2.5

Wm − 3 reduces this shallow-level gradient to about

16 ◦ Ckm − 1 .

Basal heat flow
If the basal heat flow is doubled from 21 10 − 3 Wm − 2 , the gradient

at shallow level is increased to about 40 ◦ Ckm − 1 (curve d in Fig. 7.3). If the basal
heat flow is halved to 10.5

10 − 3 to 42 × ×

10 − 3 Wm − 2 , the shallow-level gradient is reduced
to about 27 ◦ Ckm − 1 (curve e in Fig. 7.3).

×

7.3.3 Two-layer models
The models described so far have been very simple, with a 50-km-thick surface
layer of uniform composition. This is not appropriate for the real Earth but is
a mathematically simple illustration. More realistic models have a layered crust
with the heat generation concentrated towards the top (see, e.g., Section 7.6.1).
The equilibrium geotherm for such models is calculated exactly as described
in Eqs. (7.20)-(7.28)except that each layer must be considered separately and
temperature and temperature gradients must be matched across the boundaries.