Page 142 - Physical Principles of Sedimentary Basin Analysis

124 Heat flow

0 0
(a) (b)
50
50
depth [km] 100 depth [km] 100 qs = 0.08W/m 2

150
qs = 0.06W/m 2
150 z m = 60 km qs = 0.04W/m 2
= 50 km 200
z m
= 40 km 2
z m qs = 0.02W/m
200 250
0 500 1000 1500 0 500 1000 1500
temperature [°C] temperature [°C]
Figure 6.8. (a) The geotherm in stable continents is plotted for different thicknesses of the crust.
(b) The geotherm is plotted for different values of the surface heat flow.

transition between the lithosphere and the asthenosphere is in a temperature interval around
1300 C.) The heat conductivities of the crust and the mantle are λ c = 2.5W m −1 K −1 and
◦
λ m = 3.0W m −1 K −1 . Figure 6.8 shows a series of geotherms with these crustal and
mantle heat conductivities, but here the crustal thickness and the mantle heat flow are
varied.
An advantage of such simple analytical estimates is that it is straightforward to analyze
the sensitivity of the model with respect to the parameters. For instance an uncertainty z m
in the crustal thickness gives an uncertainty

1 λ m
q s
z a = 1 − 1 + z m (6.89)
2 λ c q m
in the lithospheric thickness.

6.6 Stationary geotherms in the lithospheric mantle
◦
Heat conductivity is not constant over temperature intervals spanning several hundred C.
In fact most rocks have a decreasing heat conductivity with increasing temperature. This
temperature dependence is often expressed as

λ 0
λ A (T ) = (6.90)
1 + c 0 T
◦
where λ 0 is the heat conductivity and the temperature is in C(Seipold, 1995, 1998). (See
also Table 2.3, which lists the heat conductivities of some crystalline rocks.) We see that
◦
T = 1/c 0 is the temperature increase from 0 C that makes the heat conductivity decrease
◦
C
by half. The coefficient c 0 is typically of order 10 −3 ◦ −1 , which gives 1000 C as an esti-
mate of this temperature increase. Temperature dependent heat conductivity is of especial
◦
interest for the lithospheric mantle that spans a temperature range of roughly 1000 C. We
will now look at four alternative mantle heat conductivities and compare the corresponding