Heat - The Solid Earth - page 321

8. Calculate the geotherms for the models shown in Fig. 7.14. Discuss the reason for the
difference at depth between these geotherms and the geotherm shown as a solid line
in Fig. 7.14.
9. Calculate an equilibrium geotherm for the model Archaean crust shown in Fig. 7.4.
Discuss your estimates.
10. To what depth are temperatures in the Earth affected by ice ages? (Use thermal con-
ductivity 2.5 W m − 1 ◦ C − 1 and specific heat 10 3 Jkg − 1 ◦ C − 1 .)
11. Calculate the equilibrium geotherm for a two-layered crust. The upper layer, 10 km
thick, has an internal heat generation of 2.5 Wm − 3 , and the lower layer, 25 km thick,
has no internal heat generation. Assume that the heat flow at the base of the crust is
20 × 10 − 3 Wm − 2 and that the thermal conductivity is 2.5 W m − 1 ◦ C − 1 .
12. Repeat the calculation of Problem 11 when the upper layer has no internal heat gener-
ation and the lower layer has internal heat generation of 1 Wm − 3 . Comment on the
effect that the distribution of heat-generating elements has on geotherms.
13. Calculate geotherms for a layered continental crust and comment on the significance
of your results for the following cases.
(a) A 10-km-thick upper layer with heat generation of 2.5 Wm − 3

overlying a

30-km-thick layer with heat generation of 0.4 Wm − 3 .
(b) A 30-km-thick upper layer with heat generation of 0.4

Wm − 3 overlying a 10-

km-thick layer with heat generation of 2.5 Wm − 3 .For both cases, assume a

surface temperature of zero, heat flow from the mantle of 20 × 10 − 3 Wm − 2 and

thermal conductivity of 2.5 W m − 1 ◦ C − 1 .
14. A 1-m-wide dyke with a temperature of 1050 ◦ Cisintruded into country rock at a
temperature of 50 ◦ C.
(a) Calculate how long the dyke will take to solidify.
(b) After two weeks, what will the temperature of the dyke be?
(Assume a diffusivity of 10 − 5 m − 2 s − 1 and a solidus temperature of 800 ◦ C.)
15. Volcanic flood basalts can be several kilometres thick and extend over very large areas
(the Karoo basalt in southern Africa is one example). A 2-km-thick basalt is erupted at
1200 ◦ C. If the solidus temperature is 900 ◦ C, estimate the time required for the basalt
to solidify. If this basalt is later eroded and the underlying rocks exposed, indicate
how far you would expect the metamorphism to extend from the basalt. State all your
assumptions in answering this question.
16. (a) Calculate the difference in depth of the seabed at the intersection of a mid-ocean
ridge and a transform fault. Assume that the ridge is spreading at 5 cm yr − 1 and

that the ridge axis is offset 200 km by the transform fault.
(b) Calculate the difference in depth on either side of the same fault 1000 km from
the ridge axis and 3000 km from the ridge axis. (See Section 9.5 for information
on transform faults.)
17. Calculate the 60-Ma geotherm in the oceanic lithosphere for the simple model of
Section 7.5.2. What is the thickness of the 60-Ma-old lithosphere? Use an astheno-
sphere temperature of 1300 ◦ C and assume a temperature of 1150 ◦ C for the base of
the lithosphere