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11. Derive an equation for the initial subsidence of an instantaneously stretched litho-
sphere, when no water fills the surface depression.
12. Assume that the earthquake shown in Fig. 10.59 took place in the upper crust
(
α
=
6kms
−
1
,
β
=
3.5 km s
−
1
).
(a) Use the P- and S-wave arrival times to calculate the distance from the focus to the
seismometer.
(b) What estimates can you make about the height of the focus above the reflecting
horizon and the depth of that horizon beneath the surface?
13. What can deep seismic profiling reveal about the structure of the continental litho-
sphere? (Cambridge University Natural Sciences Tripos II, 1986.)
14. A 35-km-thick continental crust is heated, resulting in an instantaneous increase in
temperature of 500
◦
C.
(a) Calculate the resulting elevation of the surface.
(b) Calculate the thickness of sediments which could finally be deposited if 500 m of
crust were eroded while the surface was elevated. (Let
ρ
s
,
ρ
c
and
ρ
m
be 2.3
×
10
3
, 2.8
×
10
3
and 3.3
×
10
3
kg m
−
3
, respectively;
α
,3
×
10
−
5
◦
C
−
1
.)
15. Assume that continental lithosphere, thickness 125 km, undergoes instantaneous
extension. What is the minimum value of the stretching factor
β
necessary for astheno-
spheric material to break through to the surface? For this value of
,what is the total
amount of subsidence that would eventually occur? (Let the crustal thickness be 35 km;
water, crustal and mantle densities, 1.03
×
10
3
, 2.8
β
10
3
kg m
−
3
,
respectively; coefficient of thermal expansion, 3
×
10
−
5
◦
C
−
1
; asthenosphere temper-
ature, 1350
◦
C.)
16. Calculate the amount of initial subsidence that would result from instantaneous exten-
sion of the continental lithosphere by factors of two and ten. Make reasonable assump-
tions for the thickness, density and temperature of the crust and mantle.
17. What evidence has been used to confirm the importance of a stretching-and-cooling
mechanism in the formation of some sedimentary basins? (Cambridge University
Natural Sciences Tripos IB, 1983.)
18. (a) Using the information available to you in this chapter, estimate the value of the
stretching factor
β
for (i) the East African Rift and (ii) the Rio Grande Rift.
Assume that both formed as a result of uniform stretching of the lithosphere.
(b) Using the values of
β
estimated in (a), calculate initial and final subsidences for
these two rifts. Do these values appear reasonable? (Remember that these rifts are
not subaqueous; assume that
ρ
w
=
0.)
(c) Now assume that the sea breaks through in the Gulf of Aden and floods the small
portion of the rift valley that is below sea level there. What might happen?
(d) Now assume that the drainage systems change and the entire East African Rift
fills with water. What would happen in this eventuality?
×
10
3
and 3.35
×
References and bibliography
Ahern, J. L. and Ditmars, R. C. 1985. Rejuvenation of continental lithosphere beneath an
intercratonic basin.
Tectonophysics
,
120
, 21-35.
