Page 246 - Physical Principles of Sedimentary Basin Analysis

228 Subsidence

Simon and Podladchikov (2008) estimate the decrease in density to be in the range from
10 kg m −3 to 90 kg m −3 depending on the composition. The crust has an initial thick-
ness c 0 = 35 km and density c = 2800 kg m −3 , and the phase boundary is given by
◦
◦
T r =−300 C and A r = 0.04 C/m. The lithosphere has the thickness a = 120 km,
◦
the surface temperature T 0 = 0 C and the temperature T a = 1300 C at the base of the
◦
lithosphere.
The mantle geotherm starts to cross the phase boundary at β 1 ≈ 2 and we see that
we then get uplift. The uplift increases until β 2 = 3 where the geotherm crosses the phase
boundary at the asthenosphere temperature. The uplift from phase change is then increasing
less. Curve (5) shows what the subsidence would have been without change of phase.
It is the sum of subsidence from crustal thinning and thermal uplift, curves (1) and (2),
respectively. The uplift by only phase change is curve (3). The total subsidence is therefore
the sum of the curves (1), (2) and (3).
This kind of uplift from a change of phase is controlled by a thermal transient and it
will therefore gradually disappear after extension, when the geotherm returns to a steady
state. The final state after a sufficiently long time is the permanent subsidence from crustal
thinning alone, given by curve (1).
There have been observed anomalous subsidence patterns that could be explained by
such phase changes (Kaus et al., 2005). It should also be mentioned that there are verti-
cal movements that are difficult to explain, like for instance the uplift of East Greenland.
Density changes associated with change of phase have been suggested among several other
possibilities – see Japsen and Chalmers (2000) for a review of the uplift around the North
Atlantic. This uplift is probably not related to lithospheric extension and it might be of a
permanent nature.

Note 7.8 Expression (7.115) for subsidence follows from isostasy by considering the
weight of a column before and after extension

c c 0 + m,ref a 0 = w s + c c + m a (7.119)

when they have the same height

c 0 + a 0 = s + c + a. (7.120)
The subsidence, the thickness of the crust, the thickness of the lithospheric mantle are s, c
and a, respectively. The subscript 0 denotes before extension. We can use equation (7.120)
to eliminate either a 0 or a. If we eliminate a 0 we get the subsidence (7.115). Alternatively,
if we eliminate a instead of a 0 we get the same subsidence, except that it is written as the
sum of two slightly different terms. The average density m appears now in the expression
for subsidence instead of the reference average density m,ref . The average m is time
dependent since it includes the thermal transient from extension. Expression (7.115)is
therefore preferred although a does not stay constant during extension.
Exercise 7.19 Consider a vertical column of the lithosphere that has a crust of thickness c
and density c and a lithospheric mantle of thickness a and density m . Assume isostasy