Page 242 - Physical Principles of Sedimentary Basin Analysis

224 Subsidence

thermal diffusivity of the lithosphere. The temperature is dominated by heat convection
when Pe
1, a condition that can be written as

Gl 2
v z l m m t 0
Pe = = = lnβ
1 (7.105)
κ κ t s
using the velocity v z = Gl m at the base of the lithosphere and the characteristic time
2
t 0 = l /κ. The strain rate is taken to be G = lnβ/t s when stretching has reached the factor
m
2 −1
β after a time interval t s . Using that l m = 120 km and κ = 1 · 10 −6 m s we get that the
lithosphere must be stretched to a β-factor 2.71 in a time interval t s much less than t 0 =
457 Ma for Pe
1. The normal (average) strain rates of rifting are therefore sufficiently
large for heat convection to dominate over heat conduction assuming a stationary state.
Pe
1 serves as a necessary condition for heat convection to dominate, but it is not a
sufficient condition, since we do not reach a stationary state.

Exercise 7.18 Check that the temperature T (x, z, t) = (T a /l m ) ze Gt solves the tempera-
ture equation (7.99) when the velocity field is v = (Gx, −Gz).

7.11 Lithospheric extension, phase changes and subsidence/uplift
We will in this section look at subsidence or uplift caused by density changes in the crust
and the mantle. For example the formation of eclogite in the crust leads to a larger density,
which again implies subsidence. The assumption of isostatic equilibrium can be used to
estimate the subsidence caused by a change in the density. We get the subsidence

c
s = c (7.106)
( m − w )
when the average density of the crust is changed by c , the crust has the thickness c,
the mantle has the density m and the depression is filled with water with a density w .
A small change c = 23 kg m −3 gives just s = 100 m of subsidence for a 10 km thick
crust, when the mantle and water densities are m = 3300 kg m −3 and w = 1000 kg m −3 ,
respectively. A more substantial change of the average crustal density, c = 230 kg m −3 ,
leads to 1 km of subsidence. It is the difference in the average density that controls the
subsidence, and it is therefore important to know both how much it has changed and in
which depth interval the change took place.
Similarly, a change in the average density of the lithospheric mantle leads to either sub-
sidence or uplift. (An increase in the average density gives subsidence and a decrease gives
uplift.) The assumption of isostasy implies that a change m in the average mantle density
gives the subsidence
m
s = a (7.107)
( m − w )
where the thickness of the lithospheric mantle is a. We looked in Section 7.8 at the thermal
transient created by lithospheric extension and the associated thermal expansion of the