Page 224 - Physical Principles of Sedimentary Basin Analysis

206 Subsidence

It is shown in the next section how conductive cooling leads to further (thermal) subsi-
dence through time, and that the maximum amount of thermal subsidence is the difference
between initial subsidence (with thermal expansion and thermal uplift) and the subsidence
without thermal expansion. The maximum thermal subsidence in Figure 7.9 is therefore
the difference between the solid line and the dashed line for the same crustal thickness.
The initial subsidence (7.28) can be rewritten as

s I = s max − s T,max (7.31)

where
1 ( m,0 − c,0 )

s max = 1 − c (7.32)
β ( m,0 − s )
is the maximum subsidence and where
1 1
m,0
s T,max = 1 − αT a a (7.33)
2 β ( m,0 − s )
is the maximal thermal subsidence. Expression (7.31) was obtained by a slight simplifica-
tion of expression (7.28) using the approximation 1 − αT a /2 ≈ 1. The maximum thermal
subsidence is the same as the maximum uplift caused by the upwelling hot mantle. In
a later section we will see how the initial thermal uplift dies out with the thermal tran-
sient. The condition (7.30) for initial subsidence to be positive is simply an expression for
when the maximum subsidence (s max ) is larger than maximum thermal subsidence (s T,max ).
The maximum thermal subsidence becomes s T,max /c = 0.07, 0.11 and 0.13 for the three
stretching factors β = 1.5, 2 and 2.5usedinFigure 7.9.
Note 7.1 The subsidence (7.28) is found by carrying out the integrations in equation (7.27)
and then solving for s. When the initial lithospheric temperature T 0 (z) (7.25) is inserted
into the temperature dependent densities (7.24) on the left-hand side of equation (7.28), and
the temperature after stretching T I (z) (7.26) is inserted into the densities on the right-hand
side, and we get
c
z a
z
c,0 1 − αT a dz + m,0 1 − αT a dz
0 a c a
c/β a/β

z
z
= c,0 1 − αT a β dz + m,0 1 − αT a β dz
0 a c/β a
a

+ a − − s m,0 (1 − αT a ) + s s . (7.34)
β
The integrations are straightforward to carry out, and when the terms with the subsidence
are collected on the left-hand side, we arrive at the subsidence (7.28).
Exercise 7.6 Verify that the initial subsidence (7.28)(s I ) becomes expression (7.21)for
maximum subsidence (s max ) with constant densities when the thermal expansibility is zero.