Page 232 - Physical Principles of Sedimentary Basin Analysis

214 Subsidence

−5
total subsidence
max subsidence
thermal uplift
0
subsidence [km] 5

10
0 100 200 300 400 500
time [Ma]
Figure 7.13. The subsidence of the McKenzie model is plotted as a function of time for stretching
with a factor β = 2. The subsidence is plotted as the initial subsidence s I given by equation (7.28)
added to the thermal subsidence s T (t) given by equation (7.70).

temperature solution. We notice that the crust is absent in equation (7.69) for thermal
subsidence. The assumption that the crust has the same density as the mantle is a simpli-
fication that applies as long as the crust is much thinner than the lithosphere. The thermal
subsidence (7.69) becomes

∞
4βαT a m,0 sin((2m + 1)π/β)
2
s T (t) = a 1 − e −((2m+1)π) t/t 0 (7.70)
( m,0 − s ) ((2m + 1)π) 3
m=0
once the integrations have been carried out, as shown in Note 7.4. Figure 7.13 shows the
thermal subsidence (7.70)for β = 2, when the crust is c = 36 km thick, the densi-
ties of the sediments, crust and the mantle are s = 2300 kg m −3 , c = 2800 kg m −3
and m = 3300 kg m −3 , respectively, the thermal expansibility is α = 3 · 10 −5 K −1 and
the temperature at the base of the lithosphere is T a = 1300 C. The initial (and instan-
◦
taneous) subsidence s I given by equation (7.28) is taken as the starting point for the
thermal subsidence. The subsidence s = s I + s T (t) is therefore the total subsidence of
the McKenzie model, where the thermal subsidence approaches the maximum thermal
subsidence, s T (t) → s T,max , with increasing time. (See Exercise 7.11.)

Note 7.4 Equation (7.69) can be rewritten as

1
ˆ
ˆ
( m,0 − s )s T = m,0 αT a a U(ˆz, ˆ t = 0) − U(ˆz, ˆ t) dˆz (7.71)
0
using the dimensionless expression (7.45) for the thermal transient. When the series for U
ˆ
is inserted and the integration is carried out we get
2
sin(nπ/β)
−(nπ) ˆ t
( m,0 − s )s T = 2 m,0 αT a a 1 − e (1 − cos(nπ)). (7.72)
(nπ) 3
n=1