Page 222 - Physical Principles of Sedimentary Basin Analysis
P. 222
204 Subsidence
is the thermal expansibility. The density has the reference value 0 at the reference temper-
◦
ature T 0 , which is taken to be 0 C. A typical value for the thermal expansibility of mantle
rocks is 3 · 10 −5 K −1 . The temperature difference between the top and the base of the
◦
lithosphere is roughly 1000 C, and the density difference between the base and the top is
therefore ∼3%. Although a density difference of only 3% may be considered small it is
nevertheless important. The crust and the mantle have different densities, and they are as a
function of temperature:
c (T ) = c,0 (1 − αT ) and m (T ) = m,0 (1 − αT ) (7.24)
where the subscripts c and m denotes crust and mantle, respectively. The thermal expansi-
bility α is taken to be the same for both rock types. We need the temperature as a function
of depth before we can use the densities (7.24) in a subsidence calculation. The initial
lithospheric temperature is
z
T 0 (z) = T a (7.25)
a
and the temperature after instantaneous and uniform stretching is (see Figure 7.8)
z a
⎧
⎨ T a β , 0 ≤ z ≤
⎪
+ a β
T I (z, t = 0 ) = a (7.26)
⎩ T a , < z ≤ a.
⎪
β
The assumption of isostasy states that the pressure at the same depth in the asthenosphere
remains the same:
c a
c dz + m dz =
0 c
c/β a/β
a
c dz + m dz + a − − s I m (T a ) + s I s . (7.27)
0 c/β β
The right-hand side is the pressure in the asthenosphere beneath the unstretched litho-
sphere, and the left-hand side is the pressure beneath the stretched lithosphere. The initial
temperature (7.25) is therefore used in the densities on the left-hand side of equation (7.27),
and the transient temperature (7.26) is used on the right-hand side. The contribution s s
from a sedimentary basin of thickness s, where s is the average density of the sedi-
ments, is added on the right-hand side. The sedimentary cover is considered so thin that
any temperature dependence can be neglected. Isostatic equilibrium (7.27) gives the basin
subsidence
c 1 c 1
m,0 − c,0 1 − α T a − m,0 α T a
1 a 2 a 2
s I = a 1 −
(7.28)
β 1
m,0 1 − α T a − s
2
after the integrations over the densities are carried out (see Note 7.1 for details). The
subsidence (7.28) accounts for the hot lithosphere that results from the uniform and instan-
taneous stretching. Thermal expansion of the lithospheric mantle leads to reduced subsi-
dence, which can be seen from equation (7.28). We notice that the last term m,0 αT a /2 can