Page 245 - Physical Principles of Sedimentary Basin Analysis

7.11 Lithospheric extension, phase changes and subsidence/uplift 227

c 0
T r + A r z = T 0 + A 0 βz and z = (7.111)
β
which has as solution the minimum β-factor needed for the top of the mantle to enter the
plagioclase phase
A 0 c 0
β 1 = . (7.112)
T 0 − T r + A 0 c 0
The mantle is then plagioclase–peridotite from the top of the crust down to the depth where
the geotherm crosses the phase boundary, which is the interval
c 0 T 0 − T r
z top = to z bot = . (7.113)
β A r − A 0 β
The depth where the geotherm crosses the phase boundary increases with increasing β-
factor until it reaches the asthenosphere temperature T a (see Figure 7.20a) for the β-factor
T a − T r A r

β 2 = . (7.114)
T a − T 0 A 0
The subsidence during extension has two components as we have already seen – subsidence
from thinning of the crust and subsidence/uplift from a change m in the average mantle
density:

m,ref − c
1 m
s = 1 − c 0 + a. (7.115)
m,ref − w β m,ref − w
The last part is what gives thermal uplift by the density difference (7.108). The average
mantle density is initially m,ref and it becomes m = m,ref + m with increasing
stretching. We can now include the phase change in the average mantle density m and
we get

1
1
m =− m,0 α m 1 − T a (7.116)
2 β
1
+ ( x,0 − m,0 )(z top − z bot ) (7.117)
a
1 2 2
− ( x,0 α x − m,0 α m )(z top − z bot )βT a (7.118)
2a 2
where equation (7.113) gives how z bot and z top depend on the β-factor. The first
term (7.116) is the (familiar) change in mantle density from thermal expansion, when we
have only one phase, and it is this term that causes thermal uplift. The second term (7.117)
is the change in average mantle density for plagioclase–peridotite in the depth interval from
z top to z bot . The third term (7.118) is a correction to the first term that accounts for thermal
expansion in the plagioclase-peridotite interval, and it is normally insignificant compared
to the other two terms.
Curve (4) in Figure 7.20b shows the subsidence during extension as a function of
the β-factor. The density parameters are m,0 = 3300 kg m −3 , x,0 = 3250 kg m −3 ,
α m = α x = 3 · 10 −11 K −1 , which are also used in the phase diagram in Figure 7.19.