Page 270 - Physical Principles of Sedimentary Basin Analysis

252 Subsidence

which gives the cumulative stretching factors
c 0
β max,i = (7.194)
c i
and finally the β-factors
β max,i+1
β i = . (7.195)
β max,i
These results are collected in the four last columns in Table 7.2. The estimation of the β-
factors by this algorithm suggests that the deep Naagrid syncline was mainly created by the
last two rift phases, each with β ≈ 2. The crust has been stretched from 35 km thickness to
the present-day 8 km, which gives that the total (accumulative) β-factor is β max,5 = 4.38.

Exercise 7.32 The extension factor β i depends on the water depths w i = w(t i ) and
w i+1 = w(t i+1 ).
(a) Show that
w i
β i =− f w β max,i+1 . (7.196)
c 0
(b) How large is the change β i when the water depth is increased by w i = 500 m?
Assume that w = 1000 kg m −3 , c = 2800 kg m −3 , c = 3500 kg m −3 , c 0 = 35 km and
β max,i+1 = 3.
(c) Show that
∂β i 1
=− f w β i β max,i+1 . (7.197)
∂w i+1 c 0
(d) Estimate the change β i+1 when w i = 500 m, β i = 1.5 and the other parameters
areasin(b).

7.16 Stretching and thinning of the sediments

Section 7.15 showed how the β-factors for each rift phase could be obtained from the
cumulative amount of crustal stretching, which again is found from knowledge of the basin
weight and the water depth through the geohistory. It is also possible to use a constant
mantle density if the time spans between the rift phases are “long.” We will now look at
one problem with this approach, which is that the stretching and thinning of the sediments
is not accounted for. Only the crust is stretched and thinned. It is reasonable to assume that
the sedimentary basin undergoes the same extension and thinning as the crust. If not we
may have a mass conservation problem, unless we can explain how the crust is stretched
without affecting the basin. In this section we will take the basin into account too, and
make a formulation that is mass-conservative for the entire lithosphere during stretching
and thinning. Before we do that we need to review some notation – we have that s 1 to s 5
are the thicknesses the sedimentary basin would have had, at the respective times t 1 to t 5 ,
according to the present-day amount of net (porosity-free) rock in each formation. These