Page 274 - Physical Principles of Sedimentary Basin Analysis

256 Subsidence

1
1/2

1 2
Figure 7.35. The porosity during extension.

The third (Late Jurassic) rift phase, which makes space for the thick Cretaceous formations,
is now stronger. The last rift phase cannot have been strong, with β ≈ 2, because it implies
that all the sediments deposited prior to the last rift phase would have been twice as thick
prior to rifting.
Note 7.17 The β-factors: The last β-factor is given as

β max,5 c 0 − f w w 4 − β 4 f 4 s 4
β 4 = = (7.207)
β max,4 c 0 − f w w 5 − f 5 s 5
which gives β 4 as expressed by (7.203). The next β-factor is found in the same way from

β max,4 c 0 − f w w 3 − β 3 β 4 f 3 s 3
β 3 = = (7.208)
β max,3 c 0 − f w w 4 − β 4 f 4 s 4
where we solve for β 3 without inserting β 4 , and we get β 3 as given by (7.204). The two
remaining β-factors are found by a straightforward continuation.

Note 7.18 Mass-conservative stretching of the sedimentary basin: The mass of a sedi-
mentary basin of thickness s and width l before and after extension is

s
M = av sl = av (lβ) (7.209)
β
and it is conserved as long as the average basin density av remains unchanged by the
extension. The average basin density can be related to the average basin porosity φ av by

av = φ av w + (1 − φ av ) s (7.210)
where w and s are the water and the matrix densities, respectively. The extension
becomes mass-conservative if the average porosity is unchanged. The average porosity
is not constant in general, but it remains constant for porosity functions of the form
φ(z) = f (z/z 0 ), when the characteristic length z 0 is also stretched. See Figure 7.35.The
new characteristic length after a rift phase becomes z 0 /β.Wehave
1 s 1 s

φ av = f (z/z 0 ) dz = f (z /z ) dz (7.211)
0
s 0 s 0

when both the integration variable z = z/β and the characteristic depth z = z 0 /β are
0
scaled with the β-factor.