Page 235 - Physical Principles of Sedimentary Basin Analysis

7.9 Lithospheric stretching of finite duration 217

0.0 0.0

0.2 0.2

0.4 0.4
^ z
^ z
0.6 0.6

0.8 0.8

1.0 1.0
−1.0 −0.5 0.0 0.5 1.0 −1.0 −0.6 −0.2 0.2 0.6 1.0
^ ^
x
x
(a) (b)
Figure 7.14. Lithospheric flow during uniform stretching. (a) The flow field (7.85). (b) The
streamlines (7.84).

The β-factor measures how much a rectangular shaped part of the lithosphere becomes
stretched,

x(t)
t

β(t) = = exp G(t )dt (7.86)
x 0 0
when the strain rate is independent of position (equal to G everywhere). The stretching
factor increases exponentially with time in the case of a constant strain rate. Relation (7.86)
can be inverted to give the strain rate as a function of the stretching factor

1 dβ
G = . (7.87)
β dt
This relationship also follows directly from the definition of strain rate (see Exercise 7.16).
If we only know the total stretching factor β s , and can assume that the stretching took place
with a constant strain rate during a time interval t s , then it follows from equation (7.86) that
the strain rate is

lnβ s
G = . (7.88)
t s
Stretching of the lithosphere is normally restricted to certain rift phases, where the strain
rate is zero in the periods between. It then follows from equation (7.86) that the total
β-factor is the product of the β-factors of each rift phase, because equation (7.86) can be
written as