Page 236 - Physical Principles of Sedimentary Basin Analysis

218 Subsidence

t

β = exp G(t )dt
0

t 2 t 4

= exp G(t )dt + G(t )dt + ···
t 1 t 3

t 2
t 4

= exp G(t )dt · exp G(t )dt ···

t 1 t 3
= β 1 · β 2 · β 3 ··· (7.89)
where the β-factor of stretching in phase 1 from t 1 to t 2 is β 1 , and so on. The strain rate is
zero in the periods t 2 to t 3 and t 4 to t 5 , which are the intervals between the rifting phases.
The lithospheric extension has so far been treated as pure shear deformation. The upper
part of the crust is brittle and deforms by faulting, which is the topic of Exercises 7.13
and 7.14. Notes 7.5 and 7.6 look at depth-dependent stretching and stretching that is
dependent on the lateral position, respectively.
Note 7.5 Depth-dependent stretching: In order to better calibrate models it has been pro-
posed that the crust and the mantle are stretched with different factors (Royden and Keen,
1980). The crust is then stretched with a factor β and the mantle with a different factor δ.
Different β- and δ-factors give depth-dependent stretching. The stretching of the mantle
and the crust by different factors allows the thermal transient of the mantle to be calibrated
independently of the thinning of the crust. One might for instance create substantial uplift
(and erosion) by stretching the mantle by a large δ-factor, while the thinning of the crust
is by a moderate β-factor. One problem with such a simple approach to depth-dependent
stretching is mass conservation (see Figure 7.15). It also implies that the Moho (crust
mantle boundary) becomes a large detachment zone. The streamlines for lithospheric flow
become discontinuous across the Moho. Depth-dependent stretching is possible, as demon-
strated by numerical simulation of ductile flow, but it then involves quite complex flow
patterns (Huismans and Beaumont, 2008).

Note 7.6 We have so far assumed that stretching takes place with a strain rate that is inde-
pendent of x- and z-positions across an entire profile, only dependent on time. This is
not the case for real extensional basins where different parts of the basin and the litho-
sphere underneath have undergone different amount of stretching. It is often sufficient to
assume that the stretching is only laterally dependent (only dependent on the x-position).
An important consequence of an x-dependent strain rate is that vertical lines remain vertical
during stretching, because v x is the same for all positions along a vertical line. The simplest

Crust β
Lithospheric mantle δ

Asthenosphere
Figure 7.15. The crust is stretched with a factor β and the lithospheric mantle by a factor δ.