Page 295 - Physical Principles of Sedimentary Basin Analysis

8.7 Ductile flow and yield strength envelopes 277

2.5
(1) rifting: 400 to 360
(2) rifting: 310 to 260
(3) rifting: 160 to 140
(4) rifting: 90 to 56
2.0
beta−factor [−] 1 3

1.5

4
2
1.0
0 100 200 300
x−position [km]
(a)
1.2
(1) rifting: 400 to 360
(2) rifting: 310 to 260
strain rate (x 10 −15 ) [1/s] 1.0 4
(3) rifting: 160 to 140
3
(4) rifting: 90 to 56
0.8
0.6
0.4

0.2 1
2
0.0
0 100 200 300
x−position [km]
(b)
Figure 8.16. (a) β-factors for four rift phases. (b) The strain rates of the rift phases. All rift phases
are plotted with the present day lateral positions.

where b is the average bulk density of the lithosphere. The force needed to stretch the
lithosphere is
z a 1 2

F = σ 1 dz = S l + b gz a (8.45)
0 2
which is the lithospheric strength S l added to a gravity term. Variations in the gravity term
are mostly due to the density difference between the crust and mantle. Unless the thickness
of the crust is changing or the thermal state of the lithosphere is altered the gravity term
will not change much, and it can often be taken as a constant offset.
How the lithospheric strength (8.44) depends on radioactive heat production in the crust,
crustal thickness and strain rate is shown in Figure 8.17. Figure 8.17a shows how the
lithosphere gets weaker with increasing amounts of crustal heat generation. The geotherms
for four values of crustal heat generation are shown in Figure 8.15b. Figure 8.17bshows