Page 219 - Physical Principles of Sedimentary Basin Analysis

7.4 Basin subsidence by crustal thinning 201

1 β
s
c c /β

l

l

a

Figure 7.6. A basin of depth s forms when the crust is stretched by a factor β. The initial thick-
ness of the crust is c, the initial thickness of lithospheric mantle is l and a is the thickness of the
asthenosphere that moves upwards and becomes the lower part of the stretched lithosphere.

leads to a heavier lithosphere that floats deeper on the ductile mantle. The stretching and
uniform thinning of the crust is shown in Figure 7.6. An initially unstretched lithosphere
is shown to the left and the same lithosphere after uniform stretching and subsidence is
shown to the right. From mass conservation we get that the initial thickness of the crust
c becomes reduced to c/β when it is stretched uniformly by a factor β. Figure 7.6 also
shows the upwelling asthenospheric mantle that has cooled and formed new lithospheric
mantle. The subsidence of the stretched lithosphere is found by isostasy. We will assume
that the lithosphere is stretched so slowly that the temperature through the lithosphere
stays stationary even though there is a flow of mantle rocks upwards. Isostasy says that the
pressure at the same depth in the asthenosphere remains the same:

c c + m l = s s + c (c/β) + m l + m a. (7.19)

We have that l is the initial thickness of the lithospheric mantle, s is the thickness of the
sedimentary basin, and a is the thickness of the asthenosphere that moves upwards due to
stretching and becomes part of the new lithosphere. The pressure in equation (7.19)isat
the top of the asthenosphere, which is at the depth
c + l = s + (c/β) + l + a. (7.20)

We see that all terms with l drop out in both equations (7.19) and (7.20), and by inserting
a = c − (c/β) − s from equation (7.20) into equation (7.19) we get that the subsidence s
as a function of the stretching factor β is
( m − c ) 1
s = 1 − c. (7.21)
( m − s ) β
The basin subsidence s divided by the initial thickness of the crust is plotted as a function
of β in Figure 7.7 for s = 2300 kg m −3 , c = 2900 kg m −3 and m = 3300 kg m −3 .The