Page 221 - Physical Principles of Sedimentary Basin Analysis

7.5 The McKenzie model of basin subsidence 203

1 T m
T
c crust

a
lithosphere

z
β T m
T
c/β crust

a/β
lithosphere

asthenosphere a−a /β

z
Figure 7.8. An almost instantaneous and uniform stretching of the lithosphere leads to upwelling of
the hot asthenosphere and a steeper thermal gradient in the lithosphere. The basin part is considered
thin compared to the thickness of the lithosphere and its contribution to the temperature is therefore
omitted.

lithospheric material as it is instantaneously stretched and the geotherm becomes steeper
after stretching. The initial geothermal gradient is dT/dz = T a /a, where T a is the tem-
perature at the asthenosphere–lithosphere boundary and a is the initial thickness of the
lithosphere. The temperature gradient immediately after stretching becomes a factor β-
higher (dT/dz = β T a /a). The asthenosphere that replaces the stretched lithosphere is
assumed to have the temperature T a . The elevated temperature of the lithosphere after
stretching is a transient state, and the temperature will return to its initial state by conduc-
tive cooling. The asthenosphere–lithosphere boundary therefore moves back to its initial
position as a consequence of conductive cooling.
The temperature dependence of a rock density can be approximated to first order as

= 0 1 − α(T − T 0 ) (7.22)

where
1 ∂
α = (7.23)
∂T
p