Page 257 - Physical Principles of Sedimentary Basin Analysis

7.13 Thermal subsidence of the oceanic lithosphere 239

ridge
x = ut
t 1 water w(t)
t 2
u
u lithosphere
h(t)
asthenosphere

Figure 7.27. The oceanic lithosphere is created at the mid-ocean ridge, and the plates subside as they
move away from the ridge and cool.

the same mantle temperature from the surface to a “large” depth. As the column moves
away from the ridge it starts to cool from the surface. This is precisely the problem of a
heating/cooling of a semi-infinite half-space discussed in Section 6.14. The temperature in
the column is therefore given by equation (6.205),

z
T (z) = T s + (T a − T s ) erf √ , (7.157)
2 κt
where T s is the surface temperature, T a is the temperature of the upwelling hot mantle, and
where κ is the thermal diffusivity. The base of the lithospheric plate is now approximated
by the isotherm T = 0.9 × T a , which allows us to find the thickness of the plate as a
function of time. We have that erf(1.2) ≈ 0.9, and the surface temperature T s = 0gives
the thickness h(t) of the lithosphere as

h(t)
√ = 1.2 (7.158)
2 κt
or
√
h(t) = 2.4 κt. (7.159)
The thickness of the oceanic lithosphere is controlled by conductive cooling by means of
2 −1
only one parameter, the thermal diffusivity κ. Using that κ = 1 · 10 −6 m s gives the
plate thicknesses h = 13.4kmfor t = 1Ma, h = 42 km for t = 10 Ma and h = 134 km
for t = 100 Ma.
The oceanic lithosphere subsides as it cools and gets denser. It gets denser because
it contracts thermally, which follows from the mantle density function m (T ) =
m,0 (1 − αT ). The thermal subsidence is found by assuming isostatic equilibrium, which
says that the pressure is the same at the same depths in the ductile mantle. The pressure
in the mantle below the oceanic lithosphere is therefore equal to the pressure at the same
depth below the ridge

h

w w + m (T (z , t)) dz = (w + h) m (T a ) (7.160)
0