Heat - The Solid Earth - page 293

Table 7.4 Thermal parameters for oceanic-lithosphere models

GDH1 PSM HS

L , plate thickness (km) 95 ± 10 125 ± 10 —

T a , temperature at base of

plate ( ◦ C)

1450 ± 100 1350 ± 275 1365 ± 10

10 −5 10 −5 10 −5 α , coefficient of thermal

expansion ( ◦ C −1 )

3.1 × 3.28 × 3.1 ×

k , thermal conductivity

(W m −1 )

3.138 3.138 3.138

c P , specific heat

(kJ kg −1 )

1.171 1.171 1.171

10 −6 10 −6 10 −6 κ , thermal diffusivity

(m 2 s −1 )

0.804 × 0.804 × 0.804 ×

ρ m , mantle density

(kg m −3 )

3330 3330 3330

ρ w , water density

(kg m −3 )

1000 1000 1000

d r , ridge depth (km) 2.6 2.5 2.6

(a) Half-space cooling models

x

Abbreviations : GDH, global depth and heat; PSM, Parsons, Sclater and McKenzie;
HS, halfspace.
Sources : Stein and Stein (1992), Parsons and Sclater (1977) and Carlson and Johnson
(1994).

T=0

T =0

of the lithosphere is defined by an isotherm (Fig. 7.8). The boundary condi-
tion at the base of the lithosphere is that the heat flux from the mantle is specified.
The bathymetric depth predicted by these models increases as t 1 / 2 for all t .Itis
apparent from Fig. 7.7(a) that, although this model fits the observed depths out to
about 60-70 Ma, for greater ages the predicted depth is too great. The heat-flow
values predicted by the model decrease as t − 1 / 2 for all t . These predicted heat
flows are close to, but lower than, the observed values (Fig. 7.7(b)). For ages
greater than a few million years, the temperature and lithospheric thickness pre-
dicted by the simple model are very close to the values for the boundary-layer
model.

z

(b) Plate model

x

T=0 T =0

T = T a

z

The plate model
In the plate models, the oceanic lithosphere is taken to be of constant thickness
L , the base of the lithosphere is at the same constant temperature T a as the
vertical ridge axis and the top surface of the lithosphere and the seabed is another
isotherm, usually put at 0 ◦ C(Fig. 7.8). The solution to Eq. (7.59) with these
boundary conditions, T

Figure 7.8. Schematic
diagrams of (a) the
half-space cooling and
boundary-layer models
and (b) the plate model of
the oceanic lithosphere.
Lithosphere is shaded.

= T a on z = L , T = 0on z = 0 and T = T a on t = 0, is

= T a z

exp uL
2 κ

2 ut
L

u 2 L 2
4 κ

sin n π z
L

∞

2
n π

T

L +

− + n 2 π (7.74)

2

n = 1