Geoscience Reference
In-Depth Information
When the horizontal conduction of heat is ignored, this simplifies to
z
L
+
exp
sin
n
∞
n
2
2
2
n
π
z
π
κ
t
T
=
T
a
−
π
L
L
2
n
=
1
L
2
2
A thermal time constant can be defined as
t
0
=
).
The surface heat flow as a function of plate age,
Q
(
t
), for this model is
/
(
π
κ
1
exp
∞
n
2
2
t
kT
a
L
π
Q
(
t
)
=
+
2
−
L
2
n
=
1
The asymptotic value for the heat flow over old lithosphere is therefore
kT
a
/
L
.
The depth of the seabed as a function of plate age,
d
(
t
), for this model is
calculated in exactly the same way as for the simple half-space model:
1
n
2
∞
ρ
a
α
n
2
π
2
κ
T
a
L
8
π
t
d
(
t
)
=
d
r
+
−
−
ρ
a
−
ρ
w
)
2
L
2
2(
n
=
1
The asymptotic value for the ocean depth over old lithosphere is therefore
ρ
a
α
T
a
L
d
r
+
ρ
a
−
ρ
w
)
Isotherms for the two plate models, PSM and GDH1, with temperatures of
1350 and 1450
◦
C, respectively, at the base of the lithosphere and at the ridge
axis are shown in Fig. 7.9.Asthe lithosphere ages and moves away from the
ridge axis, the isotherms descend until, far from the ridge, they essentially reach
equilibrium. Figures 7.6 and 7.7 show that the heat flow and bathymetric depths
predicted by these models are in good agreement with observations. Note that
there is effectively no difference between the heat flows predicted by the HS
and PSM models, compared with the scatter in the data (Figs. 7.6, 7.7(b) and
Table 7.5). The differences between ocean depths predicted by the plate models
and by the boundary-layer model become apparent beyond about 60-70 Ma and
2(
the deviation of the ocean depth from the
√
t
curve predicted by the half-space
model shows up clearly in Fig. 7.7(c). Since there is no limit to how cool the
upper regions of the boundary-layer model can become, there is no limit to its
predicted ocean depths. The plate model has a uniformly thick lithosphere, so
temperatures in the lithosphere, as well as ocean depths, predicted by that model
approach equilibrium as age increases. For the same reason, differences between
the surface heat flows predicted by the two types of model begin to become
apparent for ages greater than about 100 Ma - the boundary-layer model keeps
on cooling whereas the plate models approach equilibrium.
Any thermal model must account for the
√
t
dependence of ocean depth on
age for young oceanic lithosphere. Additionally the model must account for the
asymptotic behaviour both of ocean depth and of heat flow on old lithosphere.
The GDH1 plate model fits the whole dataset best (with the lowest residuals),
but a half-space model fits the ocean-depth dataset for young lithosphere best.
