instance, magnetic anomalies, and if we assume values for the conductivity and diffusivity, Eq.
(5.17) can be used to determine the temperature difference between the top and the bottom of the
plate
(5.18)
Parsons & Sclater did this (JGR, 1977); assuming
JK
m
s
,
Jkg
K
, and
kgm
and using
mWm
as the best fit to the data they
found:
C.
Comparison to observed heat flow data:
Near the ridge crest the observed heat flow is significantly lower than the heat flow predicted from
the cooling halfspace model. In old oceanic basins the heat flow seems to level off at around 46
mW/m , which suggests that beyond a certain age of the lithosphere the rate of conductive cooling
either becomes smaller or the cooling is partly off set by additional heat production.
Possible
sources of heat which could prevent the halfspace cooling are:
1. radioactivity (A is not zero!)
2. shear heating
3. smallscale convection below plate
4. hot upwelings (plumes)
5.4. THERMAL STRUCTURE OF THE OCEANIC LITHOSPHERE
177
Figure 5.11: .
Intermezzo 5.2
P
LATE

COOLING
M
ODELS
There are two basic models for the description of the cooling oceanic lithosphere, a cooling of a uniform
half space
and the cooling of a
layer
with some finite thickness. The former is referred to as the
halfspace
model
(first described in this context by Turcotte and Oxburgh, 1967); The latter is also known as the
plate
model
(first described by McKenzie, 1967).
Both models assume that the plate moves as a unit, that the surface of the lithosphere is at an isothermal
condition of 0 C, and that the main method of heat transfer is
conduction
(a good assumption, except at the
ridge crest). The major difference (apart from the mathematical description) is that in the halfspace model
the base of the lithosphere is defined by an isotherm (for instance 1300 C) so that plate thickness can grow
indefinitely whereas in the plate model the plate thickness is limited by some thickness
.
The two models give the same results for young plates near the ridge crest, i.e. the thickness is such that the
”bottom” of the lithosphere is not yet ”sensed”. However, they differ significantly after 50 Myr for heat flow
predictions and 70 Myr for topography predictions. It was realized early on that at large distances from the
ridge (i.e., large ages of the lithosphere) the oceans were not as deep and heat flow not as low as expected
from the halfspace cooling model (there does not seem to be much thermal difference between lithosphere
of 80 and 160 Myr of age). The plate model was proposed to get a better fit to the data, but its conceptual
disadvantage is that it does not explain why the lithosphere has a maximum thickness of
. The half space
model makes more sense physically and its mathematical description is more straightforward. Therefore,
we will discuss only the half space cooling model, but we will also give some relevant comparisons with
the plate model.
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 Fall '13
 BertrandI.Halperin
 Physics, Plate Tectonics, Convection, Heat, Heat Flow, oceanic lithosphere, convecting mantle