Geology Reference
In-Depth Information
Fig. 1.4
Isentropic adiabat
upwelling geotherms for an
asthenosphere (
red line
)
with potential temperature
T
p
D
1,280
ı
C(seetext)
and for MORB (in
blue
).
Dry and wet peridotite
solidi are also shown
Thus, the two curves intersect at a point and
partial melting becomes a necessary consequence
of the passive upwelling of asthenosphere, as
showninFig.
1.4
.
The concept of
potential temperature
,
T
p
,is
related to the necessity to perform comparisons of
the heat content of a volume element at different
depths (hence at different
p
and
T
conditions).
If the material is incompressible, then a differ-
ence of heat content,
dQ
, between two volume
elements at different (
p
,
T
) will be proportional to
the difference of temperature,
dT
.However,ifitis
not, then
dQ
will be proportional to
dT
only if the
two volume elements will be brought to the same
pressure through an isentropic path. The reason
is that if the material is compressed or stretched
by a variation of pressure, so that its volume
is reduced or expanded, it will be also heated
or cooled as a result of the work done by the
external or internal pressure fields. Therefore, it is
a common practice in geodynamics to introduce
the quantity
T
p
, which is the temperature that a
volume element would have if it were brought
isentropically to a reference pressure
p
0
(usu-
ally 1 atm). After this reduction, differences of
temperature measure variations in heat content,
thereby
T
p
only changes when the entropy of the
material changes. To find the potential tempera-
ture associated with the actual temperature
T
at
depth
z
we simply integrate Eq. (
1.8
) between
z
and the Earth's surface:
Z
T
p
Z
0
dT
0
T
0
D
'g
c
p
d
z
0
(1.10)
z
T
T
p
D
T.
z
/e
˛g
z
=c
p
(1.11)
McKenzie and Bickle (
1988
) estimated a
potential temperature of the asthenosphere of
1,280
ı
C to generate a 7 km thick oceanic
crust. More recent estimates suggest that
T
p
beneath ridges varies linearly between 1,280
and 1,400
ı
C as a function of the MgO content
in primary magma (10-13 % wt MgO, e.g.
McKenzie et al.
2005
; Herzberg et al.
2007
).
