Geoscience Reference
In-Depth Information
Theoretically, the effects of temperature
decrease with compression, and this is borne
out by the seismic data. In the lower mantle
the lateral variation of seismic velocities is dom-
inated by variations in the rigidity. This is sim-
ilar to the situation in the upper mantle where
it is caused by nonelastic processes, such as par-
tial melting and dislocation relaxation, phenom-
ena accompanied by increased attenuation, and
phase changes. In the lower mantle the effect
is caused by anharmonic phenomena and intrin-
sic temperature effects that are more important
in shear than in compression. Iron-partitioning
and phase changes, including spin-pairing and
melting, may be important in the deep mantle.
One cannot assume that physical properties are a
function of volume alone, or that classical high-
temperature behavior prevails, or that shear and
compressional modes exhibit similar variations.
On a much more basic level, one cannot simply
adopt laboratory values of temperature deriva-
tives to estimate the effect of temperature on den-
sity and elastic-wave velocities in slabs and in the
deep mantle.
If one ignores the possibility of phase changes
and chemical stratification, one can estimate
lower-mantle properties. From the seismic data
for the lower mantle, we can obtain the follow-
ing estimates of
in-situ
values:
∂
/∂
ρ
.
.
(
ln
G
ln
)
P
5
8to7
0
∂
/∂
ρ
.
.
(
ln
G
ln
)
T
2
6to2
9
(
∂
ln
K
S
/∂
ln
ρ
)
T
1
.
8to1
.
0
(
∂
ln
K
S
/∂
ln
ρ
)
T
2
.
8to3
.
6
(
∂
ln
γ/∂
ln
ρ
)
T
−
1
+
ε
−
(
∂
ln
α/∂
ln
ρ
)
T
3to2
For the intrinsic temperature terms we obtain:
1
α
∂
ln
G
∂
T
V
≈−
3
.
2to
−
4
.
1
∂
ln
K
S
∂
T
1
α
V
≈+
+
.
1to
2
6
An interesting implication of the seismic data is
that the bulk modulus and rigidity are similar
functions of volume at constant temperature. On
the other hand,
G
is a stronger function of vol-
ume and
K
s
a much weaker function of volume
at constant pressure than they are at constant
temperature.
Extrapolation of lower mantle values to the sur-
face, ignoring chemical and phase changes, gives:
ρ
o
=
3
.
97
−
4
.
00 g/cm
3
K
o
=
2
.
12
−
2
.
23 kbar
G
o
=
1
.
30
−
1
.
35 kbar
(
K
o
)
S
=
3
.
8
−
4
.
1
(
G
o
)
S
=
1
.
5
−
1
.
8
