Geoscience Reference
In-Depth Information
Table 18.3
Extrinsic and intrinsic of derivations
Extrinsic
Intrinsic
∂
∂
∂
∂
ln
K
s
∂
ln
ρ
ln
K
s
∂
ln
ρ
1
α
ln
K
s
∂
T
ln
K
s
∂
T
Substance
P
T
V
V
(10
−
5
/
deg)
MgO
3.0
3.8
0.8
2.3
CaO
3.9
4.8
0.9
2.6
SrO
4.7
5.1
0.4
1.6
TiO
2
10.5
6.8
−
3.7
−
8.7
GeO
2
10.2
6.1
−
4.1
−
5.6
Al
2
O
3
4.3
4.3
0.0
0.0
Mg
2
SiO
4
4.7
5.4
0.7
0.03
MgAl
2
O
4
4.0
4.2
0.2
0.4
Garnet
5.2
5.5
0.3
0.5
SrTiO
3
7.9
5.7
−
2.2
−
6.2
∂
ln
G
∂
ln
ρ
∂
ln
G
∂
ln
ρ
∂
ln
G
∂
T
∂
ln
G
∂
T
1
α
Substance
P
T
V
V
(10
−
5
/
deg)
MgO
5.8
3.0
2.8
8.6
−
−
CaO
6.3
2.4
3.9
11.2
−
−
SrO
4.9
2.2
2.7
11.3
−
−
TiO
2
8.4
1.2
7.2
16.9
−
−
GeO
2
5.8
2.1
3.7
5.1
−
−
Al
2
O
3
7.5
2.6
−
4.9
−
16.5
Mg
2
SiO
4
6.5
2.8
−
3.7
−
9.2
MgAl
2
O
4
5.9
1.3
−
4.6
−
7.4
Garnet
5.4
2.6
−
2.8
−
6.1
SrTiO
3
7.9
3.1
−
4.8
−
13.4
Sumino and Anderson (1984).
measurements as a function of both temperature
and pressure. These are tabulated in Table 18.3
for a variety of oxides and silicates.
Generally, the intrinsic temperature effect on
rigidity is greater than on the bulk modulus;
G
is a weaker function of volume at constant
T
than at constant
P
;and
G
is a weaker func-
tion of volume, at constant
T
, than is the bulk
modulus. The extrinsic terms are functions of
pressure through the moduli and their pressure
derivatives.
The coefficient of thermal expansion, at con-
stant temperature, decreases by about 80% from
P
create buoyancy at the base of the mantle. This
also means that all temperature derivatives of the
moduli and the seismic velocities are low in the
deep mantle. The inferred intrinsic temperature
effect on the bulk modulus is generally small
and can be either negative or positive (Table
18.3). The bulk modulus and its derivatives must
be computed from differences of the directly
measured moduli and therefore they have much
larger errors than the shear moduli. The intrin-
sic component of the temperature derivative of
the rigidity is often larger than the extrinsic,
or volume-dependent, component and is invari-
ably negative; an increase in temperature causes
=
0 to the base of the mantle. It is hard to
