Geology Reference
In-Depth Information
The orthogonality property (1.205) then allows the expressions (9.85) to be
reduced to
d
ρ
0
(
r
)
4
2
4
1
r
3
3
u
0
(
r
)
15
u
2
(
r
)
5
u
2
(
r
)
30
u
−
2
(
r
)
Δ
I
11
=
4π
+
−
−
0
10
v
−
2
(
r
)
dr
,
2
5
v
12
5
v
1
0
2
(
r
)
+
−
−
2
(
r
)
d
ρ
0
(
r
)
4
2
4
1
r
3
3
u
0
(
r
)
15
u
2
(
r
)
5
u
2
(
r
)
30
u
−
2
(
r
)
Δ
I
22
=
4π
+
+
+
0
10
v
−
2
(
r
)
dr
,
2
5
v
12
3
v
1
0
2
(
r
)
+
2
(
r
)
+
+
d
ρ
0
(
r
)
4
2
(
r
)
dr
,
4
4
5
v
r
3
3
u
0
(
r
)
15
u
2
(
r
)
0
Δ
I
33
=
4π
−
−
(9.91)
0
ρ
0
(
r
)
10
v
−
2
(
r
)
dr
,
Δ
I
12
=
4π
i
d
0
4
1
12
5
v
1
r
3
5
u
2
(
r
)
+
30
u
−
2
(
r
)
−
2
(
r
)
+
−
d
ρ
0
(
r
)
2
5
v
−
2
(
r
)
dr
,
1
6
5
v
1
r
3
5
u
2
(
r
)
15
u
−
2
(
r
)
1
Δ
I
13
=
4π
−
+
2
(
r
)
−
0
ρ
0
(
r
)
2
5
v
−
2
(
r
)
dr
,
4π
i
d
0
1
6
5
v
1
r
3
5
u
2
(
r
)
15
u
−
2
(
r
)
1
Δ
=
+
+
+
I
23
2
(
r
)
with
d
the radius of the Earth.
As shown in Section 9.2, the solid boundaries of the outer core can penetrate
the gravitational equipotentials coincident with the boundaries of the outer core in
the undeformed state. This gives further contributions to the changes in the inertia
tensor, which for the core-mantle boundary amount to
ρ
0
(
b
−
)
4
u
−
2
2
15
Δ
4
5
Δ
1
30
Δ
2π
b
4
u
0
+
u
2
−
u
2
−
Δ
J
11
=
3
Δ
,
ρ
0
(
b
−
)
4
2
15
Δ
4
5
Δ
1
30
Δ
2π
b
4
u
0
+
u
2
+
u
2
+
u
−
2
Δ
J
22
=
3
Δ
,
2
ρ
0
(
b
−
)
4
u
2
4
15
Δ
2π
b
4
u
0
−
Δ
J
33
=
3
Δ
,
(9.92)
ρ
0
(
b
−
)
u
−
2
4
5
Δ
1
30
Δ
2π
b
4
u
2
+
Δ
=
−
J
12
,
ρ
0
(
b
−
)
2
u
−
2
1
15
Δ
2π
b
4
u
2
−
Δ
J
13
=
5
Δ
,
ρ
0
(
b
−
)
2
u
−
2
1
15
Δ
2π
b
4
u
2
+
Δ
J
23
=
5
Δ
,
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