Static deformations and dislocation theory - Earth Dynamics: Deformations and Oscillations of the Rotating Earth - page 497

10 L

9 L

− 1

8 L 0.0

− 2

7 L

6 L

− 4

5 L

1

− 8

4 L

− 14

3 L

2

2 L − 30

4

8

L 14

30

0

0 L 2 L 3 L 5 L

Distance from strike

4 L 6 L 7 L 8 L 9 L 10 L

Figure 9.5 Contours of the displacement field component vertically downward in
millimetres. The field is shown for 10 fault lengths along the strike ( L

=

700 km),
from the midpoint, and 10 fault lengths orthogonal to the strike, from the mid-
point. Uplift as shown is negative.

9.2 The theory for realistic Earth models

The elasticity theory of dislocations presented in the previous section was for a
uniform, not self-gravitating, elastic half-space, taken to be a Poisson solid
(λ = μ). We now extend the theory to more realistic, rotating, self-gravitating,
radially inhomogeneous Earth models with a liquid outer core and solid inner core.
Deformations in such realistic Earth models have been considered in Chapter 3.
We first consider the equations (3.63) through (3.67) governing spheroidal deform-
ations in the liquid outer core for degree n

1. In the static case, the dynamical
body force terms vanish and the governing system becomes

≥

d y 1
dr =−

2
r y 1 +

1
λ y 2 +

n ( n 1)

r y 3 ,

+

(9.26)

2g 0

2 y 1

n ( n + 1 )

r ρ 0 g 0 y 3

d y 2
dr =−

2 ρ 0
r

+ r Ω + − ρ 0 y 6 , (9.27)

= ρ 0 g 0

1

r y 2 − ρ 0

0

r y 1 − r y 5 ,

(9.28)

d y 5
dr =

4π G ρ 0 y 1 + y 6 , (9.29)

4π G ρ 0 n ( n +

1 )
r y 3

n ( n + 1 )

d y 6
dr =−

2
r y 6 .

+ y 5 − (9.30)

r 2