Earth deformations - Earth Dynamics: Deformations and Oscillations of the Rotating Earth - page 257

ν = 3, η = n + 2, and (3.143) for ν = 4, η = n + 3, which combine to yield the 6 × 6

system

⎝ ⎠

⎝ ⎠

0

A 1,3
A 2,2
A 3,3
A 4,2
A 5,4
A 6,3

4γ + ω

2 A 1,1 +

2

− + 2 Ω ( n 1 γ + 2 m ω Ω ) A 3,1 − A 6,1

0

ω

2 m ω Ω / n 1 A 3,1

A · = ρ 0 , (3.309)

2

(γ + 2 m ω Ω / n 1 ) A 1,1 − − − A 5,2

0
0

where the coe cient matrix, A ,is

⎝ ⎠

2λβ + n + 3 − β − n 1 λβ 0 0 0

− 2δ 4μβ + n + 2 n 1 δ − n 1 0 0

1 0 n + 2 − 1/μ 0 0

, (3.310)

δ λβ − n + 50 0

2

− 3γ − 2 Ω 0 0 0 n + 4 − 1

3γ +

2 n 1

0 0 2 Ω 0 − n 1 n + 5

with 4π G ρ 0 replaced by the right side of relation (3.129). The third terms in the
first and second fundamental solutions are given by the systems (3.139) for ν = 5,

η = n + 2, and (3.143) for ν = 6, η = n + 3, which combine to yield the 6 × 6 system

⎝ ⎠

⎝ ⎠

0

A 1,5
A 2,4
A 3,5
A 4,4
A 5,6
A 6,5

4γ + ω

2 A 1,3 +

2

− + 2 Ω ( n 1 γ + 2 m ω Ω ) A 3,3 − A 6,3

0

ω

2 m ω Ω / n 1 A 3,3 −

A · = ρ 0 . (3.311)

2

(γ + 2 m ω Ω / n 1 ) A 1,3 − − A 5,4

0
0

The third terms in the third fundamental solution are given by the systems (3.139)
for ν = 5, η = n + 4, and (3.143) for ν = 6, η = n + 5, which combine to yield the

6 × 6 system

⎝ ⎠

⎝ ⎠

0

A 1,5
A 2,4
A 3,5
A 4,4
A 5,6
A 6,5

4γ + ω

2 A 1,3 2

− + 2 Ω + ( n 1 γ + 2 m ω Ω ) A 3,3 − A 6,3

0

A ·

ω

2 m ω Ω / n 1 A 3,3

= ρ 0 , (3.312)

2

(γ + 2 m ω Ω / n 1 ) A 1,3 − − − A 5,4

0
0