Static deformations and dislocation theory - Earth Dynamics: Deformations and Oscillations of the Rotating Earth - page 506

In summary, co-ordinate curvature contributes the extra double-force density
terms for the dip-slip system,

r r 0 sin 2α +

θ cot θ 0 φ r 0 cos 2α,

r 0 δsin 2α +

(9.79)

and the extra double-force density terms for the strike-slip system,

θ r 0 cosα + φ cot θ 0

−

r 0 δsinα.

(9.80)

Using the orthogonality relations (1.205) and (1.209), as outlined, the radial
spheroidal, transverse spheroidal and torsional radial coe cients can be extrac-

ted from the dipole force densities for the dip-slip system (9.63). In the limit as θ 0
approaches zero, we find

2 n + 1

u n ( r )

4π r 2 δ ( r

= − r 0 ) sin 2α,

i ( 2 n + 1 )

u − n ( r ) =− n ( n + 1)δ( r − r 0 )cos2α,

8π r 3

i (2 n 1)

8π r 3 δ( r

+

u n ( r ) =− − r 0 )cos2α,

i (2 n + 1)

v − n ( r )

8π r 2 δ ( r

= − r 0 )cos2α,

i (2 n + 1)

1

1) δ ( r

v

n ( r )

= − r 0 )cos2α,

8π r 2 n ( n

+

2 n 1

8π r 3

+

v − n ( r )

=− ( n − 1)( n + 2)δ( r − r 0 ) sin 2α, (9.81)

2 n + 1

n ( r )

v =−

1) δ( r

− r 0 ) sin 2α,

8π r 3 n ( n +

2 n + 1

t − n ( r )

8π r 2 δ ( r

=− − r 0 )cos2α,

+

2 n 1

t n ( r )

1) δ ( r

= − r 0 )cos2α,

8π r 2 n ( n

+

i (2 n + 1)

t − n ( r ) =− ( n − 1)( n + 2)δ( r − r 0 ) sin 2α,

8π r 3

i (2 n + 1)

t n ( r ) =

1) δ( r

− r 0 ) sin 2α.

8π r 3 n ( n +