Static deformations and dislocation theory - Earth Dynamics: Deformations and Oscillations of the Rotating Earth - page 505

θ have been transported in the

transported in the θ-direction and the unit vectors ±

r -direction. From (9.65) and (9.66), we find that
∂ r
∂θ =

θ
∂ r =

θ and ∂

0. (9.73)

Thus, only transport in the θ-direction gives a non-null result. With arguments that
are similar to those made before, we find co-ordinate curvature contributes the term
in double-force density,

θ r 0 cosα,

− (9.74)

arising from the double-couple term for strike-slip faults and illustrated in the top
right of Figure 9.7.
For the double-force system arising from the dip-slip expression and illustrated
in the lower left of Figure 9.7, the unit vectors ± r have been transported in the

φ have been transported in the φ-direction. From

r -direction and the unit vectors ±

(9.65) and (9.67), we find
∂ r
∂ r =

φ
∂φ =−

0 d ∂

θ cosθ.

r sinθ − (9.75)

Thus, only transport in the φ-direction gives a non-null result. With arguments
similar to those made before, we find co-ordinate curvature contributes the term in
double-force density,

r r 0 sin 2α +

θ cot θ

r 0 δsin 2α,

(9.76)

arising from the double-force term for dip-slip faults and illustrated in the lower
left of Figure 9.7.
For the double-couple force system arising from the dip-slip expression and
illustrated in the lower right of Figure 9.7, the unit vectors ± r have been transported

φ have been transported in the r -direction.
From (9.65), (9.66) and (9.67), we find that
∂ r
∂φ =

in the φ-direction and the unit vectors ±

φ
∂ r =

φ sinθ and ∂

0. (9.77)

Thus, only transport in the φ-direction gives a non-null result. With arguments
similar to those made before, we find co-ordinate curvature contributes the term in
double-force density,

φ r 0 cos 2α,

(9.78)

arising from the double-couple term for dip-slip faults and illustrated in the lower
right of Figure 9.7.