Geology Reference
In-Depth Information
X
1
X
2
q
d
D
x
X
3
Figure 9.1 Inclined fault geometry and co-ordinates.
If the slip is along the strike of the fault, it is called a
strike-slip
. For a strike-
slip
U
1
in the direction of co-ordinate
x
1
, the slip vector is
(
U
1
,0,0). Once
again, carrying out the implied summations over
i
and
j
, Volterra's formula for a
strike-slip fault gives
Δ
u
=
⎣
⎝
⎠
⎝
⎠
⎦
=
μ
U
1
∂
u
k
∂
u
k
∂ξ
1
∂
u
k
∂
u
k
∂ξ
1
dS
.
u
k
∂ξ
2
+
sinθ
−
∂ξ
3
+
cosθ
(9.9)
S
By the chain rule for partial derivatives, with
u
(ξ
2
,ξ
3
) a function of the
co-ordinates ξ
2
and ξ
3
,
∂
u
∂ξ
=
cosθ
∂
u
sinθ
∂
u
∂ξ
2
+
∂ξ
3
.
(9.10)
Using this relation, the expression for the displacement field of the dip-slip fault
may be transformed to
⎣
2
⎝
⎠
+
⎝
⎠
⎦
D
L
sinθ
∂
u
k
cosθ
∂
u
k
∂ξ
∂
u
k
∂
u
k
∂ξ
3
u
k
=
μ
U
∂ξ
−
∂ξ
2
−
d
ξ
1
d
ξ,
(9.11)
d
−
L
while the expression for the displacement field of the strike-slip fault remains as
⎣
⎝
⎠
⎝
⎠
⎦
D
L
∂
u
k
∂
u
k
∂ξ
1
∂
u
k
∂
u
k
∂ξ
1
u
k
=
μ
U
1
∂ξ
2
+
sinθ
−
∂ξ
3
+
cosθ
d
ξ
1
d
ξ.
(9.12)
d
−
L
The point force displacement fields required for the evaluation of the dip-slip
and strike-slip integrals are provided by the solutions of Mindlin problems I (1.527)
and II (1.529). The Mindlin problems are solutions for point forces of magnitude
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