Geology Reference
In-Depth Information
f
r
strike-slip
X
1
X
1
X
3
X
2
q
q
r
r
X
2
X
2
f
f
dip - slip
X
3
X
3
Figure 9.7 Double force and moment transport.
Thus, only transport in the φ-direction gives a non-null result. In Cartesian geo-
metry the double couple involved is
δ
x
2
→
0
δ(
x
2
+
δ
x
2
/2)
−
δ(
x
2
−
δ
x
2
/2)
δ
x
2
e
1
sinαδ(
x
1
)δ(
x
3
) lim
.
(9.69)
Each of the two forces gain small extra components
θ
∂φ
δ(φ
±
δφ/2)δ(
r
1
2
δφ
∂
−
r
0
)δ(θ
−
θ
0
)sinα
(9.70)
before division by δ
x
2
and parallel transport into the limit as δ
x
2
→
0. Since
δ
x
2
=
r
0
sinθ
0
δφ, this produces the extra term
1
r
0
sinθ
0
δφ
1
r
0
sinθ
0
δφ
φ
cosθ
0
δ(φ)δ(
r
−
r
0
)δ(θ
−
θ
0
)sinα,
(9.71)
expressed per unit volume. Hence, co-ordinate curvature contributes the term in
double-force density
φ
cot
θ
0
r
0
δsinα,
(9.72)
arising from the double-couple term for strike-slip faults and illustrated in the top
left of Figure 9.7.
In the case of the double-couple force system arising from the strike-slip expres-
sion and illustrated in the upper right of Figure 9.7, the unit vectors
±
r
have been
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