Geology Reference
In-Depth Information
5.4.2
Orientation
Quantitative methods for the determination of the attitude of axial surfaces are given
in this section. The orientation of an axial surface is related to the bed thickness change
across it. In a cross section perpendicular to the hinge line, if a bed maintains constant
thickness across the hinge, the axial surface bisects the hinge. The relationship be-
tween bed thickness and axial surface orientation is obtained as follows. Both limbs of
the fold meet along the axial surface (Fig. 5.17) and have the common length
h
and
therefore must satisfy the relationship
h
=
t
1
/sin
γ
1
=
t
2
/sin
γ
2
.
(5.9)
γ
2
and the axial surface bisects the hinge (Fig. 5.17a). If the bed
changes thickness across the axial surface, then the axial surface cannot bisect the hinge
(Fig. 5.17b). The thickness ratio across the axial surface is
If
t
1
=
t
2
, then
γ
1
=
t
1
/
t
2
=sin
γ
1
/sin
γ
2
.
(5.10)
If the thickness ratio and the interlimb angle are known, then from the relationship
(Fig. 5.17b)
γ
=
γ
1
+
γ
2
,
(5.11)
where
γ
= the interlimb angle and
γ
2
= the angle between the axial surface and the dip
of limb 2. Substitute
γ
2
from Eq. 5.11 into 5.10, apply the trigonometric iden-
tity for the sine of the difference between two angles, and solve to find
γ
1
=
γ
-
γ
2
as
γ
2
=arctan[
t
2
sin
γ
/(
t
1
+
t
2
cos
γ
)] .
(5.12)
The axial surface orientation in three dimensions can be found from a stereogram
plot of the limbs. If the bed maintains constant thickness, the interlimb angle is bi-
Fig. 5.17.
Axial-surface geometry of a dip-domain fold hinge in cross section.
a
Constant bed thick-
ness.
b
Variable bed thickness
