Geology Reference
In-Depth Information
lower detachment along the radius
R
*, orthogonal to the regional, located where the
hangingwall marker bed in the anticline returns to regional dip. Rigid-block rotation
is possible for the main part of the hangingwall (shaded, Fig. 11.27). The original dip
of the fault at regional is
θ
0
, which, together with the width of the structure,
W
, is a
function of the radius of curvature,
r
, of the marker bed
r
=
W
/tan
θ
0
.
(11.40)
The center of curvature of the fault is located a distance
r
above the regional along
R
*.
If the dip of the fault at regional is not visible, then it can be found from the dip of the
fault at its tip,
θ
1
, from
θ
0
=
θ
1
-
∆
,
(11.41)
where
dip of the fault block. Once
r
and
W
are known, the radius,
R
, to the detach-
ment from the center of curvature is
∆
R
=(
W
2
+
r
2
)
1/2
.
(11.42)
The depth to the lower detachment from the regional is
H
, where
H
=
R
-
r
.
(11.43)
The displacements are
d
=
r
/ 57.3 ,
(11.44)
∆
D
=
R
∆
/ 57.3 ,
(11.45)
where
d
= displacement at the level of the regional datum,
D
= displacement on the
lower detachment, and
is in degrees.
Total rigid-block rotation is impossible because the trailing edge of the rotated
block (unshaded, Fig. 11.27) moves from a planar lower detachment onto the curved
ramp, requiring some form of internal deformation. If the original hangingwall re-
mains rigid, the displacement increases downward toward the detachment. To main-
tain constant bed length and bed thickness behind the rigid block, flexural slip is
required and would cause the trailing pin line to rotate (solid head, Fig. 11.27). The
magnitude of the slip is
∆
δ
d
=
D
-
d
=
H
tan
∆
.
(11.46)
The final geometry of the trailing pin line is of great importance. If the pin line
rotates to maintain constant bed length and bed thickness, as shown by the solid-
head pin in Fig. 11.27, then the rotated block will impose regional layer-parallel shear
on the hinterland of the structure. Mechanically it seems much more likely that dis-
