Geology Reference
In-Depth Information
The Wills Valley anticline provides an example of rigid-block rotation above a cir-
cular-arc thrust and of a model-based sequential restoration. The cross section is
from the middle of an approximately 140 km long, straight, anticline located in the
frontal part of the southern Appalachian fold-thrust belt. The cross section on which
Fig. 11.28c is based is derived from outcrop geology and a seismic reflection profile
(Fig. 1.46). This structure fits a circular-block model with best-fit measurements of
∆
θ
0
= 22°. From Eqs. 11.40, 11.42, and 11.43, respectively,
r
= 21.98 km,
R
= 23.7 km, and
H
= 1.73 km. From Eq. 11.45, the displacement that
produced the structure is
D
= 4.137 km. These values allow the structure to be re-
stored to zero displacement (Fig. 11.28a), from which the bed lengths are measured
and included in Fig. 11.28c. From Eqs. 11.46 and 11.47, respectively,
= 10°,
W
= 8.88 km and
d
= 301 m, and
δ
10
5
m
2
. These values are included in Fig. 11.28c with the displacement ac-
commodated by the hangingwall splay thrusts and the excess area accommodated by
the uplift on the splays.
A footwall syncline is preserved beneath the master thrust indicating a fault-tip
fold was once present, which is reconstructed in Fig. 11.28b. The outer limits of the
region inferred to be affected by fault-tip folding are indicated by the pin lines shown
in Fig. 11.28a,b. The outer limit of folding on the footwall is obtained directly from
the cross section. The outer limit of folding on the hangingwall is somewhat arbitrary
because the fold has been eroded from the hangingwall. The pin is placed at the
hangingwall cutoff of the top OCk, which is appears not to be folded, and is sloped
sharply outward to include comparable widths of PM in the hangingwall and foot-
wall, giving a length
L
0
of 5 745 m at the base of the PM. If
L
0
is too short, the neces-
sary area cannot be obtained on the hangingwall; if it is too long, an unrealistic amount
of the hangingwall is folded. The reconstruction of Fig. 11.28b is constrained by the
known geometry of the footwall folds, area balance, and maintaining constant bed
length at the base of the PM. A 3° rotation of the hangingwall and attendant displace-
ment causes the straight-line distance between the endpoints of
L
0
to be reduced to
4 751 m. These constraints require folding on the hangingwall as well as the footwall.
For a 3° rotation,
A
=5.3
×
d
at the top of the Cc is 117 m (Eq. 11.46) and the excess area re-
quired to maintain a vertical trailing pin line is
A
=1.6
δ
10
5
m
2
(Eq. 11.47). These
values are incorporated into the geometry of the hangingwall as displacement and
thickening on the splay faults and their hangingwalls.
×
11.6
Flexural-Slip Deformation
Flexural-slip restoration is based on the model that bed lengths do not change during
deformation (Chamberlin 1910; Dahlstrom 1969; Woodward et al. 1985, 1989). Inter-
nal deformation is assumed to occur mainly by layer-parallel simple shear (Fig. 11.3b).
For the area to remain constant, the bed thicknesses must be unchanged by the defor-
mation as well. This is the constant bed length, constant bed thickness (constant BLT)
model. Flexural-slip restoration is particularly suitable where the beds are folded and
structurally induced thickness changes are small, the style of deformation in many
compressional structures. Flexural slip is also commonly used to restore the complex
deformation above salt layers (Hossack 1996).
