Geology Reference
In-Depth Information
Fig. 11.13.
Area restoration.
A
0
: Original
area;
t
0
: original bed thickness;
L
0
: original bed length. Shape of
the restored area depends on
assumed original orientations of
the pin lines.
a
Deformed-state
cross section.
b
Section restored
to vertical pin lines.
c
Section
restored to tilted pin lines
of the restored area depends on the assumed original shape (Mitra and Namson 1989).
Ordinarily the unit is restored to horizontal, leaving only the orientations of the pin
lines to be determined. A folded area might be appropriately restored to a rectangular
prism (Fig. 11.13b), whereas a block bounded by faults would be restored to fit be-
tween the presumed original fault shapes (Fig. 11.13c).
11.4.2
Depth to Detachment and Layer-Parallel Strain
The first predictive uses of the concept of area balance were to determine the depth to
detachment of the structure (Chamberlin 1910; Hansen 1965). Area uplifted above the
regional as a result of compressional deformation is termed the excess area (Fig. 11.14).
Area that drops below regional as a result of extensional deformation is termed lost
area. More generally, these can be called the displaced areas. The classical displaced-
area method is designed to find the detachment depth from the excess or lost area of
one horizon in a structure. The displaced area is produced by displacement along the
lower detachment such that
S
=
D
H
,
(11.18)
where
S
= area above or below the regional,
D
= displacement, and
H
= depth to de-
tachment from regional (Fig. 11.14). A unique depth to detachment can be calculated
from a measurement of the excess area
if
the displacement that formed the structure
is known. Chamberlin (1910) and many subsequent authors have assumed that bed
length remains constant and so the displacement is the difference between the curved-
bed length of the marker horizon and its length at regional:
D
=
L
0
-
W
,
(11.19)
where
D
= displacement,
L
0
= curved-bed length (assumed equal to original bed length)
and
W
= width of structure at regional. Substituting Eq. 11.19 into 11.18:
H
c
=
S
/(
L
0
-
W
) ,
(11.20)
where
H
c
indicates the detachment depth if bed length is constant.
