Geology Reference
In-Depth Information
11.4.3.2
Strain
Layer-parallel strain can be determined from the area-depth relationship if either the
displacement is known (from the area-depth graph), or the detachment location is
known (by direct observation or from the area-depth relationship). The method ap-
plies to growth beds as well as to pre-growth beds.
The length of a particular horizon as seen on a cross section is its final length
L
1
which may include bed-length changes. From the geometry of Fig. 11.16, the original
length of the horizon (
L
0
) is
L
0
=
W
+
d
=
W
+
S
/
H
,
(11.24)
where
W
= the width of the structure at the regional of the horizon and
d
= the dis-
placement of any horizon, including a growth horizon (Groshong et al. 2003a). A
lowercase
d
is used here for a growth-bed displacement and an uppercase
D
for the
total displacement of a pre-growth unit. Either value can be substituted into Eq. 11.24.
W
is always measured parallel to the regional and is tilted if the regional is tilted. The
value of
L
0
calculated from the displaced area is independent of the stratigraphic growth
of the unit because it depends only on the length along the upper surface of the unit,
not on the thickness. The bed-length change is
∆
L
=
L
1
-
L
0
=
L
1
-(
W
+
S
/
H
) .
(11.25)
The length difference can be converted to layer-parallel strain,
e
, by dividing Eq. 11.25
by Eq. 11.24:
e
L
=(
H
L
1
/(
H
W
+
S
)) - 1 .
(11.26)
If the total displacement,
D
, is known from the area-depth relationship, an alterna-
tive form of the equation is convenient:
e
L
=(
L
1
/(
W
+
D
)) - 1 .
(11.27)
11.4.4
Area-Depth Relationships of Regionally Balanced Structures
For regionally balanced structures, material is transported across vertical pin lines
bounding the structure of interest (Fig. 11.5c,d). A representative example of a region-
ally balanced structure is a fault-bend fold (Figs. 11.5c, 11.19a). In a fault-bend fold,
one of the original pin lines is offset along an upper detachment horizon (Fig. 11.19a).
Part of the area displaced above the upper detachment is within the anticline and part is
outside the anticline. Material may be displaced toward the foreland or toward the hin-
terland; the area-balance is the same. Two area-depth lines are produced, one for the strati-
graphic levels below the upper detachment and one for the stratigraphic levels above the
