Geology Reference
In-Depth Information
L
= 0, then
L
f
=
L
0
, and this equation reduces to the constant bed-length rela-
tionship (Eq. 11.20).
The effect of bed-length change on the depth-to-detachment relationship for the example
in Fig. 11.14 is seen by substituting the measured values of
S
,
L
f
,
W
, and a range of
If
∆
L
values (including zero) into Eq. 11.22 and graphing the result (Fig. 11.15). The most general
result is obtained by plotting layer-parallel strain (Eq. 11.2) versus detachment depth. The
maximum possible detachment depth (3.943 km) occurs for zero strain. The detachment at
2.0 km shown in Fig. 11.14 requires a layer-parallel shortening of -0.1 (-10%) in the marker
horizon. A shallower detachment is possible if the layer-parallel strain is sufficient.
∆
11.4.3
Area-Depth Relationship of Locally Balanced Structures
The relationship between the areas of multiple horizons on a cross section and their depths
allows a cross section to be tested for area balance and internal consistency without resto-
ration. Detachment depth can be determined without knowledge of the layer-parallel strain,
and the layer-parallel strain can be determined once the detachment location is known.
Displacement causes an amount of the original area to be pushed above the regional
(excess area) or dropped below the regional (lost area) as shown in Fig. 11.16. Mea-
surements are made of the excess or lost areas above or below the regional and the
elevation of the regional with respect to the reference level for each horizon. This in-
formation is plotted on a graph of area versus depth (elevation) (Fig. 11.17a). For a
locally balanced structure, the data from multiple horizons give points that define a
straight line, the equation of which is
h
=(1/
D
)
S
+
H
e
,
(11.23)
where
h
= elevation of a surface above or below the reference level,
D
= displacement
on the lower detachment,
S
= net displaced area, either excess or lost, and
H
e
= the el-
evation at which the area
S
goes to zero, which represents the position of the detach-
Fig. 11.16.
Area-balance terminology.
S:
Excess or lost area;
D:
displacement on the lower detachment;
H:
distance from the lower detachment to the regional;
h:
elevation of the regional above or below the
reference level;
L
1
:
bed length after deformation.
a
Extension (after Groshong 1996).
b
Contraction (af-
ter Groshong and Epard 1994)
