Geology Reference
In-Depth Information
Fig. 11.20.
Length and displacement mea-
surements for strain calculation
Sub-resolution strains are determined from the displacement and the width of the
structure at regional. The appropriate relationship depends on whether the bed is
stratigraphically below or above the level of the upper detachment horizon (Fig. 11.20).
The final bed lengths are the observed lengths between the points where the struc-
ture departs from regional. The original bed lengths are given by the following equa-
tions:
b
L
0
=
b
W
+
D
,
(11.30)
a
L
0
=
a
W
+(
D
-
d
) ,
(11.31)
where
i
L
0
= original bed length,
i
W
= width of structure parallel to regional at regional,
i
= a or b,
D
= displacement on the lower detachment, and
d
= displacement on the
upper detachment. The layer-parallel strain is
e
=(
i
L
1
/
i
L
0
) - 1 ,
(11.32)
where
e
= layer-parallel strain as a fraction,
i
L
1
= measured bed length, and
i
L
0
=cor-
responding original bed length from Eqs. 11.30 or 11.31.
Other regionally balanced styles of importance are those produced with simple-
shear transport of material into the closed structure (Fig. 11.5d). A linear shear profile
has been treated by Epard and Groshong (1993). The total displacement is a combina-
tion of the constant component,
D
, and the distributed simple-shear component,
D
s
.
The excess area is the sum of the constant-displacement component,
Dh
and the dis-
tributed shear component,
S
s
:
S
=
Dh
+
S
s
.
(11.33)
Assuming linear simple shear:
S
s
=
D
s
h
,
(11.34)
Ä
where
D
s
=
h
tan
ψ
,
(11.35)
