Geology Reference
In-Depth Information
Fig. 6.41.
Projection along plunge into the plane of the cross section.
a
Perspective diagram.
b
Horizontal
map projection. The projection of the section plane onto the map is
shaded
of the cross section. The sign convention requires that the positive (down) plunge
direction be in the negative
y
direction. The elevation of a point is
z
. The dip of the
plunge line =
φ
, the angle between the plunge line and the normal to the cross
section =
. The plunge line is constant in direc-
tion in a cylindrical fold but may be different for every location in a conical fold.
The general equations for the projected position of a point P', derived at the end of
the chapter (Eqs. 6.36 and 6.41), are:
, and the dip of the cross section =
α
δ
x
'=
x
+
y
tan
+tan
(
z
cos
-
y
tan
) / (tan
+tan
cos
) ,
(6.13)
α
α
α
φ
φ
δ
α
z
'=(
z
cos
α
-
y
tan
φ
) / (tan
φ
cos
δ
+sin
δ
cos
α
) .
(6.14)
For a vertical cross section, from Eqs. 6.42 and 6.43,
x
'=
x
+
y
tan
α
,
(6.15)
z
'=
z
-(
y
tan
φ
)/cos
α
.
(6.16)
A cross section perpendicular to the fold axis is possible only for a cylindrical fold.
The equations for projection to the normal section are (from Eqs. 6.44 and 6.45)
x
'=
x
,
(6.17)
z
'=
z
cos
-
y
sin
.
(6.18)
φ
φ
