Geology Reference
In-Depth Information
v
=
z
-
L
tan
,
(6.33)
φ
and by using the law of sines with angles AQP' and QP'A in triangle QAP', along with
cos
φ
=sin(90-
φ
),
q
=
v
/ (tan
cos
'+sin
') .
(6.34)
φ
δ
δ
In the plane of the map (Fig. 6.51d)
L
=
y
/cos
α
.
(6.35)
Substitute Eqs. 6.29, 6.31, 6.33, 6.34 and 6.35 into 6.30 to obtain
z
'=(
z
cos
α
-
y
tan
φ
) / (tan
φ
cos
δ
+sin
δ
cos
α
) .
(6.36)
The
x
' coordinate is found from (Fig. 6.51a)
x
'=
x
+
∆
x
+
b
.
(6.37)
In the plane of the map (Fig. 6.51d)
∆
x
=
y
tan
α
,
(6.38)
b
= OB tan
α
.
(6.39)
In the plane normal to the cross section (Fig. 6.51c)
OB = OP' / tan
δ
.
(6.40)
Substitute Eqs. 6.29, 6.31-6.35 and 6.38-6.40, into 6.37 to obtain
x
'=
x
+
y
tan
α
+tan
α
(
z
cos
α
-
y
tan
φ
) / (tan
φ
+tan
δ
cos
α
) .
(6.41)
For a vertical cross section,
δ
= 90° and Eqs. 6.36 and 6.41 reduce to
x
'=
x
+
y
tan
,
(6.42)
α
z
'=
z
-
y
tan
φ
/cos
α
.
(6.43)
For a cross section normal to the plunge line, possible only for a cylindrical fold,
=0,
= (90 -
) and Eqs. 6.36 and 6.41 reduce to
α
δ
φ
x
'=
x
,
(6.44)
z
'=
z
cos
φ
-
y
sin
φ
.
(6.45)
