Geology Reference
In-Depth Information
Fig. 6.51.
Projection along plunge.
a
Per-
spective diagram.
b
Ve r t i c a l
plane through plunge line
PP'
.
c
Vertical plane normal to the
cross section through line
OP'
.
d
Plan view. Projection of the
cross section is
shaded
. Point
Q
is vertically above
A
at
A
-
Q
and
point
P'
is vertically above
O
at
O
-
P'
the position of point P (
x
,
y
,
z
) is P' (
x
',
z
'). The apparent dip of the intersection line,
q
,
of the vertical plane through PP' with the cross section is
δ
'. The relationship between
the apparent dip and the true dip,
δ
, of the
z
' line, is given by Eq. 2.18 as
tan
δ
'=tan
δ
cos
α
.
(6.29)
Begin by finding
z
'. In the plane normal to the cross section (Fig. 6.51a,c),
z
'=OP'/sin
δ
.
(6.30)
In the plane of the plunge (Fig. 6.51b), using triangles AQP' and PQR,
OP' =
q
sin
δ
' ,
(6.31)
∆
z
=
L
tan
φ
,
(6.32)