Geology Reference
In-Depth Information
tan
δ
v
=
v
v
/
h
,
(6.21a)
tan
δ
h
=
v
/
h
h
.
(6.21b)
Replace
h
in Eq. 6.21a and
v
in 6.21b with the values from Eq. 6.19 and use the defini-
tion of the exaggeration to obtain the relationship between original and exaggerated dips:
tan
δ
v
=
V
e
tan
δ
,
(6.22a)
tan
δ
h
=tan
δ
/
H
e
.
(6.22b)
To relate the horizontal to the vertical exaggeration, substitute the value of tan
δ
from Eq. 6.22a into 6.22b to obtain
V
e
H
e
=tan
δ
v
/tan
δ
h
.
(6.23)
To obtain the same exaggerated angle by either horizontal or vertical exaggeration,
set
δ
v
=
δ
h
in Eq. 6.23:
V
e
=1/
H
e
.
(6.24)
The thickness of a unit on a horizontally exaggerated profile (Fig. 6.50b),
t
h
, is
sin (90 -
δ
h
)=cos
δ
h
=
t
h
/
L
.
(6.25)
Eliminate
L
by dividing Eq. 6.25 by 6.20:
t
h
/
t
=cos
δ
h
/cos
δ
.
(6.26)
The thickness of a unit on a vertically exaggerated profile (Fig. 6.50c),
t
v
, is
cos
δ
v
=
t
v
/(
V
e
L
) .
(6.27)
Eliminate
L
by dividing Eq. 6.27 by Eq. 6.20:
t
v
/
t
=
V
e
(cos
δ
v
/cos
) .
(6.28)
δ
6.8.2
Analytical Projection along Plunge Lines
The point P is to be projected parallel to plunge to point P' on the cross section
(Fig. 6.51a). The plunge direction makes an angle of
to the direction of the perpen-
dicular to the cross section (Fig. 6.51d) and the plunge is
α
. Following the method of
De Paor (1988), the
x
coordinate axis is taken parallel to the line of the section and the
plane of section intersects the
x
axis at zero elevation. In the plane of the cross section,
φ
