Geology Reference
In-Depth Information
Method 2. Using bed dip vector and points on top and base of unit
If the locations of the unit boundaries are given by their
xyz
coordinates, and the ori-
entation of bedding by its azimuth and dip, the angle
ρ
required in Eq. 4.1 may be
found by substituting Eq. 12.9 into Eq. 12.25:
=cos
-1
{[(
x
1
-
x
2
)/
L
] sin
θ
b
sin
δ
b
+[(
y
1
-
y
2
)/
L
] cos
θ
b
sin
ρ
δ
b
+[(
z
2
-
z
1
)/
L
] cos
δ
b
} ,
(4.4)
where
δ
b
=, respectively, the azimuth and dip of the bed dip vector, and
L
, the
apparent length, is
θ
b
and
L
=[(
x
2
-
x
1
)
2
+(
y
2
-
y
1
)
2
+(
z
2
-
z
1
)
2
]
1/2
.
(4.5)
Method 3. Using bed dip vector and line on map
If the line of the thickness measurement is defined by its map length,
h
, change in
elevation,
v
, and orientation given by the azimuth,
, to the lower end of the line, then
θ
the angle
ρ
required in Eq. 4.1 may be found by substituting Eq. 12.7 into Eq. 12.25:
=cos
-1
{cos
ρ
δ
b
sin [arctan (
v
/
h
)]
-sin
δ
b
cos [arctan (
v
/
h
)] (cos
θ
b
cos
θ
+sin
θ
b
sin
θ
)} ,
(4.6)
where
δ
b
=, respectively, the azimuth and dip of the bed dip vector, and
L
, the
apparent length, is
θ
b
and
L
=(
v
2
+
h
2
)
1/2
,
(4.7)
where
v
= vertical distance between end points and
h
= the horizontal distance between end
points. The angle in Eq. 4.6 must be acute and must be changed to 180 -
ρ
if it is obtuse.
4.1.2
Thickness between Structure Contours
The thickness determined between structure contours is straightforward to compute and
generally shows much less variability than that determined between individual points on an
outcrop map. This approach provides a more reliable value in situations where the attitudes
and contact locations are uncertain on a map. Determining the best-fit structure contours
uses a large amount of data simultaneously to improve the attitude of bedding and the
contact locations. This method requires a structure contour at the top and base of the bed
(Figs. 4.4, 4.5a). The width of the unit is always measured in the dip direction, perpen-
dicular to the structure contours. If contours at the same elevation can be constructed on
the top and base of the unit, from the geometry of Fig. 4.5b, the thickness of the unit is
t
=
h
c
sin
δ
,
(4.8)
where
h
c
= horizontal distance between contours at equal elevations on the top and
base of the unit,
t
= true thickness, and
δ
= true dip. If the contours on the top and
