Geology Reference
In-Depth Information
As an example, in Fig. 4.5a, the 600-ft contour has been located on both the top and
base of the Mpm, and so the simplest means of thickness determination is with Eq. 4.8.
The value of h c measured from the map is 1 387 ft, and the dip,
δ
, is 04°, giving a thick-
ness of 97 ft.
4.1.3
Map-Angle Thickness Equations
The calculation of the thickness of a unit based entirely on map distances and direc-
tions results in two equations, depending on whether the topographic slope is in the
same direction as the dip of the unit or the opposite direction to it. For the bed dip and
topographic slope in the same direction, the equation (derived at the end of this chap-
ter as Eqs. 4.18 and 4.21) is
t =| h cos
α
sin
δ
- v cos
δ
| ,
(4.10)
where the notation |…| = the positive value of the expression between the bars. For a
bed dip and topographic slope that are in opposite directions:
t = h cos
α
sin
δ
+ v cos
δ
,
(4.11)
where h (Fig. 4.6) = the horizontal distance along a line between the upper and lower
contacts on the map,
α
= the angle between the measurement line and the dip direc-
tion,
= the true dip of the unit, and v = the elevation difference between the end points
of the measurement line. If the measurement is in the dip direction,
δ
α
=0 and cos
α
=1;
if the base and top of the unit are both at the same elevation, v =0.
As an example, determine the thickness of the Pride Mountain Formation (Mpm)
indicated by its outcrop width on the map of Fig. 4.7. Along line a on the map, the
horizontal width of the outcrop is h = 1 250 ft, the vertical drop from highest to lowest
contact is v = 100 ft, the attitude of bedding is
δ
= 07° (the average of the 06 and 08° dips
mapped) at an azimuth
θ
= 135°, and the angle between the dip direction and the
measurement line is
= 85°. The bed and topography slope in the same direction (strike
of bedding = 225° and the thickness traverse is along azimuth 220°), making Eq. 4.10
appropriate. The resulting thickness is 86 ft.
α
Fig. 4.6.
Map data needed to determine
the thickness of a unit from
outcrop observations using the
map-angle thickness Eqs. 4.10
and 4.11
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