Geology Reference
In-Depth Information
Fig. 2.19.
True dip,
δ
, and apparent dip,
δ
'.
a
Perspective view.
b
Map view.
N:
north. For explanation
of
a
-
h
and
v
, see text
2.4.1
Graphical Three-Point Problem
The attitude of a plane can be uniquely determined from three points that are not on
a straight line. Let the highest elevation be point a and the lowest be point d (Fig. 2.19).
The intermediate elevation,
f
, must also occur along the line joining a and d as point e.
The line fe is the strike line. The horizontal (map) distance from a to e by linear
interploation is ab, where
ab = (ac
×
be) / cd .
(2.10)
Plot the length ab on the map (Fig. 2.19b) and join point f and b to obtain the strike
line. The dip vector lies along the perpendicular to the strike, directed from the high
point to the intermediate elevation along the strike line. The dip amount is
δ
=arctan(
v
/
h
) ,
(2.11)
where
v
= the elevation difference between the highest and the lowest points and
h
=the
horizontal (map) distance between the highest point and a strike-parallel line through d.
The azimuth of the dip is measured directly from the map direction of the dip.
A typical example of a 3-point problem is seen on the map of Fig. 2.20a. The map
shows the elevations of three locations identified in the field as being on the same
contact (a, f, d). These points could just as easily be the elevations of a formation bound-
ary identified in three wells. To find the attitude of the contact, draw a line between the
highest and lowest points (a-d, Fig. 2.20b) and measure its length. Use Eq. 2.10 to find the
distance along the line from the high point to the level of the intermediate elevation (
e
).
Connect the two intermediate elevations to find the strike line (Fig. 2.20b,c). Draw a
perpendicular from the strike line (e-f ) to the lowest point (d, Fig. 2.20d). The hori-
zontal length of the line is
h
and the elevation change is
v
. Determine the dip from
Eq. 2.11. The azimuth of the dip is measured from the map. The dip vector in this
example is 22, 125.
