Geology Reference
In-Depth Information
Fig. 2.18.
Apparent dip on a tangent diagram.
a
Apparent dip from true dip.
b
True dip from two ap-
parent dips. (After Bengtson 1980)
For example, given a dip vector of a bed
δ
1
, find the apparent dip in the direction of
δ
2
.
Project the tip of
δ
1
. The projection is along a line perpendicu-
lar to the apparent dip. The length of the projected bedding vector in the direction of
the apparent dip is the amount of the apparent dip. The true dip can be found from
two apparent dips. The perpendiculars from the apparent dips (
δ
2
onto the direction of
δ
1
and
δ
2
) intersect at
the tip of the true dip vector (Fig. 2.18b).
2.4
Finding the Orientations of Planes
The attitude of a plane measured by hand with a compass or given by a dipmeter log
is effectively the value at a single point. Measured over such a small area, the attitude
is very sensitive to small measurement errors, surface irregularities, and the presence
of small-scale structures. The following two sections describe how to find the attitude
from three points that can be widely separated and from structure contours. Both
methods provide an average attitude representative of the map-scale structure.
The farther the points depart from a straight line, the more reliable the expected
result because small irregularities or location errors will have less influence on the
result. If more than three points are available to find the attitude of the plane, a best-
fit can be determined using planar regression or moment of inertia analysis (Fernández
2005). A typical situation for this application would be a series of points along the
outcrop trace of a plane (e.g., Fig. 2.4). On the other hand, the farther the points are
from one another, the greater the possibility that they no longer fall on a single plane.
A high-quality calculated dip will be compatible with the surrounding data as demon-
strated with a structure contour map (Chap. 3) and cross section (Chap. 6). If the unit
thickness is known (Chap. 4), a very powerful test of the quality of a calculated dip is
to show that both the top and base of the unit fit their respective outcrop traces.
