Last Time
• We left off with some applications of
stereonets to position planes and lines in
space.
• Now let’s add some examples from true and
apparent dip problems
4: Apparent Dip knowing True Dip
The attitude of a dike is 205, 65 (S25W, 65SE = N25E, 65SE). What is its
apparent dip on a vertical quarry wall trending 350 = N10W?
Visualize the problem (a) and plot the dike (b)
Apparent Dip knowing true dip
The attitude of a dike is 205, 65 (N25E, 65SE). What is its apparent dip on
a vertical quarry wall trending 350 = N10W?
Return North to 0o, then plot the vertical quarry wall N10W.
Apparent Dip knowing true dip
The attitude of a dike is 205, 65 (N25E, 65SE). What is its
apparent dip on a vertical quarry wall trending 350?
d. Rotate the transparency so the wall is along the vertical
axis. The apparent dip angle is from the primitive to the
intersection, 52o.
5. True Dip from two Apparent Dips
Question: A layer intersecting a road cut trends 256, 32. The
same layer intersects the road cut around a bend and
trends 125, 27. What is the strike & dip of the layer?
Visualize the problem (a) and then plot the intersections for
the road cuts and the layer (b & c)
Mark 256, rotate it to vertical
Count in apparent dip 32o
Mark 125, rotate it to vertical
Count in apparent dip 27o
True Dip from two Apparent Dips
Question: A layer intersecting a road cut trends 256, 32. The
same layer intersects the road cut around a bend and
trends 125, 27. What is the strike & dip of the layer?
Because the two road cut intersections lie on the dike, rotate
the transparency so the two points line on the same great
circle. Draw the great circle (d). Notice they define the
plane of the dike.
True Dip from two Apparent Dips
Question: A layer intersecting a road cut trends 256, 32. The same layer
intersects the road cut around a bend and trends 125, 27. What is the
strike & dip of the layer?
That great circle is the attitude of the dike; measure its dip
along the equator from the primitive to the great circle (d).
Now rotate the transparency so that its N coincides with 0 on
the net. Measure the strike and note its dip direction (e),
here about N77W 54S
Structural Geology
Stereographic Projections
Part 2 - Folds
So far, we have represented a plane on the stereographic
projection as a great circle. If we plot many planes, the
projection soon gets cluttered.
A plane, however, can
be represented by its
pole, the unique line
drawn perpendicular to
the plane. Because the
pole is a line, it plots as
a point on the
stereographic
projection.
Poles to Planes
Poles to Planes
1. A bed is 330, 50 (N30W, 50SW) Plot the plane and its pole.
Plot the plane as usual (6-2b). Then plot the point 90o away
from the plane along the horizontal axis and that is the
pole. Mark 330, rotate it to vertical
Return north to 0o
Count in dip 50o , draw in great circle,
plot pole 90o opposite
Cylindrical Folds
• Many folds are cylindrical; that is, the rocks have been
deformed by simple bending without twisting. The axis, or
hinge, of the fold is the line of sharpest curvature of any given
layer. Wherever we measure the strike and dip of beds on
such a fold, we find that the attitudes are always parallel to a
common direction, and that direction is also parallel to the
axis of the fold.
• In the most general sense, a cylinder is defined
mathematically as a surface that is generated by a straight line
that always moves parallel to itself. The cylinder need not be
circular. While folds are usually not perfectly cylindrical, many
are sufficiently close to make this a useful approximation.
This and the next slide are
courtesy of Steve Dutch
Cylindrical Folds
• Some consequences of cylindrical geometry are:
• The line that generates the cylinder is parallel to the fold axis.
• All planes tangent to the cylinder are tangent along a line
parallel to the fold axis.
• All planes tangent to the cylinder are parallel to the fold axis.
• Therefore, any two planes tangent to the cylinder intersect in
a line parallel to the fold axis.
• All parallel cross-sections of the cylinder are identical.
• Strike and dip measurements on a cylindrical fold define
planes parallel to the fold axis. Any two of these planes
intersect in a line parallel to the fold axis.
This and the previous slide are
courtesy of Steve Dutch
Poles to Planes
2. Intersection line. The layers on the limbs of a fold will
intersect along a line parallel to the fold axis.
We can get the azimuth and plunge of a fold from this.
Limb A is 200, 60 and limb B is 060, 40
b. Plot layer A and its pole. c. Plot layer B and its pole.
Poles to Planes
Intersection line. The layers on the limbs of a fold will
intersect along a line parallel to the fold axis.
d. Now rotate the net so that the 2 poles of the layers line up
along a great circle and dash in that great circle. Measure
the angle, here 22o.
As a general rule, poles to beds folded cylindrically will all
plot on a great circle perpendicular to the fold axis.
e. Return North to 0
Draw a line perpendicular
to the great circle P2 P1
through the intersection F.
This is the fold axis. Read
its orientation, here N35E.
Include in your label the
angle from the intersection
to the primitive. This is the
plunge of the fold axis. Here
it is 22o.