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GG303 Lab 5
9/28/10
1
Stephen Martel
Lab51
University of Hawaii
SPHERICAL PROJECTIONS
I
Main Topics
A What is a spherical projection?
B Spherical projection of a line
C Spherical projection of a plane
D Determination of fold axes
E Free
spherical projection program for the MacIntosh:
"Stereonet" by Rick Allmendinger at Cornell University
II What is a spherical projection?
A A 2D projection
for describing the orientation of 3D features.
A
spherical projection shows where lines or planes that intersect the
surface of a (hemi)sphere, provided that the lines/planes also pass
through the center of the (hemi)sphere.
B Great circle: intersection of the surface of a sphere with a plane that
passes
through the center of the sphere (e.g., lines of longitude)
C Small circle: intersection of the surface of a sphere with a plane that
does not
pass through the center of the sphere (e.g., lines of latitude).
A line rotated about an axis traces a small circle too.
B Types of spherical projections
1 Equal angle projection (Wulff net)
2 Equal area projection (Schmidt net)
III Spherical projection of a line
A Technique
1 A line is at the intersection of two planes
: 1) a vertical plane coinciding
with the trend of the line and (2) an inclined plane coinciding with the
plunge of the line.
2 Trend and plunge
: The point representing a line plots away from the
center of the spherical plot in the direction of the trend of the line.
The trend of a line is measured along a horizontal great
circle.
The plunge of the line is measured along a vertical
great circle.
3 Rake: If the strike and dip of a plane is specified, the rake (pitch) of a
line in the plane can be measured along the cyclographic trace of the
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View Full DocumentGG303 Lab 5
9/28/10
2
Stephen Martel
Lab52
University of Hawaii
great circle representing that plane.
Rake is measured from the
direction of strike.
B Plane containing two lines
: Two intersecting lines uniquely define a plane.
The cyclographic trace of the great circle representing that plane will pass
through the points representing the lines.
C Angle between two lines:
This angle is measured along the cyclographic
trace of the unique great circle representing the plane containing the two
lines
IV Spherical projection of a plane
A A plane plots as the cyclographic trace of a great circle
B Strike and dip
: The strike is measured around the perimeter of
the primitive circle.
The dip of the line is measured along a
vertical great circle perpendicular to the line of strike.
C Intersection of two planes
1 Two planes intersect in a line, which projects as a point in a spherical
projection.
This point is at the intersection of the cyclographic traces
of the two planes.
2 The intersection is also 90° from the poles to the two planes; these
90° angles are measured along the great circles representing the
planes containing the poles.
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 Fall '11
 StephenMartel

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