LECTURE 15 INTRODUCTION TO
STEREOGRAPHIC PROJECTIONS
INTRODUCTION TO
STEREOGRAPHIC PROJECTIONS
? Basic principles
? Basic procedures
? Exercise in class
STEREOGRAPHIC
PROJECTION
The stereographic projection is a
graphical method to portray three-
dimensional geometrical data in two
dimensions,In this projection,
planes plots as lines (usually curves )
and lines as points.
PROBLEMS CAN BE SOLVED
? Angular relationship between lines
or planes
? Statistical properties of data that has
direction (trend and plunge)
PROJECTION SPHERE AND
PROJECTION PLANE
SPHERICAL PROJECTION
Imagine the plane
pass the center of a
sphere of radius R,
the projection
sphere.
The center of the
sphere
SPHERICAL PROJECTION
STEREOGRAPHIC PROJECTION
STEREOGRAPHIC NETS
? Wulff net---equal-angle net (Figure A)
? Schmidt net---equal-area net (Figure B)
ELEMENTS OF THE WULFF NET
primitive circle
Latitude small circle
Longitude great circle
w
1,Primitive circle,2,Central point,3,Four special
points,4,Longitude great circle,5,Latitude small
circle,Orientation,from 0 to 360,dip,from 0 to 90
PROCEDURE
1,Put the Wulff net on the table.
2,Put the tracing paper over the Wulff net.
3,Draw the primitive circle,
4,Mark a cross,+” at the center.
5,Mark points,N,E,S,W”,
6,Tack the pin through the,+”to fix the
position
7,Plotting
Techniques of plotting---plotting
a plane with attitude 120 ∠ 30
P,tracing paper,m,Wulff net
Plotting the plane,30° ∠ 45°
? 1,Count 30° from point N clockwise,get point,A”
? 2,Rotate the tracing paper and make point,A”
superposition with,E”.
? 3,Count 45° from,A”alone A—O,and get point B.
? 4,Draw the longitude great circle passing point B.
? 5,Revert the tracing paper,the great circle represents the
plane 30° ∠ 45°
Plotting a line,40° ∠ 50°
1,Count 40° from point N clockwise,mark
point,A”
2,Rotate the tracing paper and let point,A”
superpose,E” or,N”.
3,Count 50° from,A”alone A—O,mark the
point B,
4,Revert the paper,and the point B represents
the line 40° ∠ 50°,
Plotting normal to a plane 90 ∠ 40
Draw the great circle with attitude 90 ∠ 40,count
90 degree along EW from D’,mark the point P’.
It is the projection of the normal to the plane 90 ∠ 40
Solution for apparent dip from true dip
Bedding 300∠ 40
Solve the apparent dip
along the orientation of 335
degree.
1.Plot the bedding and get the
arc EHF.
2.Mark 335 on the primitive
Circle at point D’
3,Link D’O intersecting at H’
4.Count D’H’ along WE or NS.
It is the apparent dip.
solution for the intersection line of
two planes
1,Plot plane EHF and JHK
2,Link OH and extend it to
the primitive circle at G
3,Count the plunge direction
of G on the primitive circle
and the plunge angle GH
on the WE line
Please do the following problems and turn your work in on
next Tuesday.
1,Plot the following planes on the stereonet,a) 245<30,
b) 20<60,c) 340<40,d) 120<70
2,Plot the following lines on the stereonet,a) 42<62,
b) 130<45,c)220<50,d) 315<32
3,Plot the following poles to the planes on the stereonet,
a) 318<26,b) 125 < 35,c) 338 < 15
4,Find the attitude of the intersection line between two planes,
245<30 and 145<48
5,Find the apparent dip in a direction of 80,190 on the plane
oriented 154<40.
Assignment
Statistics with Schmidt net
(Self-study)
Beta Diagram
Pai diagram
Center counter
Peripheral counter
Contouring
STEREOGRAPHIC PROJECTIONS
INTRODUCTION TO
STEREOGRAPHIC PROJECTIONS
? Basic principles
? Basic procedures
? Exercise in class
STEREOGRAPHIC
PROJECTION
The stereographic projection is a
graphical method to portray three-
dimensional geometrical data in two
dimensions,In this projection,
planes plots as lines (usually curves )
and lines as points.
PROBLEMS CAN BE SOLVED
? Angular relationship between lines
or planes
? Statistical properties of data that has
direction (trend and plunge)
PROJECTION SPHERE AND
PROJECTION PLANE
SPHERICAL PROJECTION
Imagine the plane
pass the center of a
sphere of radius R,
the projection
sphere.
The center of the
sphere
SPHERICAL PROJECTION
STEREOGRAPHIC PROJECTION
STEREOGRAPHIC NETS
? Wulff net---equal-angle net (Figure A)
? Schmidt net---equal-area net (Figure B)
ELEMENTS OF THE WULFF NET
primitive circle
Latitude small circle
Longitude great circle
w
1,Primitive circle,2,Central point,3,Four special
points,4,Longitude great circle,5,Latitude small
circle,Orientation,from 0 to 360,dip,from 0 to 90
PROCEDURE
1,Put the Wulff net on the table.
2,Put the tracing paper over the Wulff net.
3,Draw the primitive circle,
4,Mark a cross,+” at the center.
5,Mark points,N,E,S,W”,
6,Tack the pin through the,+”to fix the
position
7,Plotting
Techniques of plotting---plotting
a plane with attitude 120 ∠ 30
P,tracing paper,m,Wulff net
Plotting the plane,30° ∠ 45°
? 1,Count 30° from point N clockwise,get point,A”
? 2,Rotate the tracing paper and make point,A”
superposition with,E”.
? 3,Count 45° from,A”alone A—O,and get point B.
? 4,Draw the longitude great circle passing point B.
? 5,Revert the tracing paper,the great circle represents the
plane 30° ∠ 45°
Plotting a line,40° ∠ 50°
1,Count 40° from point N clockwise,mark
point,A”
2,Rotate the tracing paper and let point,A”
superpose,E” or,N”.
3,Count 50° from,A”alone A—O,mark the
point B,
4,Revert the paper,and the point B represents
the line 40° ∠ 50°,
Plotting normal to a plane 90 ∠ 40
Draw the great circle with attitude 90 ∠ 40,count
90 degree along EW from D’,mark the point P’.
It is the projection of the normal to the plane 90 ∠ 40
Solution for apparent dip from true dip
Bedding 300∠ 40
Solve the apparent dip
along the orientation of 335
degree.
1.Plot the bedding and get the
arc EHF.
2.Mark 335 on the primitive
Circle at point D’
3,Link D’O intersecting at H’
4.Count D’H’ along WE or NS.
It is the apparent dip.
solution for the intersection line of
two planes
1,Plot plane EHF and JHK
2,Link OH and extend it to
the primitive circle at G
3,Count the plunge direction
of G on the primitive circle
and the plunge angle GH
on the WE line
Please do the following problems and turn your work in on
next Tuesday.
1,Plot the following planes on the stereonet,a) 245<30,
b) 20<60,c) 340<40,d) 120<70
2,Plot the following lines on the stereonet,a) 42<62,
b) 130<45,c)220<50,d) 315<32
3,Plot the following poles to the planes on the stereonet,
a) 318<26,b) 125 < 35,c) 338 < 15
4,Find the attitude of the intersection line between two planes,
245<30 and 145<48
5,Find the apparent dip in a direction of 80,190 on the plane
oriented 154<40.
Assignment
Statistics with Schmidt net
(Self-study)
Beta Diagram
Pai diagram
Center counter
Peripheral counter
Contouring
