Geological Mapping Stereographic projections Part A Instructor S

Geological Mapping Stereographic projections (Part A) Instructor: S. Kokkalas Assoc. Prof.

Stereonets • • Solving geometrical problems– displays geometry and orientation of lines and planes. Stereonets are used for plotting and analyzing 3 -D orientations of lines and planes in 2 -D space • It is a three-dimensional protractor. • Stereonet projection allows us to do plot of lines and planes but in 3 -dimensions. We can plot the orientation of planes, determine the intersection of two planes, angles between planes, rotate lines and planes in space about vertical, horizontal and inclined axes Applications • • • Landslide hazard/slope failure studies Earthquake studies Fracture analysis Mining and oil industry Engineering And… Practically anything that deals with relative orientations of planes and lines

Stereonets • Basic principles • Any line or plane can be assumed to pass through the center of a reference sphere • Planes intersect the lower hemisphere as GREAT CIRCLES • Lines intersect the lower hemisphere as POINTS • The great circles or points are projected on the horizontal plane to create STEREOGRAPHIC PROJECTIONS or stereograms

Lambert net (Schmidt net). equal-area Stereographic net (Wulff net). equal-angle

Stereographic Projection Two types of net are in common use: 1. Stereographic net, equal angle (Wulff net). 2. Lambert, equal-area net (Schmidt net) Stereographic net-Wulff Lambert Equal – Area Net

Lambert, equal–area net N Small circles (Look like LATITUDES) Great circles (Look like LONGITUDES) Lower hemisphere projection S

N Lambert, equal–area net Primitive circle = horizontal plane Straight lines = vertical planes 0 20 40 60 80 80 60 40 20 0 Dip angles Great circles = inclined planes Examples S Lower hemisphere projection

• Approximate method for plotting planes-lines 3 D view Map view-add symbol Equatorial projection from reference sphere Stereographic projection

Stereonets • Precise method for plotting planes N 0 90 270 Each dipping plane has its pole. 180 270 90 180 USGS

Pole of a plane §The orientation of a plane can be uniquely described by the orientation of a line perpendicular to a plane. §If the trend and plunge of a normal (pole) to a plane is known, the orientation of the plane is also known. Great circle 90 o pole

• Precise method for plotting planes With dip-direction/dip notation Plane: Dip direction/dip 230ο/60ο

Stereonets • Precise method for plotting lines N USGS

Before we go on, let’s review Pitch (or Rake) ch pit plunge