c) Equal-area stereonets are used in structural geology because they present b ) The north pole of the stereonet is the upper point where all lines of longitude. Background information on the use of stereonets in structural analysis The above is an equal area stereonet projection showing great circles as arcuate lines. Page 1. mm. WIDTH. Blunt. TUT. HT. T itillinn.
|Published (Last):||19 March 2017|
|PDF File Size:||3.32 Mb|
|ePub File Size:||7.57 Mb|
|Price:||Free* [*Free Regsitration Required]|
Map projections Conformal mapping Conformal projections Crystallography Projective geometry. Instead, it is common to use graph paper designed specifically for the task.
We can now consider how two lines the ones in green plot. This is a very useful tool because it can reduce the workload by avoiding lengthy calculations.
The onion skin overlay permits you to rotate the points being plotted with respect to the underlying, fixed reference frame. The projection that is usually chosen for this, is the Lambert Azimuthal Equal-Area Projection with equatorial aspect See: Stereographic projection plots can be carried out by a computer using the explicit formulas given above.
They are hemisphere surface paths from one line being rotated about another line the pole of rotationboth passing through the hemisphere center. The great circle is divided in to degrees like degree protractor because maps are designed based sterdonet same azimuthal bearing directional vectors. Those labeled with dip amounts on the left side, dip to the west.
J On a new page, plot the following line 40 and then find the family of lines points on the stereonet that is 20 degrees away. In the figure, the area-distorting property of the stereographic projection can arez seen by comparing a grid sector near the center of the net with one at the far atea or left. This circle maps to a circle under stereographic projection. Equal angle projection 2. Planes are lines are drawn on steronets as they intersect at the bottom of the sphere Figure 1.
Stereographic projection for structural analysis
Albers Equidistant Lambert conformal. The values X and Y produced by this projection are exactly twice those produced by the equatorial projection described in the preceding section. The rake of the fault is between the left most edge of the footwall and the displacement vector red.
These lines are sometimes thought of as circles through the point at infinity, or circles of infinite radius. The above is an equal area stereonet stereoet showing great circles as arcuate lines connecting the North and South Points and small circles as arcuate lines in a latitudinal type position.
However, the equal area steronets will reduce the area distortion.
Small circles run left-right latitudinal on the stereonets and are perpendicular to the great circles. On a merely topological level, it illustrates how the sphere is homeomorphic to the one-point compactification of the plane.
2. Stereonet — InnStereo 0 documentation
Planes plot as great circle traces. General perspective Gnomonic Orthographic Stereographic. In other words, it is often used to analyze accuracy of data from several different regions of the same area.
Remember the convention is that the first number represents the trend direction and the second represents the plunge amount.
This is the basic 3D geometry we will start with.
Lab 5: Structural Analysis using stereonets
In srea words, the sphere can be covered by two stereographic parametrizations the inverses of the projections from the plane. Euqal use slickensides to interpret the sense of motion in the field. Hence, most educational institutions prefer equal area steronets for their students over the equal angle stereonets. Then count along that great circle in degree increments moving from one stereeonet pole to the other. It is the true North which is denoted by the azimuthal angle of degrees on the primitive.
That great circle is the bisecting plane. Bonne Bottomley Polyconic American Werner. In practice, the projection is carried out by computer or by hand using a special kind of graph paper called a stereographic netshortened to stereonetor Wulff net.
Aitoff Hammer Wiechel Winkel tripel. However, for graphing by hand these formulas are unwieldy. For someone who is starting in geology or structural geology, it is highly recommended to use paper and pencil over software.
sterronet The equal-area lower-hemisphere projection defined by the Lambert azimuthal equal-area projection is also used, especially when the plot is to be subjected to subsequent statistical analysis such as density contouring. In geology this is usually referred to qrea Schmidt Netafter Walter Schmidt.
Angles are slightly distorted and make the circles appear as ellipses. This facilitates an elegant and useful notion of infinity for the complex numbers and indeed an entire theory of meromorphic functions mapping to the Riemann sphere.
In Cartesian coordinates xyz on the sphere and XY on the plane, the projection and its inverse are given by the formulas. As in crystallography, planes are typically plotted by their poles.
Unlike crystallography, the southern hemisphere is used instead of the northern one because the geological features in question lie below the Earth’s surface.
It could represent a principal stress for a conjugate fault pair. The popularity of using stereographic projections to map panoramas over other azimuthal projections is attributed to the shape preservation that equall from the conformality of the projection.