Orient plots three types of spherical projections as upper or lower hemisphere. To create a new plot, open a data file and select New Spherical Projection. The settings for projections are set from the Spherical Projections dialog box. Equal-area projections (below left) are useful for examining the distribution of data points, since area is preserved. Clusters of points near the edge show a similar density to clusters near the center. Stereographic projections (below right) distort area, but preserve angular relationships.
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Orthographic projections (below left) show data as projected from infinity, similar to a view of the Moon from Earth. Lower hemisphere projections are normally used in structural geology, while upper hemisphere projections are common in mineralogy. Orient can plot both upper and lower hemisphere projections. Below right is an upper hemisphere equal-area projection.
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Grid display and tick marks can be turned on or off, and polar grids (about Z) can be displayed. The grids shown here are meridional grids, drawn about the Y axis. Projections can be rotated about arbitrary axes if required. Below the projection has been rotated so the minimum eigenvector is parallel to Z using the Graph Rotate command. The data here are poles to bedding planes, and a second set of data representing minor fold axes has been added.
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The equal-area projection is also known as a Lambert projection, and the associated meridional grid is known as a Schmidt net. The meridional grid associated with a stereographic projection is known as a Wulff net. All of the following plots, unless noted, are lower hemisphere equal-area projections.
Data symbols are selected from the Data tab panel of the Spherical Projection dialog box. Each data type can have a different symbol, including fill and stroke colors. These settings are saved to simplify the set up of additional plots. In the diagram below left, bedding plane orientations are displayed both as poles to the beds, and as great circle arcs. Minor fold axes are displayed as red triangles. A plot of just poles to planes, as shown on the right, is referred to as an S-pole or pi diagram, and is generally the preferred method of displaying large amounts of data.
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To calculate the best fit to a set of axial data the eigenvectors are calculated from an orientation matrix formed by the summed products of the direction cosines. This gives three orthogonal vectors corresponding to the maximum, intermediate, and minimum moments. In areas of cylindrical folding the minumum eigenvector corresponds to the fold axis. Below left the minimum eigenvector and it's great circle arc is plotted. This is the best-fit great circle for axial data. Select the Data Statistics command to view the computed values. Here the fold axis trends 183° and plunges 03°. On the right all three eigenvectors are displayed along with 95% confidence cones.
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Vector mean directions, mean resultant lengths, and corresponding confidence cones can be calculated for directed data. The confidence cone assumes a symmetric unimodal distribution, valid for n >= 25. Note that these are not normally useful for undirected data.
Contouring of spherical projections is done by estimating a density function at points on the sphere surface, and contouring that function. The density functions are calculated on the surface of a sphere, back-projected onto a regular grid, and then contoured. Orient uses several contouring algorithms: modified Kamb, Schmidt, and probability density. Orient's contouring and gridding options are displayed in the Spherical Projection dialog box. Below left is a plot calculated using a modified Kamb method.
The density function can be displayed as a gradient map, with or without overlying contours. A gradient map is a bitmap where the color value of each pixel is mapped to the range of the density function. Two or three color gradient maps can be created using user selected colors. Below right is a Red-Green-Blue map.
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Contours for directed data will be different in upper and lower hemispheres. Shown below are combined gradient maps for upper (left) and lower hemispheres (right). The upper hemisphere plot is also inverted, so the -X axis in each plot is adjacent. The gradient map here maps the probability density function of magnetic remanence directions to the visible spectra.
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Fault data includes both fault plane orientations and directed slip line orientations. Because the slip line lies within the fault plane, only three independent angles are required to specify this type of data. Typically these angles are the strike and dip of the fault plane, and the rake or trend of the slip line. Additionally, since the lines are directed it is necessary to distinguish upward slip (reverse) from downward (normal). Chapter 2 explains how to enter this type of data.
Orient generates several planes and axes from the fault data. M-planes, or movement planes, are the planes containing the fault plane normal and the slip line. The M-axis is normal to the M-plane. Given n as the upward normal of the fault plane, s as the slip line, then the directed M-axis m = |n x s|. A small angle arc of the M-plane great circle defined by a negative rotation of s about m is a slip-linear. A plot of slip linears can be used to identify consistent fault movements. A set of conjugate normal faults are shown below left, with slip lines and slip linears. On the right are the corresponding M-planes and M-axes.
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P-axes (pressure axes) and T-axes (tension axes) lie in the M-planes at 45° from the fault planes. The T-axis is at a 45° rotation about m from s, and the P-axis is at a -45° rotation. The plot below left shows T-axes (yellow) and P-axes (green) for the same data set, with a contoured gradient on the P-axes. A beach ball diagram, below right, can be plotted to display the fault nodal planes. The nodal planes are estimated based on the eigenvectors of the M-axes and P-axes.
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Slip linear and beach ball plots are only available for fault data with both plane and line data entered. When setting the options for these plots note that the line data set must be selected, these options will be grayed out for the plane, M-plane, P-axis, and T-axis sets.