Spherical projections aid in the analysis of the orientation data, such as rock foliations, but they do not show their spacial distribution. To aid in spacial analysis, given map coordinates, Orient can plot the spacial distributions of orientation data. This data can be spacially averaged and used for domain analysis. For example, a common problem in mapping areas of complex geological structure is to identify domains of cylindrical folding within the map area. Orient provides special capabilities to search for such domains.
Spherical projections aid in the analysis of the orientations of geological structures such as foliations, but they do not show their spacial distribution. A common problem in mapping areas of complex geologic structure is to identify cylindrical domains within the map area.
Orient provides several indexes that may be maximized, including point, girdle, and cylindricity indexes. To locate areas of cylindrical folding the cylindricity index should be maximized:
C = (E1 + E2 - 2(E3))/N
For a set of domains the sum of the products of the domain indexes (C1, C2, C3, ...) and the number of data points within each domain (N1, N2, N3, ...):
Z = C1(N1) + C2(N2) + C3(N3) + ...
is maximized. Because:
N = N1 + N2 + N3 + ...
the maximum possible value for Z is equal to N. The normalized sum is:
C' = Z/N
Example
Plotted below is an S-pole diagram of 625 foliation planes from the Grovudalen area of Norway, and a corresponding contour diagram. Although a maxima is present there is no well defined girdle pattern to indicate a regional fold axis.
A map of poles to foliation (below left) shows some areas of consistent orientation, but the location of cylindrical domains is not obvious. This map is generated using the Map menu commands. The arrows are horizontal projections of constant length vectors, so short arrows have steep plunges.
A plot of subdomain eigenvectors (below right) brings out a clearer picture of average data trends. However, visualizing which areas share a common axis is still not straightforward. This map is generated using the Map > Domain command, and shows the maximum eigenvector orientations which are equivalent to average poles to foliations.
To locate cylindrical domains, a subdomain search is done to maximize the cylindricity sum Z. This is an interactive combination of manual and automatic searches. The automatic search proceeds by identifying subdomains that can be moved into a new domain, while maintaining connectivity, and increasing Z. A purely automatic search using three domains is shown (below left). This has raised the normalized cylindricity sum, C', from 0.297 to 0.784. Additional iterative manual editing and automatic searching locates a stable solution with C' = 0.851 (below right).
Plotting the data and on an equal area projection (below left) shows a clear segregation of the data into three girdle distributions. The three minimum eigenvectors, corresponding to fold axes, show a consistent rotation across the map area, and suggest a refolding axis plunges gently northwest.
A Point-Girdle-Random (PGR) plot (below left) shows the relative changes in cylindricity from the whole area (black) to the three domains (color). Note that the green domain is closest to a point distribution, and the blue is closest to a girdle. Below right is a map showing the domains applied to the data set.
Finally, for comparison are contour plots of the three domains, left is the red domain, right is blue, and bottom is green.
Detailed Procedure
The data must include X and Y coordinates for a domain search. Open a data set (such as the demo-2 data set used above), and a new map. The general procedure to set up a search is:
During a search use the following buttons:
Initialize all subdomains to 1, set the current domain to 2, and do an automatic search. An automatic search attempts to maximize cylindricity, C, while keeping the domains connected. For each subdomain that can be moved into the current domain, it locates the one that will maximize C. The search proceeds until no changes will increase C. The automatic search will not necessarily find the "best" solution because it works stepwise from an initial state, and is constrained by boundary conditions, but it will find a stable solution.
After an automatic search you can edit the subdomains with the mouse, but only if the domains remain connected. An iterative process using manual editing and automatic searching is required to locate the best possible solution.