# Find the Intersection of Two Planes

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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This is perhaps the most common line problem in geology. There are not many purely linear structures that persist over very long distances. Fold axes and boreholes are the most common. On the other hand, there are many cases of intersecting planes: beds and faults, beds and dikes or sills, layers in a fold and joints or foliations, and so on. One very common application of this technique is locating the edge of a planar structure (bed, dike, sill) truncated by a fault.

To solve this problem, we need to recall these facts:

• Two planes intersect in a straight line
• Two points determine a straight line
• Structure contours are lines of equal elevation

To solve the problem, we construct structure contours on the two intersecting planes. Where two contours of the same elevation cross, we have a point on the intersection line. Two or more such points determine the line. When we plot the line by connecting all the intersections, we automatically show the map trace and elevation points on the line.

## Two Common Pitfalls

Students very often commit these two errors. WATCH OUT!

• Mislocating intersections. For example, locating an intersection where the 300 and 400 meter contours cross rather than where both 300 meter contours cross. This is easy to do in the grid of intersecting contours that result from this construction.
• Using different contour intervals on the two planes. For example, one plane dips 10 degrees and the student uses 50 meter contour spacing because the contours are so far apart. The other plane dips at 50 degrees and the student uses 100 meter intervals.

There's nothing wrong with using different intervals; it may be useful and even necessary. But then, in locating the intersections, the student fails to take account of the different interval and pairs the contours like this: 100-100, 150-200, 200-300, 250-400, and so on.

The general principle in avoiding these pitfalls is this: always be sure the intersecting contours have the same elevation.

## Example

This problems combines several simpler operations, and the individual steps for those operations are omitted. Refer to the index for information on performing other operations.

 1. Given the bed and the fault shown, find their intersection 2. Plot structure contours for one plane 3. Plot the structure contours of the second plane. 4. Draw a line through the intersections of equal contours. Find trend and plunge of the line.

Created 5 January 1999, Last Update 30 January 2012
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