Find a Plane Given Two Apparent Dips

Steven Dutch, Natural and Applied Sciences,

University of Wisconsin - Green Bay
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Since apparent dip is just the plunge of a line, this problem is really identical with the previous problem.

Examples

On a steep cliff on two sides of a mountain, we observe a conspicuous sandstone layer. We can't get to it but the apparent dips can be measured. What is the true strike and dip of the bed?

We can measure the apparent dip using the clinometer of a Brunton compass. But what about the trend of the line? If it's on a highway cut or quarry wall we can measure it directly. In the case here we could measure it off a topographic map or measure it by measuring the azimuth of the place where we measure the apparent dip, then noting that the trend is at right angles to our line of sight.

1. A conspicuous sandstone layer outcrops in a cliff, and has the apparent dips shown. Determine the true strike and dip.
2. Draw lines with map traces parallel to the two apparent dip planes. Construct elevation points on both lines.
3. Draw structure contour lines through points of equal elevation.
4. Strike is simply the azimuth of the structure contours. Find dip by trigonometry or by cross-section.

However, suppose we have two highway cuts or quarry walls that expose a series of layers that are so similar there is no way to correlate beds from one exposure to the other. Possibly none of the layers correlate, but the rocks are uniformly dipping.

We can solve this problem by realizing that we are trying to find a plane parallel to two given lines. If the lines actually intersect we can use the lines themselves, if not, we can use two lines parallel to the given lines that do intersect. The plane that contains these two lines will be parallel to our two given lines.

In such a case, we are only interested in the orientation of the plane, and its location is purely arbitrary. So we can pick any convenient point for the intersection of the apparent dips. Also, the elevation points on the lines are relative and have no geographic significance. So you can assign any convenient elevation to the intersection. It's often convenient simply to use depth beneath the intersection point.

1. A series of layers have the apparent dips shown above exposed in two quarry faces. Find their strike and dip.
2. Pick a convenient point and draw map traces from it parallel to the two apparent dip directions. Construct elevation points on both lines. The elevation points can be relative to the intersection.
3. Draw structure contour lines through points of equal elevation.
4. Strike is simply the azimuth of the structure contours. Find dip by trigonometry or by cross-section.

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Created 5 January 1999, Last Update 31 January 2012
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