Find Pitch , Given Attitude Data

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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This problem is the reverse of the previous problem. Now you have the trend and plunge of a line and want to find its pitch on some plane. To be quite honest, this is a rare situation and is included mostly for completeness. You need the trend and plunge of the line and the strike and dip of the plane.

It is a certainty, on the level of death and taxes, that if you measure the strike and dip of a plane in the field, and measure the trend and plunge of a line in the plane, that the line and plane will NOT coincide when you analyze the data. The reason for the discrepancy (usually small) lies in measurement errors.

When we get to stereonet constructions, we will find out how to get an actual plot showing the discrepancy. For now, we need a way to deal with any discrepancies. In general, put the greatest weight on the measurements that are most likely to be accurate. It is usually easier to measure strike and dip accurately. In general, trend data is likely to be more accurate than plunge determinations. If the line plunges gently, it is fairly easy to see why. If the line plunges steeply, the line looks strongly foreshortened when seen from above, and the trend will be harder to determine accurately. On the other hand, a line can only plunge steeply if the plane dips steeply. There may actually be no difference in the field measurement of the two figures. In such cases small errors in dip or plunge can result in serious errors in the pitch calculation.

1. Given the fault with the strike and dip shown, and the slickensides with the trend and plunge shown, find their pitch in the fault plane. 

2. Put the greatest weight on the trend data. Plot the structure contours on the plane and draw the map trace of the line.

3. Compare the plunge of the line as determined this way with the field data as a check. They may not match exactly but they should be close.

4. Construct a true view  of structure contours for the plane. Draw the line in the true view. Measure its pitch.

Mathematical Note

Final Result

If X is the angle between the trend and the strike, P is the plunge, D is the dip of the layer, then:

In this case, we know the attitude data and want to find pitch. Pitch is obviously given by Tan(Pitch) = Tan X/Cos D = Tan P/Sin D. It may help to do the calculation both ways as a cross-check.

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Created 5 January 1999, Last Update 31 January 2012
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