Steven Dutch, Natural and Applied Sciences,
University of Wisconsin - Green Bay

First-time Visitors: Please visit Site Map and Disclaimer. Use "Back" to return here.

It is sometimes useful to characterize the orientation of a line
by referring to its direction in a dipping plane. For example,
you may have ripple marks on a bed or slickensides on a fault,
and it may be difficult to determine their trend and plunge
accurately. On the other hand, it is very important that these
lines are contained *within* some particular plane (the bed and the
fault, respectively). In cases like these, the *pitch* measurement
is sometimes used.

*Pitch* is defined as the angle between some line in a plane and a
horizontal line, measured *in the plane.* A line can have the same
pitch in two directions, so it is important to define directions
precisely.

Here's how to do this using descriptive geometry. In practice, problems like this are generally done with a stereonet. There are also special diagrams that allow the solution to be read off directly.

We can solve the problem easily if we note that structure contours on a map are foreshortened views of the real thing. If the plane dips with an angle D, the mapped contours are compressed by a factor of cos D

You can determine the true spacing of the contours by calculation or by measuring distance AB in the cross-section.
**Note: a pitching line can never have a plunge greater than the dip of
the plane!**

1. Given the fault shown and slickensides with the observed
pitch, find their trend and plunge.
2. Construct structure contours for the plane. Find the true spacing by cross-section or trigonometry and construct a second set of contours with true spacing. 3. On the true set of contours, construct the pitching line as it appears on the dipping plane. Project distances along the contours back to the map view. 4. On the map view, construct the map trace of the line. Find its trend and find the plunge by trigonometry or drawing a cross-section. |

We know the pitch and the dip. What we want to find is the trend and plunge. The trend is just the strike of the bed (given by the structure contours) plus or minus angle XAB in the top diagram. It will be plus or minus depending on which way the pitch is measured relative to the strike.

We have:

- Tan XAB = XB/AX
- Tan(Pitch) = XB'/AX. Thus:
- Tan XAB/Tan(Pitch) = XB/XB' = S/(S/Cos D) = Cos D
- Therefore,
**Tan XAB = Tan(Pitch)Cos D**

The plunge (P) is found from the diagrams below. Note: we use B to denote location in the vertical cross section, and B' to denote the same point viewed in the dipping plane.

We have:

- U Tan(Pitch) = H/Sin(Dip) or U = H/(Tan(Pitch)Sin(Dip))
- U Tan(Plunge) = H or Tan(Plunge) = H/U
- Substituting U from the first equation gives us
Tan(Plunge) =

**Tan P = Tan(Pitch)Sin D**

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

**Tan X = Tan(Pitch)Cos D****Tan P = Tan(Pitch)Sin D**

- If Pitch = 0, trend=strike, plunge = 0
- If Pitch = 90, trend=strike plus or minus 90, plunge = dip

Return to Course Syllabus

Return to Techniques Manual Index

Return to Professor Dutch's Home Page

*Created 5 January 1999, Last Updated
26 January 2012
*
Not an official UW Green Bay site