Lecture 18: Rotations

Main Ideas

Rotations on a stereonet can be used to change the orientation of a line or plane, including restoring geological features to their orientation before later tilting or deformation. The lecture covers rotations about vertical and horizontal axes.

Rotation About a Vertical Axis

• Rotating a line about a vertical axis changes its trend but not its plunge.
• For example, rotating a line with a trend of 130° and a plunge of 40° by 40° clockwise gives it a new orientation of 170° trend and 40° plunge.
• On a stereonet, the line moves while remaining the same distance from the center. Repeated rotations trace a path of constant plunge.

Rotation About a Horizontal Axis

• Rotating a plane about a horizontal axis aligned with its strike leaves the strike unchanged.
• The direction of rotation determines the change in dip:
  • Counterclockwise rotation decreases the dip.
  • Clockwise rotation increases the dip.
• On the stereonet, points on the plane’s original great circle move along small circles to the new great circle. The plane’s pole also moves along a small circle.
• A line rotated about a horizontal axis likewise moves along a small circle on the stereonet.

Restoring an Overturned Bed

The lecture applies rotations to determine the original direction of a current lineation on an overturned bed:

• The bed is oriented N 30° W, 40° SW, and the lineation has a 30° NW rake on the bedding plane.
• To infer the current’s direction when the bed was horizontal:
  1. Plot the bedding plane and lineation on the stereonet.
  2. Rotate the overlay until the bed’s strike lies on a vertical straight line. This defines the rotation axis.
  3. Rotate the bed and lineation together to restore the bed to horizontal.
  4. Because the bed is overturned, rotate it anticlockwise past vertical.
  5. Restore the stereonet overlay and read the lineation’s orientation.

The restored lineation points north, indicating the direction of the current that deposited the bed. The lineation must be restored along with the bed; its present-day orientation on the tilted plane is not the original current direction.

Speakers and Sources

• Speaker: Unnamed lecturer or narrator.
• Sources mentioned: Chapter 6 of Marshak and Mitra; a book by “Reagan” in the subtitles (possibly Ragan); and additional class exercises and later material on linear algebra and computation.