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Stereographic projection – unfolding folds

Restoring paleocurrent trends to their pre-deformation orientations

This post is part of the How To… series

Dipping bedding that is part of a fold limb

Sedimentary strata are commonly deformed. If we assume that the original depositional dip was close to horizontal (this is a reasonable assumption, although there are exceptions) then we need to account for structural dip. This is important if our sedimentary analysis includes measurement of paleocurrents, depositional dip and strike (e.g. ancient shorelines, rivers), or any paleogeographic determination.

Two methods are outlined here: the standard stereographic projection method that is usually done back in the lab unless you are lucky enough to have access to the internet in the field; and a quick field method using a field note book, pencil and compass; this method can only be used in strata folded by a single phase of deformation.

Stereographic method

In the simplest case (diagrams below), strata containing flute casts have been folded into a syncline with a horizontal fold axis; we need to correct the for dip in the fold limb to find the original orientation of the flute cast.   Bedding strikes 080o (N80E), dip 40oN; the flute cast plunges 38o at 315o (N45W).

To determine the original orientation of flute casts, we plot bedding, then unfold the bed on a stereonet

On a transparent overlay, plot the plane (strike and dip) and the line (orientation and plunge) representing the flute cast (it will be a point on the great circle) on the stereonet. To return the plane to its original pre-fold orientation, it must be rotated about its strike; the next step is to move the great circle back to its original plotting position. When the plane is rotated to horizontal all points on the great circle will move along small circles to the stereonet perimeter. The point representing the flute cast is now in its original orientation – here 332o, or N28W. The difference between the uncorrected and corrected bearing is 14o.

Plotting the flute cast plunge and azimuth - it must lie on the the great circle that is bedding

Returning the dipping bed to its original horizontal position to read the orientation of the flute cast

Direct field method

You can use this method when sedimentary structures (or any linear trend) are exposed on bedding planes.  It basically performs the same task as a stereonet correction.

A simple field method to correct paleocurrent dirextions for dip

Place a hard, flat surface on bedding – hard-cover note book or board are good – with the long edge oriented along strike. Place a pencil or similar straight-edge on the surface such that it is aligned with the structure of interest (flute long axis, ripple trend etc). Rotate the book about its long edge (i.e. about the strike) until it is horizontal – make sure the straight-edge doesn’t move. Holding the book and straight-edge in place, measure the bearing.

If you are not convinced about the accuracy of the field method, check it against the stereonet correction. You will find with practice, and not a little care, that direct field measurement provides excellent results.

Some other posts in this series:

Measuring dip and strike

Solving the three-point problem

Stereographic projection – the basics

The Rule of Vs in geological mapping

Folded rock; some terminology

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